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) 2017-2024, 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 "nodes/bitmapset.h"
32 : : #include "utils/memutils.h"
33 : :
34 : : /*
35 : : * DiscreteKnapsack
36 : : *
37 : : * The item_values input is optional; if omitted, all the items are assumed to
38 : : * have value 1.
39 : : *
40 : : * Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for
41 : : * inclusion in the solution.
42 : : *
43 : : * This uses the usual dynamic-programming algorithm, adapted to reuse the
44 : : * memory on each pass (by working from larger weights to smaller). At the
45 : : * start of pass number i, the values[w] array contains the largest value
46 : : * computed with total weight <= w, using only items with indices < i; and
47 : : * sets[w] contains the bitmap of items actually used for that value. (The
48 : : * bitmapsets are all pre-initialized with an unused high bit so that memory
49 : : * allocation is done only once.)
50 : : */
51 : : Bitmapset *
2575 rhodiumtoad@postgres 52 :CBC 198 : DiscreteKnapsack(int max_weight, int num_items,
53 : : int *item_weights, double *item_values)
54 : : {
55 : 198 : MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
56 : : "Knapsack",
57 : : ALLOCSET_SMALL_SIZES);
58 : 198 : MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
59 : : double *values;
60 : : Bitmapset **sets;
61 : : Bitmapset *result;
62 : : int i,
63 : : j;
64 : :
65 [ - + ]: 198 : Assert(max_weight >= 0);
66 [ + - - + ]: 198 : Assert(num_items > 0 && item_weights);
67 : :
68 : 198 : values = palloc((1 + max_weight) * sizeof(double));
69 : 198 : sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
70 : :
71 [ + + ]: 10476 : for (i = 0; i <= max_weight; ++i)
72 : : {
73 : 10278 : values[i] = 0;
74 : 10278 : sets[i] = bms_make_singleton(num_items);
75 : : }
76 : :
77 [ + + ]: 504 : for (i = 0; i < num_items; ++i)
78 : : {
79 : 306 : int iw = item_weights[i];
80 [ - + ]: 306 : double iv = item_values ? item_values[i] : 1;
81 : :
82 [ + + ]: 18969 : for (j = max_weight; j >= iw; --j)
83 : : {
84 : 18663 : int ow = j - iw;
85 : :
86 [ + - ]: 18663 : if (values[j] <= values[ow] + iv)
87 : : {
88 : : /* copy sets[ow] to sets[j] without realloc */
89 [ + + ]: 18663 : if (j != ow)
86 drowley@postgresql.o 90 :GNC 6450 : sets[j] = bms_replace_members(sets[j], sets[ow]);
91 : :
2575 rhodiumtoad@postgres 92 :CBC 18663 : sets[j] = bms_add_member(sets[j], i);
93 : :
94 : 18663 : values[j] = values[ow] + iv;
95 : : }
96 : : }
97 : : }
98 : :
99 : 198 : MemoryContextSwitchTo(oldctx);
100 : :
101 : 198 : result = bms_del_member(bms_copy(sets[max_weight]), num_items);
102 : :
103 : 198 : MemoryContextDelete(local_ctx);
104 : :
105 : 198 : return result;
106 : : }
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