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POJ1149 PIGS 【最大流】

2024-07-25 07:11:42   226人阅读

PIGS
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 16555 Accepted: 7416

Description

Mirko works on a pig farm that consists of M locked pig-houses and Mirko can‘t unlock any pighouse because he doesn‘t have the keys. Customers come to the farm one after another. Each of them has keys to some pig-houses and wants to buy a certain number of pigs. 
All data concerning customers planning to visit the farm on that particular day are available to Mirko early in the morning so that he can make a sales-plan in order to maximize the number of pigs sold. 
More precisely, the procedure is as following: the customer arrives, opens all pig-houses to which he has the key, Mirko sells a certain number of pigs from all the unlocked pig-houses to him, and, if Mirko wants, he can redistribute the remaining pigs across the unlocked pig-houses. 
An unlimited number of pigs can be placed in every pig-house. 
Write a program that will find the maximum number of pigs that he can sell on that day.

Input

The first line of input contains two integers M and N, 1 <= M <= 1000, 1 <= N <= 100, number of pighouses and number of customers. Pig houses are numbered from 1 to M and customers are numbered from 1 to N. 
The next line contains M integeres, for each pig-house initial number of pigs. The number of pigs in each pig-house is greater or equal to 0 and less or equal to 1000. 
The next N lines contains records about the customers in the following form ( record about the i-th customer is written in the (i+2)-th line): 
A K1 K2 ... KA B It means that this customer has key to the pig-houses marked with the numbers K1, K2, ..., KA (sorted nondecreasingly ) and that he wants to buy B pigs. Numbers A and B can be equal to 0.

Output

The first and only line of the output should contain the number of sold pigs.

Sample Input

3 3
3 1 10
2 1 2 2
2 1 3 3
1 2 6

Sample Output

7

Source

Croatia OI 2002 Final Exam - First day

题目大意
 Mirko养着一些猪 猪关在一些猪圈里面 猪圈是锁着的
他自己没有钥匙（汗）
 只有要来买猪的顾客才有钥匙
 顾客依次来 每个顾客会用他的钥匙打开一些猪圈 买
走一些猪 然后锁上
 在锁上之前 Mirko有机会重新分配这几个已打开猪圈
的猪
 现在给出一开始每个猪圈的猪数 每个顾客所有的钥匙
和要买走的猪数 问Mirko最多能卖掉几头猪

题解：对于每个猪圈的第一个购买的人，添加一条源点到这个人的边，权为这个猪圈的猪数，对于后来的且想要购买该猪圈的人，添加一条第一个购买该猪圈的人到该人的边，权为inf，然后添加每个人到汇点一条边，权值为该人想要购买的猪的头数。至此，构图完成。


#include <stdio.h>
#include <string.h>
#define inf 0x3fffffff
#define maxn 110
#define maxm 1002

int pig[maxm], m, n, sink;
int G[maxn][maxn], queue[maxn];
bool vis[maxn]; int Layer[maxn];

bool countLayer() {
    memset(Layer, 0, sizeof(Layer));
    int id = 0, front = 0, now, i; 
    Layer[0] = 1; queue[id++] = 0;
    while(front < id) {
        now = queue[front++];
        for(i = 0; i <= sink; ++i)
            if(G[now][i] && !Layer[i]) {
                Layer[i] = Layer[now] + 1;
                if(i == sink) return true;
                else queue[id++] = i;
            }
    }
    return false;
}

int Dinic() {
    int minCut, pos, maxFlow = 0;
    int i, id = 0, u, v, now;
    while(countLayer()) {
        memset(vis, 0, sizeof(vis));
        vis[0] = 1; queue[id++] = 0;
        while(id) {
            now = queue[id - 1];
            if(now == sink) {
                minCut = inf;
                for(i = 1; i < id; ++i) {
                    u = queue[i - 1];
                    v = queue[i];
                    if(G[u][v] < minCut) {
                        minCut = G[u][v];
                        pos = u;
                    }
                }
                maxFlow += minCut;
                for(i = 1; i < id; ++i) {
                    u = queue[i - 1];
                    v = queue[i];
                    G[u][v] -= minCut;
                    G[v][u] += minCut;
                }
                while(queue[id - 1] != pos)
                    vis[queue[--id]] = 0;
            } else {
                for(i = 0; i <= sink; ++i) {
                    if(G[now][i] && Layer[now] + 1 == Layer[i] && !vis[i]) {
                        vis[i] = 1; queue[id++] = i; break;
                    }
                }
                if(i > sink) --id;
            }
        }
    }
    return maxFlow;
}

int main() {
    //freopen("stdin.txt", "r", stdin);
    int i, keys, num;
    while(scanf("%d%d", &m, &n) == 2) {
        sink = n + 1;
        for(i = 1; i <= m; ++i)
            scanf("%d", &pig[i]);
        memset(G, 0, sizeof(G));
        for(i = 1; i <= n; ++i) {
            scanf("%d", &keys);
            while(keys--) {
                scanf("%d", &num);
                if(pig[num] >= 0) {
                    G[0][i] += pig[num]; // 0 is source
                    pig[num] = -i; // 这里是标记第num个猪圈联通的第一个人
                } else G[-pig[num]][i] = inf;
            }
            scanf("%d", &G[i][sink]);
        }
        printf("%d\n", Dinic());
    }
    return 0;
}


POJ1149 PIGS 【最大流】


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