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POJ1422 Air Raid 【DAG最小路径覆盖】

2024-07-26 17:14:21   220人阅读

Air Raid
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 6763 Accepted: 4034

Description

Consider a town where all the streets are one-way and each street leads from one intersection to another. It is also known that starting from an intersection and walking through town‘s streets you can never reach the same intersection i.e. the town‘s streets form no cycles. 

With these assumptions your task is to write a program that finds the minimum number of paratroopers that can descend on the town and visit all the intersections of this town in such a way that more than one paratrooper visits no intersection. Each paratrooper lands at an intersection and can visit other intersections following the town streets. There are no restrictions about the starting intersection for each paratrooper. 

Input

Your program should read sets of data. The first line of the input file contains the number of the data sets. Each data set specifies the structure of a town and has the format: 

no_of_intersections 
no_of_streets 
S1 E1 
S2 E2 
...... 
Sno_of_streets Eno_of_streets 

The first line of each data set contains a positive integer no_of_intersections (greater than 0 and less or equal to 120), which is the number of intersections in the town. The second line contains a positive integer no_of_streets, which is the number of streets in the town. The next no_of_streets lines, one for each street in the town, are randomly ordered and represent the town‘s streets. The line corresponding to street k (k <= no_of_streets) consists of two positive integers, separated by one blank: Sk (1 <= Sk <= no_of_intersections) - the number of the intersection that is the start of the street, and Ek (1 <= Ek <= no_of_intersections) - the number of the intersection that is the end of the street. Intersections are represented by integers from 1 to no_of_intersections. 

There are no blank lines between consecutive sets of data. Input data are correct. 

Output

The result of the program is on standard output. For each input data set the program prints on a single line, starting from the beginning of the line, one integer: the minimum number of paratroopers required to visit all the intersections in the town. 

Sample Input

2
4
3
3 4
1 3
2 3
3
3
1 3
1 2
2 3

Sample Output

2
1

Source

Dhaka 2002

对于DAG，求最小路径覆盖有如下公式：最小路径覆盖数 = 节点数 - 对应的二分图最大匹配数。

用电脑自带的画图画了张草图，挫爆了 -_-!


题意：输入数据详解，t组数据，n个节点（从1开始），m条有向边，u到v。

题解：套公式。


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

const int maxn = 125;
int n, m;
int cx[maxn], cy[maxn];
bool visy[maxn], G[maxn][maxn];

void getMap() {
    memset(G, 0, sizeof(G));
    int u, v;
    scanf("%d%d", &n, &m);
    while(m--) {
        scanf("%d%d", &u, &v);
        G[u][v] = true;
    }
}

int findPath(int x) {
    int i;
    for(i = 1; i <= n; ++i) {
        if(G[x][i] && !visy[i]) {
            visy[i] = 1;
            if(cy[i] == -1 || findPath(cy[i])) {
                cy[i] = x; return 1;
            }
        }
    }
    return 0;
}

int MaxMatch() {
    int ans = 0, i;
    memset(cx, -1, sizeof(cx));
    memset(cy, -1, sizeof(cy));
    for(i = 1; i <= n; ++i) {
        memset(visy, 0, sizeof(visy));
        if(cx[i] == -1) ans += findPath(i);
    }
    return ans;
}

void solve() {
    printf("%d\n", n - MaxMatch());
}

int main() {
    // freopen("stdin.txt", "r", stdin);
    int t;
    scanf("%d", &t);
    while(t--) {
        getMap();
        solve();
    }
    return 0;
}


POJ1422 Air Raid 【DAG最小路径覆盖】


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