Age Owner Branch data 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) 2017-2026, 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 *
3275 rhodiumtoad@postgres 51 :CBC 249 : DiscreteKnapsack(int max_weight, int num_items,
52 : : int *item_weights, double *item_values)
53 : : {
54 : 249 : MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
55 : : "Knapsack",
56 : : ALLOCSET_SMALL_SIZES);
57 : 249 : MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
58 : : double *values;
59 : : Bitmapset **sets;
60 : : Bitmapset *result;
61 : : int i,
62 : : j;
63 : :
64 [ - + ]: 249 : Assert(max_weight >= 0);
65 [ + - - + ]: 249 : Assert(num_items > 0 && item_weights);
66 : :
67 : 249 : values = palloc((1 + max_weight) * sizeof(double));
68 : 249 : sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
69 : :
70 [ + + ]: 13098 : for (i = 0; i <= max_weight; ++i)
71 : : {
72 : 12849 : values[i] = 0;
73 : 12849 : sets[i] = bms_make_singleton(num_items);
74 : : }
75 : :
76 [ + + ]: 630 : for (i = 0; i < num_items; ++i)
77 : : {
78 : 381 : int iw = item_weights[i];
79 [ - + ]: 381 : double iv = item_values ? item_values[i] : 1;
80 : :
81 [ + + ]: 24810 : for (j = max_weight; j >= iw; --j)
82 : : {
83 : 24429 : int ow = j - iw;
84 : :
85 [ + - ]: 24429 : if (values[j] <= values[ow] + iv)
86 : : {
87 : : /* copy sets[ow] to sets[j] without realloc */
88 [ + + ]: 24429 : if (j != ow)
786 drowley@postgresql.o 89 : 6741 : sets[j] = bms_replace_members(sets[j], sets[ow]);
90 : :
3275 rhodiumtoad@postgres 91 : 24429 : sets[j] = bms_add_member(sets[j], i);
92 : :
93 : 24429 : values[j] = values[ow] + iv;
94 : : }
95 : : }
96 : : }
97 : :
98 : 249 : MemoryContextSwitchTo(oldctx);
99 : :
100 : 249 : result = bms_del_member(bms_copy(sets[max_weight]), num_items);
101 : :
102 : 249 : MemoryContextDelete(local_ctx);
103 : :
104 : 249 : return result;
105 : : }
|
