POJ3624Charm Bracelet（01背包）

最新推荐文章于 2019-08-06 15:11:09 发布

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最新推荐文章于 2019-08-06 15:11:09 发布

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分类专栏： ACM_动态规划系列

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本文介绍了一个经典的背包问题求解案例，通过使用动态规划算法，在给定的重量限制下选择最佳魅力值组合。文章详细展示了如何定义问题、初始化数据结构、执行动态规划过程，并最终输出最大魅力值。

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Charm Bracelet

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15375		Accepted: 7013

Description

Bessie has gone to the mall's jewelry store and spies a charm bracelet. Of course, she'd like to fill it with the best charms possible from the N (1 ≤ N ≤ 3,402) available charms. Each charm i in the supplied list has a weight W_i (1 ≤ W_i ≤ 400), a 'desirability' factor D_i (1 ≤ D_i ≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more than M (1 ≤ M ≤ 12,880).

Given that weight limit as a constraint and a list of the charms with their weights and desirability rating, deduce the maximum possible sum of ratings.

Input

* Line 1: Two space-separated integers: N and M
* Lines 2..N+1: Line i+1 describes charm i with two space-separated integers: W_i and D_i

Output

* Line 1: A single integer that is the greatest sum of charm desirabilities that can be achieved given the weight constraints

Sample Input

Sample Output

23
此题用二维数组很可能超内存，需要用一维数组求解，因为定义个全局变量n有在主函数里面定义个局部变量n，以为是逻辑错误，调试了近两个小时。。。
其实这个程序w[i]和v[i]数组都可以用两个变量代替，详见刘汝佳算法经典入门。。。
//date 2013.4.9 POJ 3624	Accepted	300K	282MS	C++	897B
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 3500;
const int maxm = 13000;
int w[maxn], v[maxn];
int f[maxm];//数组开小runtime error！
int weight;
int n;
using namespace std;

void DP() {
    for(int i = 1; i <= n; i++) {
        for(int j = weight; j >= w[i]; j--) {
            f[j] = max(f[j], f[j-w[i]]+v[i]);
        }
    }
}

void init() {
    memset(f, 0, sizeof(f));
    memset(v, 0, sizeof(v));
    memset(w, 0, sizeof(w));
}

int main()
{
    //int n;   注意局部变量可以隐藏全局变量，一个多小时的代价！
    while(scanf("%d%d", &n, &weight) != EOF) {
        for(int i = 1; i <= n; i++) {
            cin >> w[i];
            cin >> v[i];
        }
        DP();
        cout <<  f[weight] << endl;
        init();
    }
    return 0;
}
/*********************
TEST：
4 6
1 4
2 6
3 12
2 7
****************/