cm.c

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/***********************************************************************
 Freeciv - Copyright (C) 2002 - The Freeciv Project
   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2, or (at your option)
   any later version.
 
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
***********************************************************************/
 
#ifdef HAVE_CONFIG_H
#include <fc_config.h>
#endif
 
#include <stdlib.h>
#include <string.h>
 
/* utility */
#include "fcintl.h"
#include "log.h"
#include "mem.h"
#include "shared.h"
#include "support.h"
#include "timing.h"
 
/* common */
#include "city.h"
#include "game.h"
#include "government.h"
#include "map.h"
#include "specialist.h"
 
#include "cm.h"
 
/*
 * Terms used
 * ==========
 *
 * Stats: food, shields, trade, luxury, science, and gold.
 * Production: amount of stats you get directly from farming tiles or
 *      having specialists.
 * Surplus: amount of stats you get, taking buildings, taxes, disorder, and
 *      any other effects into account.
 *
 * Happy State: disorder (unhappy), content (!unhappy && !happy) and
 * happy (happy)
 *
 * Tile type: usually, many tiles produce the same f/s/t.  So we bin the
 *      tiles into tile types.  Specialists are also a 'tile type.'
 *
 * Unlike the original CM code, which used a dynamic programming approach,
 * this code uses a branch-and-bound approach.  The DP approach allowed
 * caching, but it was hard to guarantee the correctness of the cache, so
 * it was usually tossed and recomputed.
 *
 * The B&B approach also allows a very simple greedy search, whereas the DP
 * approach required a lot of pre-computing.  And, it appears to be very
 * slightly faster.  It evaluates about half as many solutions, but each
 * candidate solution is more expensive due to the lack of caching.
 *
 * We use highly specific knowledge about how the city computes its stats
 * in two places:
 * - setting the min_production array.  Ideally the city should tell us.
 * - computing the weighting for tiles.  Ditto.
 */
 
 
/*****************************************************************************
  Defines, structs, globals, forward declarations
*****************************************************************************/
 
/* If this is uncommented, research loop runs without limit on iterations. */
/* #define CM_LOOP_NO_LIMIT */
 
/* Maximal iterations before the search loop is stopped, or until warning is
 * printed if CM_LOOP_NO_LIMIT is defined. */
#define CM_MAX_LOOP 27500
 
#define CPUHOG_CM_MAX_LOOP (CM_MAX_LOOP * 4)
 
#ifdef DEBUG_TIMERS
#define GATHER_TIME_STATS
#endif
#ifdef FREECIV_DEBUG
#define CM_DEBUG
#endif
 
/* Whether to print every query, or just at cm_free ; matters only
   if GATHER_TIME_STATS is on */
#define PRINT_TIME_STATS_EVERY_QUERY
 
#define LOG_TIME_STATS                                  LOG_DEBUG
#define LOG_CM_STATE                                    LOG_DEBUG
#define LOG_LATTICE                                     LOG_DEBUG
#define LOG_REACHED_LEAF                                LOG_DEBUG
#define LOG_BETTER_LEAF                                 LOG_DEBUG
#define LOG_PRUNE_BRANCH                                LOG_DEBUG
 
#ifdef GATHER_TIME_STATS
static struct {
  struct one_perf {
    struct timer *wall_timer;
    int query_count;
    int apply_count;
    const char *name;
  } greedy, opt;
 
  struct one_perf *current;
} performance;
 
static void print_performance(struct one_perf *counts);
#endif /* GATHER_TIME_STATS */
 
/* Fitness of a solution.  */
struct cm_fitness {
  int weighted; /* weighted sum */
  bool sufficient; /* false => doesn't meet constraints */
};
 
 
/*
 * We have a cyclic structure here, so we need to forward-declare the
 * structs
 */
struct cm_tile_type;
struct cm_tile;
 
/*
 * A tile.  Has a pointer to the type, and the x/y coords.
 * Used mostly just for converting to cm_result.
 */
struct cm_tile {
  const struct cm_tile_type *type;
  int index; /* city map index; only valid if !is_specialist */
};
 
/* define the tile_vector as array<cm_tile> */
#define SPECVEC_TAG tile
#define SPECVEC_TYPE struct cm_tile
#include "specvec.h"
 
/* define the tile_type_vector as array <cm_tile_type*> */
#define SPECVEC_TAG tile_type
#define SPECVEC_TYPE struct cm_tile_type *
#include "specvec.h"
#define tile_type_vector_iterate(vector, var) { \
    struct cm_tile_type *var; \
    TYPED_VECTOR_ITERATE(struct cm_tile_type*, vector, var##p) { \
      var = *var##p; \
      {
#define tile_type_vector_iterate_end }} VECTOR_ITERATE_END; }
 
/*
 * A tile type.
 * Holds the production (a hill produces 1/0/0);
 * Holds a list of which tiles match this (all the hills and tundra);
 * Holds a list of other types that are strictly better
 * (grassland 2/0/0, plains 1/1/0, but not gold mine 0/1/6).
 * Holds a list of other types that are strictly worse
 * (the grassland and plains hold a pointer to the hill).
 *
 * Specialists are special types; is_specialist is set, and the tile
 * vector is empty.  We can never run out of specialists.
 */
struct cm_tile_type {
  int production[O_LAST];
  double estimated_fitness; /* weighted sum of production */
  bool is_specialist;
  Specialist_type_id spec; /* valid only if is_specialist */
  struct tile_vector tiles;  /* valid only if !is_specialist */
  struct tile_type_vector better_types;
  struct tile_type_vector worse_types;
  int lattice_index; /* index in state->lattice */
  int lattice_depth; /* depth = sum(#tiles) over all better types */
};
 
 
/*
 * A partial solution.
 * Has the count of workers assigned to each lattice position, and
 * a count of idle workers yet unassigned.
 */
struct partial_solution {
  /* indices for these two match the lattice indices */
  int *worker_counts;   /* number of workers on each type */
  int *prereqs_filled;  /* number of better types filled up */
 
  int production[O_LAST]; /* raw production, cached for the heuristic */
  int idle;             /* number of idle workers */
};
 
/*
 * State of the search.
 * This holds all the information needed to do the search, all in one
 * struct, in order to clean up the function calls.
 */
struct cm_state {
  /* input from the caller */
  struct cm_parameter parameter;
  /*mutable*/ struct city *pcity;
 
  /* the tile lattice */
  struct tile_type_vector lattice;
  struct tile_type_vector lattice_by_prod[O_LAST];
 
  /* the best known solution, and its fitness */
  struct partial_solution best;
  struct cm_fitness best_value;
 
  /* hard constraints on production: any solution with less production than
   * this fails to satisfy the constraints, so we can stop investigating
   * this branch.  A solution with more production than this may still
   * fail (for being unhappy, for instance). */
  int min_production[O_LAST];
 
  /* needed luxury to be content, this includes effects by specialists */
  int min_luxury;
 
  /* the current solution we're examining. */
  struct partial_solution current;
 
  /*
   * Where we are in the search.  When we add a worker to the current
   * partial solution, we also push the tile type index on the stack.
   */
  struct {
    int *stack;
    int size;
  } choice;
 
  bool *workers_map; /* placement of the workers within the city map */
};
 
 
/* return #fields + specialist types */
static int num_types(const struct cm_state *state);
 
 
/* debugging functions */
#ifdef CM_DEBUG
static void real_print_tile_type(enum log_level level, const char *file,
                                 const char *function, int line,
                                 const struct cm_tile_type *ptype,
                                 const char *prefix);
#define print_tile_type(loglevel, ptype, prefix)                            \
  if (log_do_output_for_level(loglevel)) {                                  \
    real_print_tile_type(loglevel, __FILE__, __FUNCTION__, __FC_LINE__,     \
                         ptype, prefix);                                    \
  }
 
static void real_print_lattice(enum log_level level, const char *file,
                               const char *function, int line,
                               const struct tile_type_vector *lattice);
#define print_lattice(loglevel, lattice)                                    \
  if (log_do_output_for_level(loglevel)) {                                  \
    real_print_lattice(loglevel, __FILE__, __FUNCTION__, __FC_LINE__,       \
                       lattice);                                            \
  }
 
static void real_print_partial_solution(enum log_level level,
                                        const char *file,
                                        const char *function, int line,
                                        const struct partial_solution *soln,
                                        const struct cm_state *state);
#define print_partial_solution(loglevel, soln, state)                       \
  if (log_do_output_for_level(loglevel)) {                                  \
    real_print_partial_solution(loglevel, __FILE__, __FUNCTION__,           \
                                 __FC_LINE__, soln, state);                 \
  }
 
#else
#define print_tile_type(loglevel, ptype, prefix)
#define print_lattice(loglevel, lattice)
#define print_partial_solution(loglevel, soln, state)
#endif /* CM_DEBUG */
 
static void cm_result_copy(struct cm_result *result,
                           const struct city *pcity, bool *workers_map);
 
static double estimate_fitness(const struct cm_state *state,
                               const int production[]);
static bool choice_is_promising(struct cm_state *state, int newchoice,
                                bool negative_ok);
 
/************************************************************************/
void cm_init(void)
{
  /* In the B&B algorithm there's not really anything to initialize. */
#ifdef GATHER_TIME_STATS
  memset(&performance, 0, sizeof(performance));
 
  performance.greedy.wall_timer = timer_new(TIMER_USER, TIMER_ACTIVE,
                                            "cm.greedy");
  performance.greedy.name = "greedy";
 
  performance.opt.wall_timer = timer_new(TIMER_USER, TIMER_ACTIVE,
                                         "cm.opt");
  performance.opt.name = "opt";
#endif /* GATHER_TIME_STATS */
}
 
/************************************************************************/
void cm_init_citymap(void)
{
  /* In the B&B algorithm there's not really anything to initialize. */
}
 
/************************************************************************/
void cm_clear_cache(struct city *pcity)
{
  /* The B&B algorithm doesn't have city caches so there's nothing to do. */
}
 
/************************************************************************/
void cm_free(void)
{
#ifdef GATHER_TIME_STATS
  print_performance(&performance.greedy);
  print_performance(&performance.opt);
 
  timer_destroy(performance.greedy.wall_timer);
  timer_destroy(performance.opt.wall_timer);
  memset(&performance, 0, sizeof(performance));
#endif /* GATHER_TIME_STATS */
}
 
/************************************************************************/
struct cm_result *cm_result_new(struct city *pcity)
{
  struct cm_result *result;
 
  /* initialise all values */
  result = fc_calloc(1, sizeof(*result));
  result->city_radius_sq = pcity ? city_map_radius_sq_get(pcity)
                                 : CITY_MAP_MAX_RADIUS_SQ;
  result->worker_positions
    = fc_calloc(city_map_tiles(result->city_radius_sq),
                sizeof(*result->worker_positions));
 
  /* test if the city pointer is valid; the cm_result struct can be
   * returned as it uses the maximal possible value for the size of
   * 'worker_positions' (= city_map_tiles(CITY_MAP_MAX_RADIUS_SQ))*/
  fc_assert_ret_val(pcity != NULL, result);
 
  return result;
}
 
/************************************************************************/
void cm_result_destroy(struct cm_result *result)
{
  if (result != NULL) {
    if (result->worker_positions != NULL) {
      FC_FREE(result->worker_positions);
    }
    FC_FREE(result);
  }
}
 
/****************************************************************************
  Functions of tile-types.
****************************************************************************/
 
/************************************************************************/
static void tile_type_init(struct cm_tile_type *type)
{
  memset(type, 0, sizeof(*type));
  tile_vector_init(&type->tiles);
  tile_type_vector_init(&type->better_types);
  tile_type_vector_init(&type->worse_types);
}
 
/************************************************************************/
static struct cm_tile_type *tile_type_dup(const struct cm_tile_type *oldtype)
{
  struct cm_tile_type *newtype = fc_malloc(sizeof(*newtype));
 
  memcpy(newtype, oldtype, sizeof(*oldtype));
  tile_vector_init(&newtype->tiles);
  tile_type_vector_init(&newtype->better_types);
  tile_type_vector_init(&newtype->worse_types);
 
  return newtype;
}
 
/************************************************************************/
static void tile_type_destroy(struct cm_tile_type *type)
{
  /* The call to vector_free() will magically free all the tiles in the
   * vector. */
  tile_vector_free(&type->tiles);
  tile_type_vector_free(&type->better_types);
  tile_type_vector_free(&type->worse_types);
}
 
/************************************************************************/
static void tile_type_vector_free_all(struct tile_type_vector *vec)
{
  tile_type_vector_iterate(vec, type) {
    /* Destroy all data in the type, and free the type itself. */
    tile_type_destroy(type);
    free(type);
  } tile_type_vector_iterate_end;
 
  tile_type_vector_free(vec);
}
 
/************************************************************************/
static bool tile_type_equal(const struct cm_tile_type *a,
                            const struct cm_tile_type *b)
{
  output_type_iterate(stat_index) {
    if (a->production[stat_index] != b->production[stat_index])  {
      return FALSE;
    }
  } output_type_iterate_end;
 
  if (a->is_specialist != b->is_specialist) {
    return FALSE;
  }
 
  return TRUE;
}
 
/************************************************************************/
static int tile_type_better(const struct cm_tile_type *a,
                            const struct cm_tile_type *b)
{
  int ret = 0;
 
  output_type_iterate(stat_index) {
    if (a->production[stat_index] < b->production[stat_index])  {
      if (ret > 0) {
        return 0;
      }
      ret = -1;
    } else if (b->production[stat_index] < a->production[stat_index])  {
      if (ret < 0) {
        return 0;
      }
      ret = 1;
    }
  } output_type_iterate_end;
 
  if (a->is_specialist && !b->is_specialist) {
    /* If A is a specialist and B isn't, and all of A's production is at
     * least as good as B's, then A is better because it doesn't tie up
     * the map tile. */
    if (ret < 0) {
      return 0;
    }
    return 1;
  } else if (!a->is_specialist && b->is_specialist) {
    /* Vice versa. */
    if (ret > 0) {
      return 0;
    }
    return -1;
  }
 
  return ret;
}
 
/************************************************************************/
static int tile_type_vector_find_equivalent(
                                const struct tile_type_vector *vec,
                                const struct cm_tile_type *ptype)
{
  int i;
 
  for (i = 0; i < vec->size; i++) {
    if (tile_type_equal(vec->p[i], ptype)) {
      return i;
    }
  }
 
  return -1;
}
 
/************************************************************************/
static int tile_type_num_tiles(const struct cm_tile_type *type)
{
  if (type->is_specialist) {
    return FC_INFINITY;
  } else {
    return tile_vector_size(&type->tiles);
  }
}
 
/************************************************************************/
static int tile_type_num_prereqs(const struct cm_tile_type *ptype)
{
  return ptype->better_types.size;
}
 
/************************************************************************/
static const struct cm_tile_type *tile_type_get(const struct cm_state *state,
                                                int type)
{
  /* Sanity check the index. */
  fc_assert_ret_val(0 <= type, NULL);
  fc_assert_ret_val(state->lattice.size > type, NULL);
 
  return state->lattice.p[type];
}
 
/************************************************************************/
static const struct cm_tile *tile_get(const struct cm_tile_type *ptype, int j)
{
  fc_assert_ret_val(!ptype->is_specialist, NULL);
  fc_assert_ret_val(0 <= j, NULL);
  fc_assert_ret_val(j < ptype->tiles.size, NULL);
 
  return &ptype->tiles.p[j];
}
 
 
/****************************************************************************
  Functions on the cm_fitness struct.
****************************************************************************/
 
/************************************************************************/
static bool fitness_better(struct cm_fitness a, struct cm_fitness b)
{
  if (a.sufficient != b.sufficient) {
    return a.sufficient;
  }
  return a.weighted > b.weighted;
}
 
/************************************************************************/
static struct cm_fitness worst_fitness(void)
{
  struct cm_fitness f;
 
  f.sufficient = FALSE;
  f.weighted = -FC_INFINITY;
  return f;
}
 
/************************************************************************/
static struct cm_fitness compute_fitness(const int surplus[],
                                         bool disorder, bool happy,
                                         const struct cm_parameter *parameter)
{
  struct cm_fitness fitness;
 
  fitness.sufficient = TRUE;
  fitness.weighted = 0;
 
  output_type_iterate(stat_index) {
    fitness.weighted += surplus[stat_index] * parameter->factor[stat_index];
    if (surplus[stat_index] < parameter->minimal_surplus[stat_index]) {
      fitness.sufficient = FALSE;
    }
  } output_type_iterate_end;
 
  if (happy) {
    fitness.weighted += parameter->happy_factor;
  } else if (parameter->require_happy) {
    fitness.sufficient = FALSE;
  }
 
  if (disorder && !parameter->allow_disorder) {
    fitness.sufficient = FALSE;
  }
 
  return fitness;
}
 
/****************************************************************************
  Handle struct partial_solution.
  - perform a deep copy
  - convert to city
  - convert to cm_result
****************************************************************************/
 
/************************************************************************/
static void init_partial_solution(struct partial_solution *into,
                                  int ntypes, int idle, bool negative_ok)
{
  into->worker_counts = fc_calloc(ntypes, sizeof(*into->worker_counts));
  into->prereqs_filled = fc_calloc(ntypes, sizeof(*into->prereqs_filled));
  if (negative_ok) {
    output_type_iterate(otype) {
      into->production[otype] = -FC_INFINITY;
    } output_type_iterate_end;
  } else {
    memset(into->production, 0, sizeof(into->production));
  }
  into->idle = idle;
}
 
/************************************************************************/
static void destroy_partial_solution(struct partial_solution *into)
{
  free(into->worker_counts);
  free(into->prereqs_filled);
}
 
/************************************************************************/
static void copy_partial_solution(struct partial_solution *dst,
                                  const struct partial_solution *src,
                                  const struct cm_state *state)
{
  memcpy(dst->worker_counts, src->worker_counts,
         sizeof(*dst->worker_counts) * num_types(state));
  memcpy(dst->prereqs_filled, src->prereqs_filled,
         sizeof(*dst->prereqs_filled) * num_types(state));
  memcpy(dst->production, src->production, sizeof(dst->production));
  dst->idle = src->idle;
}
 
 
/****************************************************************************
  Evaluating a completed solution.
****************************************************************************/
 
/************************************************************************/
static void apply_solution(struct cm_state *state,
                           const struct partial_solution *soln)
{
  struct city *pcity = state->pcity;
  int i, city_radius_sq = city_map_radius_sq_get(pcity);
  const struct civ_map *nmap = &(wld.map);
#ifndef FREECIV_NDEBUG
  int citizen_count = 0;
#endif
 
#ifdef GATHER_TIME_STATS
  performance.current->apply_count++;
#endif
 
  fc_assert_ret(0 == soln->idle);
 
  /* Clear all specialists, and remove all workers from fields (except
   * the city center). */
  memset(&pcity->specialists, 0, sizeof(pcity->specialists));
 
  city_map_iterate(city_radius_sq, cindex, x, y) {
    if (is_free_worked_index(cindex)) {
      state->workers_map[cindex] = TRUE;
    } else {
      state->workers_map[cindex] = FALSE;
    }
  } city_map_iterate_end;
 
  /* Now for each tile type, find the right number of such tiles and set them
   * as worked.  For specialists we just increase the number of specialists
   * of that type. */
  for (i = 0 ; i < num_types(state); i++) {
    int nworkers = soln->worker_counts[i];
    const struct cm_tile_type *type;
 
    if (nworkers == 0) {
      /* No citizens of this type. */
      continue;
    }
#ifndef FREECIV_NDEBUG
    citizen_count += nworkers;
#endif
 
    type = tile_type_get(state, i);
 
    if (type->is_specialist) {
      /* Just increase the number of specialists. */
      pcity->specialists[type->spec] += nworkers;
    } else {
      int j;
 
      /* Place citizen workers onto the citymap tiles. */
      for (j = 0; j < nworkers; j++) {
        const struct cm_tile *cmtile = tile_get(type, j);
 
        state->workers_map[cmtile->index] = TRUE;
      }
    }
  }
 
  /* Finally we must refresh the city to reset all the precomputed fields. */
  city_refresh_from_main_map(nmap, pcity, state->workers_map);
 
  fc_assert_ret(citizen_count == city_size_get(pcity));
}
 
/************************************************************************/
static void get_city_surplus(const struct city *pcity,
                             int surplus[],
                             bool *disorder, bool *happy)
{
  output_type_iterate(o) {
    surplus[o] = pcity->surplus[o];
  } output_type_iterate_end;
 
  *disorder = city_unhappy(pcity);
  *happy = city_happy(pcity);
}
 
/************************************************************************/
static struct cm_fitness evaluate_solution(struct cm_state *state,
    const struct partial_solution *soln)
{
  struct city *pcity = state->pcity;
  int surplus[O_LAST];
  bool disorder, happy;
 
  /* apply and evaluate the solution, backup is done in find_best_solution */
  apply_solution(state, soln);
  get_city_surplus(pcity, surplus, &disorder, &happy);
 
  /* if this solution is not content, we have an estimate on min. luxuries */
  if (disorder) {
    /* We have to consider the influence of each specialist in this
       solution possibly 'hiding' a potential unhappy citizen who
       could require luxuries.
       Since we know the city is in disorder, we can discount most
       effects that make citizens content, since they clearly weren't
       sufficient.
       This may not be sufficient luxury to make the city content (due
       to military unhappiness etc), but certainly no less will do.
       (Specialists may also be making angry citizens content, requiring
       additional luxuries, but we don't try to consider that here; this
       just means we might explore some solutions unnecessarily.) */
    int specialists_amount = city_specialists(pcity);
    int max_content = player_content_citizens(city_owner(pcity));
 
    state->min_luxury = surplus[O_LUXURY]
      + game.info.happy_cost * MAX(specialists_amount - max_content, 0)
      + 1;
  }
 
  return compute_fitness(surplus, disorder, happy, &state->parameter);
}
 
/************************************************************************/
static void convert_solution_to_result(struct cm_state *state,
                                       const struct partial_solution *soln,
                                       struct cm_result *result)
{
  struct cm_fitness fitness;
 
  if (soln->idle != 0) {
    /* If there are unplaced citizens it's not a real solution, so the
     * result is invalid. */
    result->found_a_valid = FALSE;
    return;
  }
 
  /* apply and evaluate the solution, backup is done in find_best_solution */
  apply_solution(state, soln);
  cm_result_copy(result, state->pcity, state->workers_map);
 
  /* result->found_a_valid should be only true if it matches the
   *  parameter; figure out if it does */
  fitness = compute_fitness(result->surplus, result->disorder,
                            result->happy, &state->parameter);
  result->found_a_valid = fitness.sufficient;
}
 
/****************************************************************************
  Compare functions to allow sorting lattice vectors.
****************************************************************************/
 
/************************************************************************/
static int compare_tile_type_by_lattice_order(const struct cm_tile_type *a,
                                              const struct cm_tile_type *b)
{
  if (a == b) {
    return 0;
  }
 
  /* Least depth first */
  if (a->lattice_depth != b->lattice_depth) {
    return a->lattice_depth - b->lattice_depth;
  }
 
  /* With equal depth, break ties arbitrarily, more production first. */
  output_type_iterate(stat_index) {
    if (a->production[stat_index] != b->production[stat_index]) {
      return b->production[stat_index] - a->production[stat_index];
    }
  } output_type_iterate_end;
 
  /* If we get here, then we have two copies of identical types, an error */
  fc_assert(FALSE);
  return 0;
}
 
/************************************************************************/
static int compare_tile_type_by_fitness(const void *va, const void *vb)
{
  struct cm_tile_type * const *a = va;
  struct cm_tile_type * const *b = vb;
  double diff;
 
  if (*a == *b) {
    return 0;
  }
 
  /* To avoid double->int roundoff problems, we call a result non-zero only
   * if it's larger than 0.5. */
  diff = (*b)->estimated_fitness - (*a)->estimated_fitness;
  if (diff > 0.5) {
    return 1; /* return value is int; don't round down! */
  }
  if (diff < -0.5) {
    return -1;
  }
 
  return compare_tile_type_by_lattice_order(*a, *b);
}
 
static Output_type_id compare_key;
static double compare_key_trade_bonus;
 
/************************************************************************/
static int compare_tile_type_by_stat(const void *va, const void *vb)
{
  struct cm_tile_type * const *a = va;
  struct cm_tile_type * const *b = vb;
 
  if (*a == *b) {
    return 0;
  }
 
  /* Consider the influence of trade on science, luxury, gold
     for compute_max_stats_heuristics, which uses these sorted arrays,
     it is essential, that the sorting is correct, else promising
     branches get pruned */
  double valuea = (*a)->production[compare_key] +
                    compare_key_trade_bonus * (*a)->production[O_TRADE];
  double valueb = (*b)->production[compare_key] +
                    compare_key_trade_bonus * (*b)->production[O_TRADE];
 
  /* Most production of what we care about goes first */
  /* Double compare is ok, both values are calculated in the same way
     and should only be considered equal, if equal in compare_key
     and O_TRADE */
  if (valuea != valueb) {
    /* b-a so we sort big numbers first */
    return valueb - valuea;
  }
 
  return compare_tile_type_by_lattice_order(*a, *b);
}
 
/****************************************************************************
  Compute the tile-type lattice.
****************************************************************************/
 
/************************************************************************/
static void compute_tile_production(const struct city *pcity,
                                    const struct tile *ptile,
                                    struct cm_tile_type *out)
{
  bool is_celebrating = base_city_celebrating(pcity);
 
  output_type_iterate(o) {
    out->production[o] = city_tile_output(pcity, ptile, is_celebrating, o);
  } output_type_iterate_end;
}
 
/************************************************************************/
static void tile_type_lattice_add(struct tile_type_vector *lattice,
                                  const struct cm_tile_type *newtype,
                                  int tindex)
{
  struct cm_tile_type *type;
  int i;
 
  i = tile_type_vector_find_equivalent(lattice, newtype);
  if (i >= 0) {
    /* We already have this type of tile; use it. */
    type = lattice->p[i];
  } else {
    /* This is a new tile type; add it to the lattice. */
    type = tile_type_dup(newtype);
 
    /* Link up to the types we dominate, and those that dominate us */
    tile_type_vector_iterate(lattice, other) {
      int cmp = tile_type_better(other, type);
 
      if (cmp > 0) {
        tile_type_vector_append(&type->better_types, other);
        tile_type_vector_append(&other->worse_types, type);
      } else if (cmp < 0) {
        tile_type_vector_append(&other->better_types, type);
        tile_type_vector_append(&type->worse_types, other);
      }
    } tile_type_vector_iterate_end;
 
    /* Insert into the list */
    type->lattice_index = lattice->size;
    tile_type_vector_append(lattice, type);
  }
 
  /* Finally, add the tile to the tile type. */
  if (!type->is_specialist) {
    struct cm_tile tile;
 
    tile.type = type;
    tile.index = tindex;
 
    tile_vector_append(&type->tiles, tile);
  }
}
 
/*
 * Add the specialist types to the lattice.
 */
 
/************************************************************************/
static void init_specialist_lattice_nodes(struct tile_type_vector *lattice,
                                          const struct city *pcity)
{
  struct cm_tile_type type;
 
  tile_type_init(&type);
  type.is_specialist = TRUE;
 
  /* for each specialist type, create a tile_type that has as production
   * the bonus for the specialist (if the city is allowed to use it) */
  specialist_type_iterate(i) {
    if (city_can_use_specialist(pcity, i)) {
      type.spec = i;
      output_type_iterate(output) {
        type.production[output] = get_specialist_output(pcity, i, output);
      } output_type_iterate_end;
 
      tile_type_lattice_add(lattice, &type, 0);
    }
  } specialist_type_iterate_end;
}
 
/************************************************************************/
static void top_sort_lattice(struct tile_type_vector *lattice)
{
  if (lattice->size > 0) {
    int i;
    bool marked[lattice->size];
    bool will_mark[lattice->size];
    struct tile_type_vector vectors[2];
    struct tile_type_vector *current, *next;
 
    memset(marked, 0, sizeof(marked));
    memset(will_mark, 0, sizeof(will_mark));
 
    tile_type_vector_init(&vectors[0]);
    tile_type_vector_init(&vectors[1]);
    current = &vectors[0];
    next = &vectors[1];
 
    /* Fill up 'next' */
    tile_type_vector_iterate(lattice, ptype) {
      if (tile_type_num_prereqs(ptype) == 0) {
        tile_type_vector_append(next, ptype);
      }
    } tile_type_vector_iterate_end;
 
    /* While we have nodes to process: mark the nodes whose prereqs have
     * all been visited. Then, store all the new nodes on the frontier. */
    while (next->size != 0) {
      /* What was the next frontier is now the current frontier */
      struct tile_type_vector *vtmp = current;
 
      current = next;
      next = vtmp;
      next->size = 0; /* Clear out the contents */
 
      /* Look over the current frontier and process everyone */
      tile_type_vector_iterate(current, ptype) {
        /* See if all prereqs were marked. If so, decide to mark this guy,
           and put all the descendents on 'next'.  */
        bool can_mark = TRUE;
        int sumdepth = 0;
 
        if (will_mark[ptype->lattice_index]) {
          continue; /* We've already been processed */
        }
        tile_type_vector_iterate(&ptype->better_types, better) {
          if (!marked[better->lattice_index]) {
            can_mark = FALSE;
            break;
          } else {
            sumdepth += tile_type_num_tiles(better);
            if (sumdepth >= FC_INFINITY) {
              /* If this is the case, then something better could
                 always be used, and the same holds for our children */
              sumdepth = FC_INFINITY;
              can_mark = TRUE;
              break;
            }
          }
        } tile_type_vector_iterate_end;
        if (can_mark) {
          /* Mark and put successors on the next frontier */
          will_mark[ptype->lattice_index] = TRUE;
          tile_type_vector_iterate(&ptype->worse_types, worse) {
            tile_type_vector_append(next, worse);
          } tile_type_vector_iterate_end;
 
          /* This is what we spent all this time computing. */
          ptype->lattice_depth = sumdepth;
        }
      } tile_type_vector_iterate_end;
 
      /* Now, actually mark everyone and get set for next loop */
      for (i = 0; i < lattice->size; i++) {
        marked[i] = marked[i] || will_mark[i];
        will_mark[i] = FALSE;
      }
    }
 
    tile_type_vector_free(&vectors[0]);
    tile_type_vector_free(&vectors[1]);
  }
}
 
/************************************************************************/
static void clean_lattice(struct tile_type_vector *lattice,
                          const struct city *pcity)
{
  int i, j; /* i is the index we read, j is the index we write */
  struct tile_type_vector tofree;
  bool forced_loop = FALSE;
 
  /* We collect the types we want to remove and free them in one fell
     swoop at the end, in order to avoid memory errors.  */
  tile_type_vector_init(&tofree);
 
  /* forced_loop is workaround for what seems like gcc optimization
   * bug.
   * This applies to -O2 optimization on some distributions. */
  if (lattice->size > 0) {
    forced_loop = TRUE;
  }
  for (i = 0, j = 0; i < lattice->size || forced_loop; i++) {
    struct cm_tile_type *ptype = lattice->p[i];
    citizens csize = city_size_get(pcity);
 
    forced_loop = FALSE;
 
    if (ptype->lattice_depth >= csize) {
      tile_type_vector_append(&tofree, ptype);
    } else {
      /* Remove links to children that are being removed. */
 
      int ci, cj; /* 'c' for 'child'; read from ci, write to cj */
 
      lattice->p[j] = ptype;
      lattice->p[j]->lattice_index = j;
      j++;
 
      for (ci = 0, cj = 0; ci < ptype->worse_types.size; ci++) {
        const struct cm_tile_type *ptype2 = ptype->worse_types.p[ci];
 
        if (ptype2->lattice_depth < csize) {
          ptype->worse_types.p[cj] = ptype->worse_types.p[ci];
          cj++;
        }
      }
      ptype->worse_types.size = cj;
    }
  }
  lattice->size = j;
 
  tile_type_vector_free_all(&tofree);
}
 
/************************************************************************/
static void sort_lattice_by_fitness(const struct cm_state *state,
                                    struct tile_type_vector *lattice)
{
  int i;
 
  /* compute fitness */
  tile_type_vector_iterate(lattice, ptype) {
    ptype->estimated_fitness = estimate_fitness(state, ptype->production);
  } tile_type_vector_iterate_end;
 
  /* sort by it */
  qsort(lattice->p, lattice->size, sizeof(*lattice->p),
        compare_tile_type_by_fitness);
 
  /* fix the lattice indices */
  for (i = 0; i < lattice->size; i++) {
    lattice->p[i]->lattice_index = i;
  }
 
  log_base(LOG_LATTICE, "sorted lattice:");
  print_lattice(LOG_LATTICE, lattice);
}
 
/************************************************************************/
static void init_tile_lattice(struct city *pcity,
                              struct tile_type_vector *lattice)
{
  struct cm_tile_type type;
  struct tile *pcenter = city_tile(pcity);
  const struct civ_map *nmap = &(wld.map);
 
  /* Add all the fields into the lattice */
  tile_type_init(&type); /* Init just once */
 
  city_tile_iterate_index(nmap, city_map_radius_sq_get(pcity), pcenter, ptile,
                          ctindex) {
    if (is_free_worked(pcity, ptile)) {
      continue;
    } else if (city_can_work_tile(pcity, ptile)) {
      compute_tile_production(pcity, ptile, &type); /* Clobbers type */
      tile_type_lattice_add(lattice, &type, ctindex); /* Copy type if needed */
    }
  } city_tile_iterate_index_end;
 
  /* Add all the specialists into the lattice.  */
  init_specialist_lattice_nodes(lattice, pcity);
 
  /* Set the lattice_depth fields, and clean up unreachable nodes. */
  top_sort_lattice(lattice);
  clean_lattice(lattice, pcity);
 
  /* All done now. */
  print_lattice(LOG_LATTICE, lattice);
}
 
 
/****************************************************************************
 
               Handling the choice stack for the bb algorithm.
 
****************************************************************************/
 
 
/************************************************************************/
static bool choice_stack_empty(struct cm_state *state)
{
  return state->choice.size == 0;
}
 
/************************************************************************/
static int last_choice(struct cm_state *state)
{
  fc_assert_ret_val(!choice_stack_empty(state), -1);
 
  return state->choice.stack[state->choice.size - 1];
}
 
/************************************************************************/
static int num_types(const struct cm_state *state)
{
  return tile_type_vector_size(&state->lattice);
}
 
/************************************************************************/
static void add_workers(struct partial_solution *soln,
                        int itype, int number,
                        const struct cm_state *state)
{
  const struct cm_tile_type *ptype = tile_type_get(state, itype);
  int newcount;
  int old_worker_count = soln->worker_counts[itype];
 
  if (number == 0) {
    return;
  }
 
  /* update the number of idle workers */
  newcount = soln->idle - number;
  fc_assert_ret(newcount >= 0);
  fc_assert_ret(newcount <= city_size_get(state->pcity));
  soln->idle = newcount;
 
  /* update the worker counts */
  newcount = soln->worker_counts[itype] + number;
  fc_assert_ret(newcount >= 0);
  fc_assert_ret(newcount <= tile_type_num_tiles(ptype));
  soln->worker_counts[itype] = newcount;
 
  /* update prereqs array: if we are no longer full but we were,
   * we need to decrement the count, and vice-versa. */
  if (old_worker_count == tile_type_num_tiles(ptype)) {
    fc_assert_ret(number < 0);
    tile_type_vector_iterate(&ptype->worse_types, other) {
      soln->prereqs_filled[other->lattice_index]--;
      fc_assert_ret(soln->prereqs_filled[other->lattice_index] >= 0);
    } tile_type_vector_iterate_end;
  } else if (soln->worker_counts[itype] == tile_type_num_tiles(ptype)) {
    fc_assert_ret(number > 0);
    tile_type_vector_iterate(&ptype->worse_types, other) {
      soln->prereqs_filled[other->lattice_index]++;
      fc_assert_ret(soln->prereqs_filled[other->lattice_index]
          <= tile_type_num_prereqs(other));
    } tile_type_vector_iterate_end;
  }
 
  /* update production */
  output_type_iterate(stat_index) {
    newcount = soln->production[stat_index] + number * ptype->production[stat_index];
    soln->production[stat_index] = newcount;
  } output_type_iterate_end;
}
 
/************************************************************************/
static void add_worker(struct partial_solution *soln,
                       int itype, const struct cm_state *state)
{
  add_workers(soln, itype, 1, state);
}
 
/************************************************************************/
static void remove_worker(struct partial_solution *soln,
                          int itype, const struct cm_state *state)
{
  add_workers(soln, itype, -1, state);
}
 
/************************************************************************/
static void pop_choice(struct cm_state *state)
{
  fc_assert_ret(!choice_stack_empty(state));
  remove_worker(&state->current, last_choice(state), state);
  state->choice.size--;
}
 
/************************************************************************/
static bool prereqs_filled(const struct partial_solution *soln, int type,
                           const struct cm_state *state)
{
  const struct cm_tile_type *ptype = tile_type_get(state, type);
  int prereqs = tile_type_num_prereqs(ptype);
 
  return soln->prereqs_filled[type] == prereqs;
}
 
/************************************************************************/
static int next_choice(struct cm_state *state, int oldchoice, bool negative_ok)
{
  int newchoice;
 
  for (newchoice = oldchoice + 1;
       newchoice < num_types(state); newchoice++) {
    const struct cm_tile_type *ptype = tile_type_get(state, newchoice);
 
    if (!ptype->is_specialist && (state->current.worker_counts[newchoice]
                                  == tile_vector_size(&ptype->tiles))) {
      /* we've already used all these tiles */
      continue;
    }
    if (!prereqs_filled(&state->current, newchoice, state)) {
      /* we could use a strictly better tile instead */
      continue;
    }
    if (!choice_is_promising(state, newchoice, negative_ok)) {
      /* heuristic says we can't beat the best going this way */
      log_base(LOG_PRUNE_BRANCH, "--- pruning branch ---");
      print_partial_solution(LOG_PRUNE_BRANCH, &state->current, state);
      print_tile_type(LOG_PRUNE_BRANCH, tile_type_get(state, newchoice),
                      " + worker on ");
      log_base(LOG_PRUNE_BRANCH, "--- branch pruned ---");
      continue;
    }
    break;
  }
 
  /* returns num_types if no next choice was available. */
  return newchoice;
}
 
 
/************************************************************************/
static bool take_sibling_choice(struct cm_state *state, bool negative_ok)
{
  int oldchoice = last_choice(state);
  int newchoice;
 
  /* need to remove first, to run the heuristic */
  remove_worker(&state->current, oldchoice, state);
  newchoice = next_choice(state, oldchoice, negative_ok);
 
  if (newchoice == num_types(state)) {
    /* add back in so the caller can then remove it again. */
    add_worker(&state->current, oldchoice, state);
    return FALSE;
  } else {
    add_worker(&state->current, newchoice, state);
    state->choice.stack[state->choice.size-1] = newchoice;
    /* choice.size is unchanged */
    return TRUE;
  }
}
 
/************************************************************************/
static bool take_child_choice(struct cm_state *state, bool negative_ok)
{
  int oldchoice, newchoice;
 
  if (state->current.idle == 0) {
    return FALSE;
  }
 
  if (state->choice.size == 0) {
    oldchoice = 0;
  } else {
    oldchoice = last_choice(state);
  }
 
  /* oldchoice-1 because we can use oldchoice again */
  newchoice = next_choice(state, oldchoice - 1, negative_ok);
 
  /* did we fail? */
  if (newchoice == num_types(state)) {
    return FALSE;
  }
 
  /* now push the new choice on the choice stack */
  add_worker(&state->current, newchoice, state);
  state->choice.stack[state->choice.size] = newchoice;
  state->choice.size++;
 
  return TRUE;
}
 
/************************************************************************/
static void complete_solution(struct partial_solution *soln,
                              const struct cm_state *state,
                              const struct tile_type_vector *lattice)
{
  int last_worker_choice = -1;
  int i;
 
  if (soln->idle == 0) {
    return;
  }
 
  /* find the last worker type added (-1 if none) */
  for (i = 0; i < num_types(state); i++) {
    if (soln->worker_counts[i] != 0) {
      last_worker_choice = i;
    }
  }
 
  /* While there are idle workers, pick up the next-best kind of tile,
   * and assign the workers to the tiles.
   * Respect lexicographic order and prerequisites.  */
  tile_type_vector_iterate(lattice, ptype) {
    int used = soln->worker_counts[ptype->lattice_index];
    int total = tile_type_num_tiles(ptype);
    int touse;
 
    if (ptype->lattice_index < last_worker_choice) {
      /* lex-order: we can't use ptype (some other branch
         will check this combination, or already did) */
      continue;
    }
    if (!prereqs_filled(soln, ptype->lattice_index, state)) {
      /* don't bother using this tile before all better tiles are used */
      continue;
    }
 
    touse = total - used;
    if (touse > soln->idle) {
      touse = soln->idle;
    }
    add_workers(soln, ptype->lattice_index, touse, state);
 
    if (soln->idle == 0) {
      /* nothing left to do here */
      return;
    }
  } tile_type_vector_iterate_end;
}
 
/************************************************************************/
static int specialists_in_solution(const struct cm_state *state,
                                   const struct partial_solution *soln)
{
  int count = 0;
  int i;
 
  for (i = 0 ; i < num_types(state); i++) {
    if (soln->worker_counts[i] > 0 && tile_type_get(state, i)->is_specialist) {
      count += soln->worker_counts[i];
    }
  }
 
  return count;
}
 
/************************************************************************/
static void compute_max_stats_heuristic(const struct cm_state *state,
                                        const struct partial_solution *soln,
                                        int production[],
                                        int check_choice, bool negative_ok)
{
  struct partial_solution solnplus; /* Will be soln, plus some tiles */
  const struct civ_map *nmap = &(wld.map);
 
  /* Production is whatever the solution produces, plus the
     most possible of each kind of production the idle workers could
     produce */
 
  if (soln->idle == 1) {
    /* Then the total solution is soln + this new worker. So we know the
       production exactly, and can shortcut the later code. */
    const struct cm_tile_type *ptype = tile_type_get(state, check_choice);
 
    memcpy(production, soln->production, sizeof(soln->production));
    output_type_iterate(stat_index) {
      production[stat_index] += ptype->production[stat_index];
    } output_type_iterate_end;
 
  } else {
 
    /* Initialize solnplus here, after the shortcut check */
    init_partial_solution(&solnplus, num_types(state),
                          city_size_get(state->pcity),
                          negative_ok);
 
    output_type_iterate(stat_index) {
      /* compute the solution that has soln, then the check_choice,
         then complete it with the best available tiles for the stat. */
      copy_partial_solution(&solnplus, soln, state);
      add_worker(&solnplus, check_choice, state);
      complete_solution(&solnplus, state, &state->lattice_by_prod[stat_index]);
 
      production[stat_index] = solnplus.production[stat_index];
    } output_type_iterate_end;
 
    destroy_partial_solution(&solnplus);
 
  }
 
  /* We found the basic production, however, bonus, taxes,
   * free production, tithes, trade routes are missing.
   * We add free production, and have the city.c code do the rest */
 
  struct city *pcity = state->pcity;
  struct tile *pcenter = city_tile(pcity);
  bool is_celebrating = base_city_celebrating(pcity);
 
  output_type_iterate(stat_index) {
    int base = production[stat_index];
 
    city_tile_iterate(nmap, city_map_radius_sq_get(pcity), pcenter, ptile) {
      if (is_free_worked(pcity, ptile)) {
        base += city_tile_output(pcity, ptile, is_celebrating, stat_index);
      }
    } city_tile_iterate_end;
    pcity->citizen_base[stat_index] = base;
  } output_type_iterate_end;
 
  set_city_production(pcity);
  memcpy(production, pcity->prod, sizeof(pcity->prod));
}
 
/************************************************************************/
static bool choice_is_promising(struct cm_state *state, int newchoice,
                                bool negative_ok)
{
  int production[O_LAST];
  bool beats_best = FALSE;
 
  /* this computes an upper bound (componentwise) for the current branch,
     if it is worse in every component than the best, or still insufficient,
     then we can prune the whole branch */
  compute_max_stats_heuristic(state, &state->current, production, newchoice,
                              negative_ok);
 
  output_type_iterate(stat_index) {
    if (production[stat_index] < state->min_production[stat_index]) {
      log_base(LOG_PRUNE_BRANCH, "--- pruning: insufficient %s (%d < %d)",
               get_output_name(stat_index), production[stat_index],
               state->min_production[stat_index]);
      return FALSE;
    }
    if (production[stat_index] > state->best.production[stat_index]
        && state->parameter.factor[stat_index] > 0 ) {
      beats_best = TRUE;
      /* may still fail to meet min at another production type, so
       * don't short-circuit */
    }
  } output_type_iterate_end;
 
  /* If we don't get the city content, we assume using every idle worker
     as specialist and the maximum producible luxury already computed.
     If this is less than the amount of luxury we calculated in
     evaluate_solution() (where min_luxury is set), when we observed the
     city in disorder, then this is clearly not worth pursuing.
     (Since we're comparing to evaluate_solution()'s calculation, we
     don't need to take effects, angry citizens etc into account here
     either.)
     FIXME: this heuristic will break in rulesets where specialists can
     influence happiness other than by direct production of luxury. */
  {
    int specialists_amount = specialists_in_solution(state, &state->current);
    int max_content = player_content_citizens(city_owner(state->pcity));
    int specialists_suppress_unhappy
      = MAX(specialists_amount + state->current.idle - max_content, 0);
    int max_luxury = production[O_LUXURY]
          + game.info.happy_cost * specialists_suppress_unhappy;
 
    if (max_luxury < state->min_luxury ) {
      log_base(LOG_PRUNE_BRANCH, "--- pruning: disorder (%d + %d*%d < %d)",
               production[O_LUXURY],
               game.info.happy_cost,
               specialists_suppress_unhappy,
               state->min_luxury);
      return FALSE;
    }
  }
  if (!beats_best) {
    log_base(LOG_PRUNE_BRANCH, "--- pruning: best is better in all important ways");
  }
 
  return beats_best;
}
 
/************************************************************************/
static void init_min_production(struct cm_state *state)
{
  struct city *pcity = state->pcity;
 
  output_type_iterate(o) {
    state->min_production[o] = pcity->usage[o] + state->parameter.minimal_surplus[o];
  } output_type_iterate_end;
 
  /* We could get a minimum on luxury if we knew how many luxuries were
   * needed to make us content. */
}
 
/************************************************************************/
static void get_tax_rates(const struct player *pplayer, int rates[])
{
  const int SCIENCE = 0, TAX = 1, LUXURY = 2;
 
  if (game.info.changable_tax) {
    rates[SCIENCE] = pplayer->economic.science;
    rates[LUXURY] = pplayer->economic.luxury;
    rates[TAX] = 100 - rates[SCIENCE] - rates[LUXURY];
  } else {
    rates[SCIENCE] = game.info.forced_science;
    rates[LUXURY] = game.info.forced_luxury;
    rates[TAX] = game.info.forced_gold;
  }
 
  /* ANARCHY */
  if (government_of_player(pplayer) == game.government_during_revolution) {
    rates[SCIENCE] = 0;
    rates[LUXURY] = 100;
    rates[TAX] = 0;
  }
}
 
/************************************************************************/
static double estimate_fitness(const struct cm_state *state,
                               const int production[])
{
  const int SCIENCE = 0, TAX = 1, LUXURY = 2;
  const struct city *pcity = state->pcity;
  const struct player *pplayer = city_owner(pcity);
  int rates[3];
  double estimates[O_LAST];
  double sum = 0;
  int trade;
 
  output_type_iterate(stat_index) {
    estimates[stat_index] = production[stat_index];
  } output_type_iterate_end;
 
  /* bonus to trade is applied before calculating taxes, see city.c */
  trade = estimates[O_TRADE] * pcity->bonus[O_TRADE] / 100.0;
 
  get_tax_rates(pplayer, rates);
 
  /* sci/lux/gold get benefit from the tax rates (in percentage) */
  estimates[O_SCIENCE]
    += rates[SCIENCE] * trade / 100.0;
  estimates[O_LUXURY]
    += rates[LUXURY] * trade / 100.0;
  estimates[O_GOLD]
    += rates[TAX] * trade / 100.0;
 
  /* now add in the bonuses from building effects (in percentage) */
  output_type_iterate(stat_index) {
    estimates[stat_index] *= pcity->bonus[stat_index] / 100.0;
  } output_type_iterate_end;
 
  /* finally, sum it all up, weighted by the parameter, but give additional
   * weight to luxuries to take account of disorder/happy constraints */
  output_type_iterate(stat_index) {
    sum += estimates[stat_index] * state->parameter.factor[stat_index];
  } output_type_iterate_end;
  sum += estimates[O_LUXURY];
 
  return sum;
}
 
/************************************************************************/
static bool bb_next(struct cm_state *state, bool negative_ok)
{
  /* if no idle workers, then look at our solution. */
  if (state->current.idle == 0) {
    struct cm_fitness value = evaluate_solution(state, &state->current);
 
    print_partial_solution(LOG_REACHED_LEAF, &state->current, state);
    if (fitness_better(value, state->best_value)) {
      log_base(LOG_BETTER_LEAF, "-> replaces previous best");
      copy_partial_solution(&state->best, &state->current, state);
      state->best_value = value;
    }
  }
 
  /* try to move to a child branch, if we can.  If not (including if we're
     at a leaf), then move to a sibling. */
  if (!take_child_choice(state, negative_ok)) {
    /* keep trying to move to a sibling branch, or popping out a level if
       we're stuck (fully examined the current branch) */
    while ((!choice_stack_empty(state))
           && !take_sibling_choice(state, negative_ok)) {
      pop_choice(state);
    }
 
    /* if we popped out all the way, we're done */
    if (choice_stack_empty(state)) {
      return TRUE;
    }
  }
 
  /* if we didn't detect that we were done, we aren't */
  return FALSE;
}
 
/************************************************************************/
static struct cm_state *cm_state_init(struct city *pcity, bool negative_ok)
{
  const int SCIENCE = 0, TAX = 1, LUXURY = 2;
  const struct player *pplayer = city_owner(pcity);
  int numtypes;
  struct cm_state *state = fc_malloc(sizeof(*state));
  int rates[3];
  citizens csize = city_size_get(pcity);
 
  log_base(LOG_CM_STATE, "creating cm_state for %s (size %d)",
           city_name_get(pcity), csize);
 
  /* copy the arguments */
  state->pcity = pcity;
 
  /* create the lattice */
  tile_type_vector_init(&state->lattice);
  init_tile_lattice(pcity, &state->lattice);
  numtypes = tile_type_vector_size(&state->lattice);
 
  get_tax_rates(pplayer, rates);
 
  /* For the heuristic, make sorted copies of the lattice */
  output_type_iterate(stat_index) {
    int lsize = tile_type_vector_size(&state->lattice);
 
    if (lsize > 0) {
      tile_type_vector_init(&state->lattice_by_prod[stat_index]);
      tile_type_vector_copy(&state->lattice_by_prod[stat_index], &state->lattice);
      compare_key = stat_index;
      /* Calculate effect of 1 trade production on interesting production */
      switch (stat_index) {
      case O_SCIENCE:
        compare_key_trade_bonus = rates[SCIENCE] * pcity->bonus[O_TRADE] / 100.0;
        break;
      case O_LUXURY:
        compare_key_trade_bonus = rates[LUXURY] * pcity->bonus[O_TRADE] / 100.0;
        break;
      case O_GOLD:
        compare_key_trade_bonus = rates[TAX] * pcity->bonus[O_TRADE] / 100.0;
        break;
      default:
        compare_key_trade_bonus = 0.0;
        break;
      }
      qsort(state->lattice_by_prod[stat_index].p, lsize,
            sizeof(*state->lattice_by_prod[stat_index].p),
            compare_tile_type_by_stat);
    }
  } output_type_iterate_end;
 
  state->min_luxury = - FC_INFINITY;
 
  /* We have no best solution yet, so its value is the worst possible. */
  init_partial_solution(&state->best, numtypes, csize, negative_ok);
  state->best_value = worst_fitness();
 
  /* Initialize the current solution and choice stack to empty */
  init_partial_solution(&state->current, numtypes, csize, negative_ok);
  state->choice.stack = fc_malloc(csize * sizeof(*state->choice.stack));
  state->choice.size = 0;
 
  /* Initialize workers map */
  state->workers_map = fc_calloc(city_map_tiles_from_city(state->pcity),
                                 sizeof(state->workers_map));
 
  return state;
}
 
/************************************************************************/
static int min_food_surplus_for_fastest_growth(struct cm_state *state)
{
  struct city *pcity = state->pcity;
  int city_radius_sq = city_map_radius_sq_get(pcity);
  citizens city_size = city_size_get(pcity);
  int max_surplus = -game.info.food_cost * city_size;
  bool is_celebrating = base_city_celebrating(pcity);
  citizens workers = city_size;
  int food_needed = city_granary_size(city_size) - pcity->food_stock;
  int min_turns;
  const struct civ_map *nmap = &(wld.map);
 
  city_map_iterate(city_radius_sq, cindex, x, y) {
    struct tile *ptile = city_map_to_tile(nmap, pcity->tile, city_radius_sq, x, y);
    if (!ptile) {
      continue;
    }
    if (is_free_worked_index(cindex)) {
      max_surplus += city_tile_output(pcity, ptile, is_celebrating, O_FOOD);
    }
  } city_map_iterate_end;
 
  if (max_surplus <= 0) {
    return max_surplus;
  }
 
  if (food_needed <= 0) {
    return 0;
  }
 
  tile_type_vector_iterate(&state->lattice_by_prod[O_FOOD], ptype) {
    int num = tile_vector_size(&ptype->tiles);
 
    if (ptype->is_specialist || workers < num) {
      max_surplus += workers * ptype->production[O_FOOD];
      break;
    }
    max_surplus += num * ptype->production[O_FOOD];
    workers -= num;
  } tile_type_vector_iterate_end;
 
  /* min_turns will always be positive because if food_needed or
   * max_surplus are non-positive, this function returns earlier. */
  min_turns = (food_needed + max_surplus - 1) / max_surplus;
 
  return (food_needed + min_turns - 1) / min_turns;
}
 
/************************************************************************/
static void begin_search(struct cm_state *state,
                         const struct cm_parameter *parameter,
                         bool negative_ok)
{
#ifdef GATHER_TIME_STATS
  timer_start(performance.current->wall_timer);
  performance.current->query_count++;
#endif /* GATHER_TIME_STATS */
 
  /* copy the parameter and sort the main lattice by it */
  cm_copy_parameter(&state->parameter, parameter);
  sort_lattice_by_fitness(state, &state->lattice);
 
  if (parameter->max_growth) {
    state->parameter.minimal_surplus[O_FOOD] =
        min_food_surplus_for_fastest_growth(state);
  }
 
  init_min_production(state);
 
  /* Clear out the old solution */
  state->best_value = worst_fitness();
  destroy_partial_solution(&state->current);
  init_partial_solution(&state->current, num_types(state),
                        city_size_get(state->pcity),
                        negative_ok);
  state->choice.size = 0;
}
 
/************************************************************************/
static void end_search(struct cm_state *state)
{
#ifdef GATHER_TIME_STATS
  timer_stop(performance.current->wall_timer);
 
#ifdef PRINT_TIME_STATS_EVERY_QUERY
  print_performance(performance.current);
#endif /* PRINT_TIME_STATS_EVERY_QUERY */
 
  performance.current = NULL;
#endif /* GATHER_TIME_STATS */
}
 
/************************************************************************/
static void cm_state_free(struct cm_state *state)
{
  tile_type_vector_free_all(&state->lattice);
  output_type_iterate(stat_index) {
    tile_type_vector_free(&state->lattice_by_prod[stat_index]);
  } output_type_iterate_end;
  destroy_partial_solution(&state->best);
  destroy_partial_solution(&state->current);
 
  FC_FREE(state->choice.stack);
  FC_FREE(state->workers_map);
  FC_FREE(state);
}
 
/************************************************************************/
static void cm_find_best_solution(struct cm_state *state,
                                  const struct cm_parameter *const parameter,
                                  struct cm_result *result, bool negative_ok)
{
  int loop_count = 0;
  int max_count;
  struct city backup;
 
#ifdef GATHER_TIME_STATS
  performance.current = &performance.opt;
#endif
 
  begin_search(state, parameter, negative_ok);
 
  /* Make a backup of the city to restore at the very end */
  memcpy(&backup, state->pcity, sizeof(backup));
 
  if (player_is_cpuhog(city_owner(state->pcity))) {
    max_count = CPUHOG_CM_MAX_LOOP;
  } else {
    max_count = CM_MAX_LOOP;
  }
 
  result->aborted = FALSE;
 
  /* search until we find a feasible solution */
  while (!bb_next(state, negative_ok)) {
    /* Limit the number of loops. */
    loop_count++;
 
    if (loop_count == max_count + 1) {
#ifdef FREECIV_TESTMATIC
      /* This happens at a rate inversely proportional to the number of needed iterations
       *    https://osdn.net/projects/freeciv/ticket/44438
       *    we mostly find solutions in less than 100 iteration
       *        33% in less than 24 iterations
       *        66% in less than 100
       *        99% in less than 1800
       *      extremely rarely 10 000+
       *    it is not a bug it is normal, so just silent this warning
       */
      log_base(
               LOG_DEBUG,
               "Did not find a cm solution in %d iterations for %s.",
               max_count, city_name_get(state->pcity));
#endif /* FREECIV_TESTMATIC */
 
#ifndef CM_LOOP_NO_LIMIT
      result->aborted = TRUE;
      break;
#endif /* CM_LOOP_NO_LIMIT */
    }
  }
 
#ifdef CM_LOOP_NO_LIMIT
  if (loop_count > max_count) {
    log_warn("It took %d iterations to finish.", loop_count);
  }
#endif /* CM_LOOP_NO_LIMIT */
 
  /* convert to the caller's format */
  convert_solution_to_result(state, &state->best, result);
 
  memcpy(state->pcity, &backup, sizeof(backup));
 
  end_search(state);
}
 
/************************************************************************/
void cm_query_result(struct city *pcity,
                     const struct cm_parameter *param,
                     struct cm_result *result, bool negative_ok)
{
  struct cm_state *state = cm_state_init(pcity, negative_ok);
  const struct civ_map *nmap = &(wld.map);
 
  /* Refresh the city. Otherwise the CM can give wrong results or just be
   * slower than necessary. Note that cities are often passed in in an
   * unrefreshed state (which should probably be fixed). */
  city_refresh_from_main_map(nmap, pcity, NULL);
 
  cm_find_best_solution(state, param, result, negative_ok);
  cm_state_free(state);
}
 
/************************************************************************/
bool cm_are_parameter_equal(const struct cm_parameter *const p1,
                            const struct cm_parameter *const p2)
{
  output_type_iterate(i) {
    if (p1->minimal_surplus[i] != p2->minimal_surplus[i]) {
      return FALSE;
    }
    if (p1->factor[i] != p2->factor[i]) {
      return FALSE;
    }
  } output_type_iterate_end;
  if (p1->require_happy != p2->require_happy) {
    return FALSE;
  }
  if (p1->allow_disorder != p2->allow_disorder) {
    return FALSE;
  }
  if (p1->allow_specialists != p2->allow_specialists) {
    return FALSE;
  }
  if (p1->happy_factor != p2->happy_factor) {
    return FALSE;
  }
  if (p1->max_growth != p2->max_growth) {
    return FALSE;
  }
 
  return TRUE;
}
 
/************************************************************************/
void cm_copy_parameter(struct cm_parameter *dest,
                       const struct cm_parameter *const src)
{
  memcpy(dest, src, sizeof(struct cm_parameter));
}
 
/************************************************************************/
void cm_init_parameter(struct cm_parameter *dest)
{
  output_type_iterate(stat_index) {
    dest->minimal_surplus[stat_index] = 0;
    dest->factor[stat_index] = 1;
  } output_type_iterate_end;
 
  dest->happy_factor = 1;
  dest->require_happy = FALSE;
  dest->allow_disorder = FALSE;
  dest->allow_specialists = TRUE;
  dest->max_growth = FALSE;
}
 
/************************************************************************/
void cm_init_emergency_parameter(struct cm_parameter *dest)
{
  output_type_iterate(stat_index) {
    dest->minimal_surplus[stat_index] = -FC_INFINITY;
    dest->factor[stat_index] = 1;
  } output_type_iterate_end;
 
  dest->happy_factor = 1;
  dest->require_happy = FALSE;
  dest->allow_disorder = TRUE;
  dest->allow_specialists = TRUE;
  dest->max_growth = FALSE;
}
 
/************************************************************************/
int cm_result_workers(const struct cm_result *result)
{
  int count = 0;
 
  city_map_iterate(result->city_radius_sq, cindex, x, y) {
    if (is_free_worked_index(cindex)) {
      continue;
    }
 
    if (result->worker_positions[cindex]) {
      count++;
    }
  } city_map_iterate_end;
 
  return count;
}
 
/************************************************************************/
int cm_result_specialists(const struct cm_result *result)
{
  int count = 0;
 
  specialist_type_iterate(spec) {
    count += result->specialists[spec];
  } specialist_type_iterate_end;
 
  return count;
}
 
/************************************************************************/
int cm_result_citizens(const struct cm_result *result)
{
  return cm_result_workers(result) + cm_result_specialists(result);
}
 
/************************************************************************/
void cm_result_from_main_map(struct cm_result *result,
                             const struct city *pcity)
{
  cm_result_copy(result, pcity, NULL);
}
 
/************************************************************************/
static void cm_result_copy(struct cm_result *result,
                           const struct city *pcity, bool *workers_map)
{
  struct tile *pcenter = city_tile(pcity);
  const struct civ_map *nmap = &(wld.map);
 
  /* Clear worker positions */
  memset(result->worker_positions, 0,
         sizeof(*result->worker_positions)
         * city_map_tiles(result->city_radius_sq));
 
  city_tile_iterate_index(nmap, result->city_radius_sq, pcenter, ptile, ctindex) {
    if (workers_map == NULL) {
      /* Use the main map */
      struct city *pwork = tile_worked(ptile);
 
      result->worker_positions[ctindex] = (NULL != pwork && pwork == pcity);
    } else {
      result->worker_positions[ctindex] = workers_map[ctindex];
    }
  } city_tile_iterate_index_end;
 
  /* Copy the specialist counts */
  specialist_type_iterate(spec) {
    result->specialists[spec] = pcity->specialists[spec];
  } specialist_type_iterate_end;
 
  /* Find the surplus production numbers */
  get_city_surplus(pcity, result->surplus,
      &result->disorder, &result->happy);
 
  /* This is a valid result, in a sense */
  result->found_a_valid = TRUE;
}
 
/************************************************************************/
#ifdef CM_DEBUG
static void snprint_production(char *buffer, size_t bufsz,
                               const int production[])
{
  fc_snprintf(buffer, bufsz, "[%d %d %d %d %d %d]",
              production[O_FOOD], production[O_SHIELD],
              production[O_TRADE], production[O_GOLD],
              production[O_LUXURY], production[O_SCIENCE]);
}
 
/************************************************************************/
static void real_print_tile_type(enum log_level level, const char *file,
                                 const char *function, int line,
                                 const struct cm_tile_type *ptype,
                                 const char *prefix)
{
  char prodstr[256];
 
  snprint_production(prodstr, sizeof(prodstr), ptype->production);
  do_log(file, function, line, FALSE, level,
         "%s%s fitness %g depth %d, idx %d; %d tiles", prefix,
         prodstr, ptype->estimated_fitness, ptype->lattice_depth,
         ptype->lattice_index, tile_type_num_tiles(ptype));
}
 
/************************************************************************/
static void real_print_lattice(enum log_level level, const char *file,
                               const char *function, int line,
                               const struct tile_type_vector *lattice)
{
  do_log(file, function, line, FALSE, level,
         "lattice has %u terrain types", (unsigned) lattice->size);
  tile_type_vector_iterate(lattice, ptype) {
    real_print_tile_type(level, file, function, line, ptype, "  ");
  } tile_type_vector_iterate_end;
}
 
/************************************************************************/
static void real_print_partial_solution(enum log_level level,
                                        const char *file,
                                        const char *function, int line,
                                        const struct partial_solution *soln,
                                        const struct cm_state *state)
{
  int i;
  int last_type = 0;
  char buf[256];
 
  if (soln->idle != 0) {
    do_log(file, function, line, FALSE, level,
           "** partial solution has %d idle workers", soln->idle);
  } else {
    do_log(file, function, line, FALSE, level, "** completed solution:");
  }
 
  snprint_production(buf, sizeof(buf), soln->production);
  do_log(file, function, line, FALSE, level, "production: %s", buf);
 
  do_log(file, function, line, FALSE, level, "tiles used:");
  for (i = 0; i < num_types(state); i++) {
    if (soln->worker_counts[i] != 0) {
      fc_snprintf(buf, sizeof(buf), "  %d tiles of type ",
                  soln->worker_counts[i]);
      real_print_tile_type(level, file, function, line,
                           tile_type_get(state, i), buf);
    }
  }
 
  for (i = 0; i < num_types(state); i++) {
    if (soln->worker_counts[i] != 0) {
      last_type = i;
    }
  }
 
  do_log(file, function, line, FALSE, level, "tiles available:");
  for (i = last_type; i < num_types(state); i++) {
    const struct cm_tile_type *ptype = tile_type_get(state, i);
 
    if (soln->prereqs_filled[i] == tile_type_num_prereqs(ptype)
        && soln->worker_counts[i] < tile_type_num_tiles(ptype)) {
      real_print_tile_type(level, file, function, line,
                           tile_type_get(state, i), "  ");
    }
  }
}
 
#endif /* CM_DEBUG */
 
#ifdef GATHER_TIME_STATS
/************************************************************************/
static void print_performance(struct one_perf *counts)
{
  double s, ms;
  double q;
  int queries, applies;
 
  s = timer_read_seconds(counts->wall_timer);
  ms = 1000.0 * s;
 
  queries = counts->query_count;
  q = queries;
 
  applies = counts->apply_count;
 
  log_base(LOG_TIME_STATS,
           "CM-%s: overall=%fs queries=%d %fms / query, %d applies",
           counts->name, s, queries, ms / q, applies);
}
#endif /* GATHER_TIME_STATS */
 
/************************************************************************/
void cm_print_city(const struct city *pcity)
{
  struct tile *pcenter = city_tile(pcity);
  const struct civ_map *nmap = &(wld.map);
 
  log_test("cm_print_city(city %d=\"%s\")", pcity->id, city_name_get(pcity));
  log_test("  size=%d, specialists=%s",
           city_size_get(pcity), specialists_string(pcity->specialists));
 
  log_test("  workers at:");
  city_tile_iterate_index(nmap, city_map_radius_sq_get(pcity), pcenter, ptile,
                          cindex) {
    struct city *pwork = tile_worked(ptile);
 
    if (NULL != pwork && pwork == pcity) {
      int cx, cy;
 
      city_tile_index_to_xy(&cx, &cy, cindex,
                            city_map_radius_sq_get(pcity));
      log_test("    {%2d,%2d} (%4d,%4d)", cx, cy, TILE_XY(ptile));
    }
  } city_tile_iterate_index_end;
 
  log_test("  food    = %3d (%+3d)",
           pcity->prod[O_FOOD], pcity->surplus[O_FOOD]);
  log_test("  shield  = %3d (%+3d)",
           pcity->prod[O_SHIELD], pcity->surplus[O_SHIELD]);
  log_test("  trade   = %3d", pcity->surplus[O_TRADE]);
 
  log_test("  gold    = %3d (%+3d)",
           pcity->prod[O_GOLD], pcity->surplus[O_GOLD]);
  log_test("  luxury  = %3d", pcity->prod[O_LUXURY]);
  log_test("  science = %3d", pcity->prod[O_SCIENCE]);
}
 
/************************************************************************/
void cm_print_result(const struct cm_result *result)
{
  int *city_map_data = fc_calloc(city_map_tiles(result->city_radius_sq),
                                 sizeof(*city_map_data));
 
  log_test("cm_print_result(result=%p)", (void *) result);
  log_test("  found_a_valid=%d disorder=%d happy=%d",
           result->found_a_valid, result->disorder, result->happy);
 
  city_map_iterate(result->city_radius_sq, cindex, x, y) {
    if (is_free_worked_index(cindex)) {
      city_map_data[cindex] = 2;
    } else if (result->worker_positions[cindex]) {
      city_map_data[cindex] = 1;
    } else {
      city_map_data[cindex] = 0;
    }
  } city_map_iterate_end;
  log_test("workers map (2: free worked; 1: worker; 0: not used):");
  citylog_map_data(LOG_TEST, result->city_radius_sq, city_map_data);
  FC_FREE(city_map_data);
 
  log_test("  (workers/specialists) %d/%s", cm_result_workers(result),
           specialists_string(result->specialists));
 
  output_type_iterate(i) {
    log_test("  %10s surplus=%d", get_output_name(i), result->surplus[i]);
  } output_type_iterate_end;
}