82 lines
2.3 KiB
C
82 lines
2.3 KiB
C
/**
|
|
* File: unbounded_knapsack.c
|
|
* Created Time: 2023-10-02
|
|
* Author: Zuoxun (845242523@qq.com)
|
|
*/
|
|
|
|
#include "../utils/common.h"
|
|
|
|
/* Find maximum value */
|
|
int myMax(int a, int b) {
|
|
return a > b ? a : b;
|
|
}
|
|
|
|
/* Complete knapsack: Dynamic programming */
|
|
int unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {
|
|
int n = wgtSize;
|
|
// Initialize dp table
|
|
int **dp = malloc((n + 1) * sizeof(int *));
|
|
for (int i = 0; i <= n; i++) {
|
|
dp[i] = calloc(cap + 1, sizeof(int));
|
|
}
|
|
// State transition
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int c = 1; c <= cap; c++) {
|
|
if (wgt[i - 1] > c) {
|
|
// If exceeding the knapsack capacity, do not choose item i
|
|
dp[i][c] = dp[i - 1][c];
|
|
} else {
|
|
// The greater value between not choosing and choosing item i
|
|
dp[i][c] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
|
|
}
|
|
}
|
|
}
|
|
int res = dp[n][cap];
|
|
// Free memory
|
|
for (int i = 0; i <= n; i++) {
|
|
free(dp[i]);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
/* Complete knapsack: Space-optimized dynamic programming */
|
|
int unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {
|
|
int n = wgtSize;
|
|
// Initialize dp table
|
|
int *dp = calloc(cap + 1, sizeof(int));
|
|
// State transition
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int c = 1; c <= cap; c++) {
|
|
if (wgt[i - 1] > c) {
|
|
// If exceeding the knapsack capacity, do not choose item i
|
|
dp[c] = dp[c];
|
|
} else {
|
|
// The greater value between not choosing and choosing item i
|
|
dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
|
|
}
|
|
}
|
|
}
|
|
int res = dp[cap];
|
|
// Free memory
|
|
free(dp);
|
|
return res;
|
|
}
|
|
|
|
/* Driver code */
|
|
int main() {
|
|
int wgt[] = {1, 2, 3};
|
|
int val[] = {5, 11, 15};
|
|
int wgtSize = sizeof(wgt) / sizeof(wgt[0]);
|
|
int cap = 4;
|
|
|
|
// Dynamic programming
|
|
int res = unboundedKnapsackDP(wgt, val, cap, wgtSize);
|
|
printf("Maximum value of items without exceeding bag capacity = %d\n", res);
|
|
|
|
// Space-optimized dynamic programming
|
|
res = unboundedKnapsackDPComp(wgt, val, cap, wgtSize);
|
|
printf("Maximum value of items without exceeding bag capacity = %d\n", res);
|
|
|
|
return 0;
|
|
}
|