Line data    Source code

       1             : /*-------------------------------------------------------------------------
       2             :  *
       3             :  * knapsack.c
       4             :  *    Knapsack problem solver
       5             :  *
       6             :  * Given input vectors of integral item weights (must be >= 0) and values
       7             :  * (double >= 0), compute the set of items which produces the greatest total
       8             :  * value without exceeding a specified total weight; each item is included at
       9             :  * most once (this is the 0/1 knapsack problem).  Weight 0 items will always be
      10             :  * included.
      11             :  *
      12             :  * The performance of this algorithm is pseudo-polynomial, O(nW) where W is the
      13             :  * weight limit.  To use with non-integral weights or approximate solutions,
      14             :  * the caller should pre-scale the input weights to a suitable range.  This
      15             :  * allows approximate solutions in polynomial time (the general case of the
      16             :  * exact problem is NP-hard).
      17             :  *
      18             :  * Copyright (c) 2017-2026, PostgreSQL Global Development Group
      19             :  *
      20             :  * IDENTIFICATION
      21             :  *    src/backend/lib/knapsack.c
      22             :  *
      23             :  *-------------------------------------------------------------------------
      24             :  */
      25             : #include "postgres.h"
      26             : 
      27             : #include <limits.h>
      28             : 
      29             : #include "lib/knapsack.h"
      30             : #include "nodes/bitmapset.h"
      31             : #include "utils/memutils.h"
      32             : 
      33             : /*
      34             :  * DiscreteKnapsack
      35             :  *
      36             :  * The item_values input is optional; if omitted, all the items are assumed to
      37             :  * have value 1.
      38             :  *
      39             :  * Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for
      40             :  * inclusion in the solution.
      41             :  *
      42             :  * This uses the usual dynamic-programming algorithm, adapted to reuse the
      43             :  * memory on each pass (by working from larger weights to smaller).  At the
      44             :  * start of pass number i, the values[w] array contains the largest value
      45             :  * computed with total weight <= w, using only items with indices < i; and
      46             :  * sets[w] contains the bitmap of items actually used for that value.  (The
      47             :  * bitmapsets are all pre-initialized with an unused high bit so that memory
      48             :  * allocation is done only once.)
      49             :  */
      50             : Bitmapset *
      51         492 : DiscreteKnapsack(int max_weight, int num_items,
      52             :                  int *item_weights, double *item_values)
      53             : {
      54         492 :     MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
      55             :                                                     "Knapsack",
      56             :                                                     ALLOCSET_SMALL_SIZES);
      57         492 :     MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
      58             :     double     *values;
      59             :     Bitmapset **sets;
      60             :     Bitmapset  *result;
      61             :     int         i,
      62             :                 j;
      63             : 
      64             :     Assert(max_weight >= 0);
      65             :     Assert(num_items > 0 && item_weights);
      66             : 
      67         492 :     values = palloc((1 + max_weight) * sizeof(double));
      68         492 :     sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
      69             : 
      70       25944 :     for (i = 0; i <= max_weight; ++i)
      71             :     {
      72       25452 :         values[i] = 0;
      73       25452 :         sets[i] = bms_make_singleton(num_items);
      74             :     }
      75             : 
      76        1248 :     for (i = 0; i < num_items; ++i)
      77             :     {
      78         756 :         int         iw = item_weights[i];
      79         756 :         double      iv = item_values ? item_values[i] : 1;
      80             : 
      81       49368 :         for (j = max_weight; j >= iw; --j)
      82             :         {
      83       48612 :             int         ow = j - iw;
      84             : 
      85       48612 :             if (values[j] <= values[ow] + iv)
      86             :             {
      87             :                 /* copy sets[ow] to sets[j] without realloc */
      88       48612 :                 if (j != ow)
      89       13482 :                     sets[j] = bms_replace_members(sets[j], sets[ow]);
      90             : 
      91       48612 :                 sets[j] = bms_add_member(sets[j], i);
      92             : 
      93       48612 :                 values[j] = values[ow] + iv;
      94             :             }
      95             :         }
      96             :     }
      97             : 
      98         492 :     MemoryContextSwitchTo(oldctx);
      99             : 
     100         492 :     result = bms_del_member(bms_copy(sets[max_weight]), num_items);
     101             : 
     102         492 :     MemoryContextDelete(local_ctx);
     103             : 
     104         492 :     return result;
     105             : }