回溯0-1背包

#include<stdio.h>
#include<stdlib.h> 
#include<math.h>
#include<string.h>

int curval;
int curcap;
int maxval;
int bagcap;
char *ans;
char *maxans;
int n;
//每件物品的属性 
typedef struct object {
	int n;
	int val;
	int cap;
}object;

object *objects;

int comp(const void *_a, const void *_b) {
	object a = *(object *)_a;
	object b = *(object *)_b;
	double x = (double)a.val / a.cap;
	double y = (double)b.val / b.cap;
	if (y > x) {
		return 1;
	} else {
		return -1;
	}
}
//算出如果选择当前的物品所能获得的最大价值 
double bound(int cur) {
	int tempcap = curcap;
	double tempval = curval;
	while (cur < n && tempcap + objects[cur].cap < bagcap) {
		tempcap += objects[cur].cap;
		tempval += objects[cur].val;
		++cur;
	}
	if (cur < n) {
		tempval += (bagcap - tempcap) * ((double)objects[cur].val / objects[cur].cap);
	}
	return tempval;
}
//回溯依次做选择再利用bound函数做剪枝操作 
void dfs(int cur) {
	if (cur >= n) {
		if (curval > maxval) {
			strcpy(maxans, ans);
			maxval = curval;
		}
		return;
	}
	if (objects[cur].cap + curcap > bagcap) {
		if (curval > maxval) {
			strcpy(maxans, ans);
			maxval = curval;
		}
		dfs(cur + 1);
		return;
	}
	if (bound(cur) > maxval) {
		curval += objects[cur].val;
		curcap += objects[cur].cap;
		ans[objects[cur].n - 1] = '1';
		dfs(cur + 1);
		curval -= objects[cur].val;
		curcap -= objects[cur].cap;
	}
	ans[objects[cur].n - 1] = '0';
	dfs(cur + 1);
}
//输出所做的选择 
void show() {
	printf("\n"); 
	for (int i = 0; i < strlen(maxans); ++i) {
		if (maxans[i] == '1') {
			printf("选择了第%d件物品\n", i + 1);
		}
	} 
	printf("所获得的最大价值为%d", maxval);
}

int main() {
	curval = 0;
	curcap = 0;
	maxval = 0;
	printf("请输入数量");
	scanf("%d", &n);
	objects = (object*)malloc(sizeof(object) * n);
	ans = (char*)malloc(sizeof(char) * (n + 1));
	maxans = (char*)malloc(sizeof(char) * (n + 1));
	memset(ans, '0', sizeof(ans));
	memset(maxans, '0', sizeof(maxans));
	ans[n] = '\0';
	maxans[n] = '\0';
	for (int i = 0; i < n; ++i) { 
		objects[i].n = i + 1;
		printf("请输入第%d件物品的价值", i + 1);
		scanf("%d", &objects[i].val);
		printf("请输入第%d件物品的容量", i + 1);
		scanf("%d", &objects[i].cap);
	}
	printf("请输入背包的容量");
	scanf("%d", &bagcap); 
	qsort(objects, n, sizeof(object), comp);
	dfs(0);
	show();
	return 0;
}