TLA  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) 2017-2023, PostgreSQL Global Development Group
      19                 :  *
      20                 :  * IDENTIFICATION
      21                 :  *    src/backend/lib/knapsack.c
      22                 :  *
      23                 :  *-------------------------------------------------------------------------
      24                 :  */
      25                 : #include "postgres.h"
      26                 : 
      27                 : #include <math.h>
      28                 : #include <limits.h>
      29                 : 
      30                 : #include "lib/knapsack.h"
      31                 : #include "miscadmin.h"
      32                 : #include "nodes/bitmapset.h"
      33                 : #include "utils/builtins.h"
      34                 : #include "utils/memutils.h"
      35                 : 
      36                 : /*
      37                 :  * DiscreteKnapsack
      38                 :  *
      39                 :  * The item_values input is optional; if omitted, all the items are assumed to
      40                 :  * have value 1.
      41                 :  *
      42                 :  * Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for
      43                 :  * inclusion in the solution.
      44                 :  *
      45                 :  * This uses the usual dynamic-programming algorithm, adapted to reuse the
      46                 :  * memory on each pass (by working from larger weights to smaller).  At the
      47                 :  * start of pass number i, the values[w] array contains the largest value
      48                 :  * computed with total weight <= w, using only items with indices < i; and
      49                 :  * sets[w] contains the bitmap of items actually used for that value.  (The
      50                 :  * bitmapsets are all pre-initialized with an unused high bit so that memory
      51                 :  * allocation is done only once.)
      52                 :  */
      53                 : Bitmapset *
      54 CBC         198 : DiscreteKnapsack(int max_weight, int num_items,
      55                 :                  int *item_weights, double *item_values)
      56                 : {
      57             198 :     MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
      58                 :                                                     "Knapsack",
      59                 :                                                     ALLOCSET_SMALL_SIZES);
      60             198 :     MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
      61                 :     double     *values;
      62                 :     Bitmapset **sets;
      63                 :     Bitmapset  *result;
      64                 :     int         i,
      65                 :                 j;
      66                 : 
      67             198 :     Assert(max_weight >= 0);
      68             198 :     Assert(num_items > 0 && item_weights);
      69                 : 
      70             198 :     values = palloc((1 + max_weight) * sizeof(double));
      71             198 :     sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
      72                 : 
      73           10476 :     for (i = 0; i <= max_weight; ++i)
      74                 :     {
      75           10278 :         values[i] = 0;
      76           10278 :         sets[i] = bms_make_singleton(num_items);
      77                 :     }
      78                 : 
      79             504 :     for (i = 0; i < num_items; ++i)
      80                 :     {
      81             306 :         int         iw = item_weights[i];
      82             306 :         double      iv = item_values ? item_values[i] : 1;
      83                 : 
      84           18969 :         for (j = max_weight; j >= iw; --j)
      85                 :         {
      86           18663 :             int         ow = j - iw;
      87                 : 
      88           18663 :             if (values[j] <= values[ow] + iv)
      89                 :             {
      90                 :                 /* copy sets[ow] to sets[j] without realloc */
      91           18663 :                 if (j != ow)
      92                 :                 {
      93            6450 :                     sets[j] = bms_del_members(sets[j], sets[j]);
      94            6450 :                     sets[j] = bms_add_members(sets[j], sets[ow]);
      95                 :                 }
      96                 : 
      97           18663 :                 sets[j] = bms_add_member(sets[j], i);
      98                 : 
      99           18663 :                 values[j] = values[ow] + iv;
     100                 :             }
     101                 :         }
     102                 :     }
     103                 : 
     104             198 :     MemoryContextSwitchTo(oldctx);
     105                 : 
     106             198 :     result = bms_del_member(bms_copy(sets[max_weight]), num_items);
     107                 : 
     108             198 :     MemoryContextDelete(local_ctx);
     109                 : 
     110             198 :     return result;
     111                 : }