PAT 甲级 刷题日记|A 1013 Battle Over

单词积累

vitally 极其；紧要地；生死攸关地

题目

It is vitally important to have all the cities connected by highways in a war. If a city is occupied by the enemy, all the highways from/toward that city are closed. We must know immediately if we need to repair any other highways to keep the rest of the cities connected. Given the map of cities which have all the remaining highways marked, you are supposed to tell the number of highways need to be repaired, quickly.

For example, if we have 3 cities and 2 highways connecting cit y 1-cit y2 and city1-city3. Then if city1 is occupied by the enemy, we must have 1 highway repaired, that is the highway city2-city3.

Input Specification:

Each input file contains one test case. Each case starts with a line containing 3 numbers N (<1000), M and K, which are the total number of cities, the number of remaining highways, and the number of cities to be checked, respectively. Then M lines follow, each describes a highway by 2 integers, which are the numbers of the cities the highway connects. The cities are numbered from 1 to N. Finally there is a line containing K numbers, which represent the cities we concern.

Output Specification:

For each of the K cities, output in a line the number of highways need to be repaired if that city is lost.

Sample Input:

3 2 3
1 2
1 3
1 2 3
结尾无空行

Sample Output:

1
0
0
结尾无空行

思路

本质上就是求连通分量的个数。用并查集和dfs都可以。

代码

#include <bits/stdc++.h>
using namespace std;

const int maxn = 1005;
int n, m, k;
vector<vector<int>> gra;
int visit[maxn];

void dfs(int root) {
    visit[root] = 1;
    for (int i = 0; i < gra[root].size(); i++) {
        if (visit[gra[root][i]] == 0) {
            dfs(gra[root][i]);
        }
    }
}

int dfstra(int qu) {
    int times = 0;
    for (int i = 1; i <= n; i++) {
        if (i == qu) visit[i] = 1;
        else visit[i] = 0;
    }
    for (int i = 1; i <= n; i++) {
        if (visit[i] == 0) {
            times++;
            dfs(i);
        }
    }
    return times;
}

int main() {
    cin>>n>>m>>k;
    gra.resize(n+1);
    int a, b;
    for (int i = 0; i < m; i++) {
        cin>>a>>b;
        gra[a].push_back(b);
        gra[b].push_back(a);
        
    }
    int qu; 
    for (int i = 0 ; i < k; i++) {
        cin>>qu;
        cout<<dfstra(qu) - 1<<endl;
    } 
}