PostgreSQL Source Code  git master
knapsack.c
Go to the documentation of this file.
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) 2017-2019, 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 DiscreteKnapsack(int max_weight, int num_items,
55  int *item_weights, double *item_values)
56 {
58  "Knapsack",
60  MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
61  double *values;
62  Bitmapset **sets;
63  Bitmapset *result;
64  int i,
65  j;
66 
67  Assert(max_weight >= 0);
68  Assert(num_items > 0 && item_weights);
69 
70  values = palloc((1 + max_weight) * sizeof(double));
71  sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
72 
73  for (i = 0; i <= max_weight; ++i)
74  {
75  values[i] = 0;
76  sets[i] = bms_make_singleton(num_items);
77  }
78 
79  for (i = 0; i < num_items; ++i)
80  {
81  int iw = item_weights[i];
82  double iv = item_values ? item_values[i] : 1;
83 
84  for (j = max_weight; j >= iw; --j)
85  {
86  int ow = j - iw;
87 
88  if (values[j] <= values[ow] + iv)
89  {
90  /* copy sets[ow] to sets[j] without realloc */
91  if (j != ow)
92  {
93  sets[j] = bms_del_members(sets[j], sets[j]);
94  sets[j] = bms_add_members(sets[j], sets[ow]);
95  }
96 
97  sets[j] = bms_add_member(sets[j], i);
98 
99  values[j] = values[ow] + iv;
100  }
101  }
102  }
103 
104  MemoryContextSwitchTo(oldctx);
105 
106  result = bms_del_member(bms_copy(sets[max_weight]), num_items);
107 
108  MemoryContextDelete(local_ctx);
109 
110  return result;
111 }
void MemoryContextDelete(MemoryContext context)
Definition: mcxt.c:211
#define AllocSetContextCreate
Definition: memutils.h:170
Bitmapset * bms_copy(const Bitmapset *a)
Definition: bitmapset.c:74
#define ALLOCSET_SMALL_SIZES
Definition: memutils.h:202
static MemoryContext MemoryContextSwitchTo(MemoryContext context)
Definition: palloc.h:109
Bitmapset * bms_make_singleton(int x)
Definition: bitmapset.c:186
MemoryContext CurrentMemoryContext
Definition: mcxt.c:38
#define Assert(condition)
Definition: c.h:732
Bitmapset * bms_add_member(Bitmapset *a, int x)
Definition: bitmapset.c:736
Bitmapset * bms_del_members(Bitmapset *a, const Bitmapset *b)
Definition: bitmapset.c:928
static Datum values[MAXATTR]
Definition: bootstrap.c:167
void * palloc(Size size)
Definition: mcxt.c:949
int i
Bitmapset * bms_del_member(Bitmapset *a, int x)
Definition: bitmapset.c:773
Bitmapset * DiscreteKnapsack(int max_weight, int num_items, int *item_weights, double *item_values)
Definition: knapsack.c:54
Bitmapset * bms_add_members(Bitmapset *a, const Bitmapset *b)
Definition: bitmapset.c:793