107 lines
3.0 KiB
C
107 lines
3.0 KiB
C
/*-------------------------------------------------------------------------
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*
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* knapsack.c
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* Knapsack problem solver
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*
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* Given input vectors of integral item weights (must be >= 0) and values
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* (double >= 0), compute the set of items which produces the greatest total
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* value without exceeding a specified total weight; each item is included at
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* most once (this is the 0/1 knapsack problem). Weight 0 items will always be
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* included.
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*
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* The performance of this algorithm is pseudo-polynomial, O(nW) where W is the
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* weight limit. To use with non-integral weights or approximate solutions,
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* the caller should pre-scale the input weights to a suitable range. This
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* allows approximate solutions in polynomial time (the general case of the
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* exact problem is NP-hard).
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*
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* Copyright (c) 2017-2024, PostgreSQL Global Development Group
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*
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* IDENTIFICATION
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* src/backend/lib/knapsack.c
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*
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*-------------------------------------------------------------------------
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*/
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#include "postgres.h"
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#include <math.h>
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#include <limits.h>
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#include "lib/knapsack.h"
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#include "nodes/bitmapset.h"
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#include "utils/memutils.h"
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/*
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* DiscreteKnapsack
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*
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* The item_values input is optional; if omitted, all the items are assumed to
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* have value 1.
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*
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* Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for
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* inclusion in the solution.
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*
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* This uses the usual dynamic-programming algorithm, adapted to reuse the
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* memory on each pass (by working from larger weights to smaller). At the
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* start of pass number i, the values[w] array contains the largest value
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* computed with total weight <= w, using only items with indices < i; and
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* sets[w] contains the bitmap of items actually used for that value. (The
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* bitmapsets are all pre-initialized with an unused high bit so that memory
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* allocation is done only once.)
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*/
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Bitmapset *
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DiscreteKnapsack(int max_weight, int num_items,
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int *item_weights, double *item_values)
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{
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MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
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"Knapsack",
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ALLOCSET_SMALL_SIZES);
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MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
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double *values;
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Bitmapset **sets;
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Bitmapset *result;
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int i,
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j;
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Assert(max_weight >= 0);
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Assert(num_items > 0 && item_weights);
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values = palloc((1 + max_weight) * sizeof(double));
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sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
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for (i = 0; i <= max_weight; ++i)
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{
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values[i] = 0;
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sets[i] = bms_make_singleton(num_items);
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}
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for (i = 0; i < num_items; ++i)
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{
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int iw = item_weights[i];
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double iv = item_values ? item_values[i] : 1;
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for (j = max_weight; j >= iw; --j)
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{
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int ow = j - iw;
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if (values[j] <= values[ow] + iv)
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{
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/* copy sets[ow] to sets[j] without realloc */
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if (j != ow)
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sets[j] = bms_replace_members(sets[j], sets[ow]);
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sets[j] = bms_add_member(sets[j], i);
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values[j] = values[ow] + iv;
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}
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}
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}
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MemoryContextSwitchTo(oldctx);
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result = bms_del_member(bms_copy(sets[max_weight]), num_items);
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MemoryContextDelete(local_ctx);
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return result;
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}
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