题目链接：51nod_1086

解题思路：多重背包+二进制优化

AC代码

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <queue>
#include <map>
#include <stack>
#include <vector>
#include <utility>
using namespace std;

const int maxn = (int)1e2+10;

int dp[50010],n,V;
int cost[maxn],value[maxn],amount[maxn];

inline int Max (int a,int b) {
	return a>b?a:b;
}

void ZeroOnePack (int cost, int value) {
	for (int i = V; i >= cost; i--) {
		dp[i] = Max(dp[i], dp[i-cost]+value);
	}
}

void CompletePack (int cost, int value) {
	for (int i = cost; i <= V; i++) {
		dp[i] = Max(dp[i], dp[i-cost]+value);
	}
}

void MultiplePack (int cost, int value, int amount) {
	if(V <= amount*cost) {
		CompletePack(cost,value);
		return ;
	}
	int k = 1;
	while (k < amount) {
		ZeroOnePack(k*cost,k*value);
		amount -= k;
		k<<=1;
	}
	ZeroOnePack(amount*cost,amount*value);
	return ;
}

int main() {
	int T;
	scanf("%d%d", &n, &V);
	for (int i = 0; i < n; i++) {
		scanf("%d%d%d", &cost[i], &value[i], &amount[i]);
	}
	memset(dp,0,sizeof(dp));
	for (int i = 0; i < n; i++) {
		MultiplePack(cost[i],value[i],amount[i]);
	}
	printf("%d\n",dp[V]);
	return 0;
}