/*-------------------------------------------------------------------------

 *

 * knapsack.c

 *    Knapsack problem solver

 *

 * Given input vectors of integral item weights (must be >= 0) and values

 * (double >= 0), compute the set of items which produces the greatest total

 * value without exceeding a specified total weight; each item is included at

 * most once (this is the 0/1 knapsack problem).  Weight 0 items will always be

 * included.

 *

 * The performance of this algorithm is pseudo-polynomial, O(nW) where W is the

 * weight limit.  To use with non-integral weights or approximate solutions,

 * the caller should pre-scale the input weights to a suitable range.  This

 * allows approximate solutions in polynomial time (the general case of the

 * exact problem is NP-hard).

 *

 * Copyright (c) 2017-2025, PostgreSQL Global Development Group

 *

 * IDENTIFICATION

 *    src/backend/lib/knapsack.c

 *

 *-------------------------------------------------------------------------

 */

#include "postgres.h"

#include <math.h>

#include <limits.h>

#include "lib/knapsack.h"

#include "nodes/bitmapset.h"

#include "utils/memutils.h"

/*

 * DiscreteKnapsack

 *

 * The item_values input is optional; if omitted, all the items are assumed to

 * have value 1.

 *

 * Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for

 * inclusion in the solution.

 *

 * This uses the usual dynamic-programming algorithm, adapted to reuse the

 * memory on each pass (by working from larger weights to smaller).  At the

 * start of pass number i, the values[w] array contains the largest value

 * computed with total weight <= w, using only items with indices < i; and

 * sets[w] contains the bitmap of items actually used for that value.  (The

 * bitmapsets are all pre-initialized with an unused high bit so that memory

 * allocation is done only once.)

 */

Bitmapset *

DiscreteKnapsack(int max_weight, int num_items,

         int *item_weights, double *item_values)

{

  MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,

                          "Knapsack",

                          ALLOCSET_SMALL_SIZES);

  MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);

  double     *values;

  Bitmapset **sets;

  Bitmapset  *result;

  int     i,

        j;

  Assert(max_weight >= 0);

  Assert(num_items > 0 && item_weights);

  values = palloc((1 + max_weight) * sizeof(double));

  sets = palloc((1 + max_weight) * sizeof(Bitmapset *));

  for (i = 0; i <= max_weight; ++i)

  {

    values[i] = 0;

    sets[i] = bms_make_singleton(num_items);

  }

  for (i = 0; i < num_items; ++i)

  {

    int     iw = item_weights[i];

    double    iv = item_values ? item_values[i] : 1;

    for (j = max_weight; j >= iw; --j)

    {

      int     ow = j - iw;

      if (values[j] <= values[ow] + iv)

      {

        /* copy sets[ow] to sets[j] without realloc */

        if (j != ow)

          sets[j] = bms_replace_members(sets[j], sets[ow]);

        sets[j] = bms_add_member(sets[j], i);

        values[j] = values[ow] + iv;

      }

    }

  }

  MemoryContextSwitchTo(oldctx);

  result = bms_del_member(bms_copy(sets[max_weight]), num_items);

  MemoryContextDelete(local_ctx);

  return result;

}