85 lines
2.1 KiB
C
85 lines
2.1 KiB
C
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdbool.h>
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#define MAX_N 100
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#define MAX_C 100
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// 定义结构体以存储背包问题的相关数据
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typedef struct {
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int N; // 物体的个数
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int C; // 背包的容量
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int weight[MAX_N]; // 每个物体的重量
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int value[MAX_N]; // 每个物体的价值
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int DP[MAX_N][MAX_C]; // 动态规划表
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} Bag;
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void bag01NoRec(Bag* bag) {
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// 初始化 DP 表
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for (int j = 0; j <= bag->C; j++) {
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bag->DP[0][j] = 0;
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}
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// 填充 DP 表
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for (int i = 1; i <= bag->N; i++) {
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for (int j = 0; j <= bag->C; j++) {
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if (j >= bag->weight[i]) { // 如果容量为 j 的背包能够放下第 i 个物体
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bag->DP[i][j] = (bag->DP[i - 1][j - bag->weight[i]] + bag->value[i] > bag->DP[i - 1][j]) ?
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(bag->DP[i - 1][j - bag->weight[i]] + bag->value[i]) : bag->DP[i - 1][j];
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} else {
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// 物体放不下，仅选择不放该物体
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bag->DP[i][j] = bag->DP[i - 1][j];
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}
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}
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}
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// 打印 DP 表
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for (int i = 0; i <= bag->N; i++) {
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for (int j = 0; j <= bag->C; j++) {
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printf("%d ", bag->DP[i][j]);
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}
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printf("\n");
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}
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}
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void printResult(Bag* bag, int n, int v) {
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bool isAdd[MAX_N] = {false};
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for (int i = n; i >= 1; i--) {
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if (bag->DP[i][v] == bag->DP[i - 1][v])
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isAdd[i] = false;
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else {
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isAdd[i] = true;
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v -= bag->weight[i];
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}
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}
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for (int i = 1; i <= n; i++) {
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printf("%d号 %s; ", i, isAdd[i] ? "放" : "不放");
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}
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printf("\n");
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}
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// 使用 init2 函数初始化，并测试背包算法
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void init2(Bag* bag) {
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bag->C = 6;
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bag->weight[1] = 3;
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bag->weight[2] = 2;
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bag->weight[3] = 6;
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bag->weight[4] = 5;
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bag->weight[5] = 4;
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bag->value[1] = 30;
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bag->value[2] = 60;
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bag->value[3] = 50;
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bag->value[4] = 40;
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bag->value[5] = 60;
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bag->N = 5;
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bag01NoRec(bag);
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printResult(bag, bag->N, bag->C);
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}
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int main() {
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Bag bag;
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init2(&bag);
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return 0;
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}
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