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61 lines
1.7 KiB
61 lines
1.7 KiB
/**
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* File: fractional_knapsack.c
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* Created Time: 2023-09-14
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* Author: xianii (xianyi.xia@outlook.com)
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*/
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#include "../utils/common.h"
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/* 物品 */
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typedef struct {
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int w; // 物品重量
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int v; // 物品價值
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} Item;
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/* 按照價值密度排序 */
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int sortByValueDensity(const void *a, const void *b) {
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Item *t1 = (Item *)a;
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Item *t2 = (Item *)b;
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return (float)(t1->v) / t1->w < (float)(t2->v) / t2->w;
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}
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/* 分數背包：貪婪 */
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float fractionalKnapsack(int wgt[], int val[], int itemCount, int cap) {
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// 建立物品串列，包含兩個屬性：重量、價值
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Item *items = malloc(sizeof(Item) * itemCount);
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for (int i = 0; i < itemCount; i++) {
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items[i] = (Item){.w = wgt[i], .v = val[i]};
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}
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// 按照單位價值 item.v / item.w 從高到低進行排序
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qsort(items, (size_t)itemCount, sizeof(Item), sortByValueDensity);
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// 迴圈貪婪選擇
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float res = 0.0;
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for (int i = 0; i < itemCount; i++) {
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if (items[i].w <= cap) {
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// 若剩餘容量充足，則將當前物品整個裝進背包
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res += items[i].v;
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cap -= items[i].w;
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} else {
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// 若剩餘容量不足，則將當前物品的一部分裝進背包
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res += (float)cap / items[i].w * items[i].v;
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cap = 0;
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break;
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}
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}
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free(items);
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return res;
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}
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/* Driver Code */
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int main(void) {
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int wgt[] = {10, 20, 30, 40, 50};
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int val[] = {50, 120, 150, 210, 240};
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int capacity = 50;
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// 貪婪演算法
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float res = fractionalKnapsack(wgt, val, sizeof(wgt) / sizeof(int), capacity);
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printf("不超過背包容量的最大物品價值為 %0.2f\n", res);
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return 0;
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}
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