1122 Hamiltonian Cycle

The "Hamilton cycle problem" is to find a simple cycle that contains every vertex in a graph. Such a cycle is called a "Hamiltonian cycle".

In this problem, you are supposed to tell if a given cycle is a Hamiltonian cycle.

Input Specification:

Each input file contains one test case. For each case, the first line contains 2 positive integers N (2), the number of vertices, and M, the number of edges in an undirected graph. Then M lines follow, each describes an edge in the format Vertex1 Vertex2, where the vertices are numbered from 1 to N. The next line gives a positive integer K which is the number of queries, followed by K lines of queries, each in the format:

n V​1​​ V​2​​ ... V​n​​

where n is the number of vertices in the list, and V​i​​'s are the vertices on a path.

Output Specification:

For each query, print in a line YES if the path does form a Hamiltonian cycle, or NO if not.

Sample Input:

6 10
6 2
3 4
1 5
2 5
3 1
4 1
1 6
6 3
1 2
4 5
6
7 5 1 4 3 6 2 5
6 5 1 4 3 6 2
9 6 2 1 6 3 4 5 2 6
4 1 2 5 1
7 6 1 3 4 5 2 6
7 6 1 2 5 4 3 1

 

Sample Output:

YES
NO
NO
NO
YES
NO

题意：

　　给出一个图，判断所给的节点是不是哈密尔顿路径。

思路：

　　1. 首先判断所给的路径是不是连通。

　　2. 判断是不是给出了图中的全部结点。

　　3. 判断路径的起点和终点是不是相同。

Code：

#include <bits/stdc++.h>

using namespace std;

int main() {
    int n, m, k;
    cin >> n >> m;
    vector<vector<int> > grap(n + 1, vector<int>(n + 1, 0));
    int v1, v2;
    for (int i = 0; i < m; ++i) {
        cin >> v1 >> v2;
        grap[v1][v2] = 1;
        grap[v2][v1] = 1;
    }
    cin >> k;
    int num;
    set<int> s;
    bool isHamiltonianCycle;
    for (int i = 0; i < k; ++i) {
        cin >> num;
        vector<int> v(num);
        s.clear();
        isHamiltonianCycle = true;
        for (int j = 0; j < num; ++j) {
            cin >> v[j];
            s.insert(v[j]);
        }
        if (num != n + 1 || s.size() != n)
            isHamiltonianCycle = false;
        else {
            for (int j = 1; j < num; ++j) {
                if (grap[v[j]][v[j - 1]] == 0) {
                    isHamiltonianCycle = false;
                    break;
                }
            }
        }
        if (v[0] != v[num - 1]) isHamiltonianCycle = false;
        if (isHamiltonianCycle)
            cout << "YES" << endl;
        else
            cout << "NO" << endl;
    }
    return 0;
}