Graph Theory
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others) Total Submission(s): 0 Accepted Submission(s): 0
Problem Description Little Q loves playing with different kinds of graphs very much. One day he thought about an interesting category of graphs called “Cool Graph”, which are generated in the following way: Let the set of vertices be {1, 2, 3, …, n}. You have to consider every vertice from left to right (i.e. from vertice 2 to n). At vertice i, you must make one of the following two decisions: (1) Add edges between this vertex and all the previous vertices (i.e. from vertex 1 to i−1). (2) Not add any edge between this vertex and any of the previous vertices. In the mathematical discipline of graph theory, a matching in a graph is a set of edges without common vertices. A perfect matching is a matching that each vertice is covered by an edge in the set. Now Little Q is interested in checking whether a ”Cool Graph” has perfect matching. Please write a program to help him.
Input The first line of the input contains an integer T(1≤T≤50), denoting the number of test cases. In each test case, there is an integer n(2≤n≤100000) in the first line, denoting the number of vertices of the graph. The following line contains n−1 integers a2,a3,…,an(1≤ai≤2), denoting the decision on each vertice.
Output For each test case, output a string in the first line. If the graph has perfect matching, output ”Yes”, otherwise output ”No”.
Sample Input 3 2 1 2 2 4 1 1 2
Sample Output Yes No No
#include<iostream> #include<cstring> #include<algorithm> #include<cstdio> #include<string> #include<iomanip> #include<cmath> #define ll long long int #define maxsize 105000 #define INF 99999999 using namespace std; int a[maxsize]; int main() { int t;int n; while (cin >> t) { while (t--) { int sum = 0; cin >> n;int flag = 0; for (int i = 2;i <= n;i++) { cin >> a[i]; if (a[i] == 1) { if (sum<i-1) { sum += 2; } } } if (n % 2) { cout << "No" << endl; } else { if (sum == n) cout << "Yes" << endl; else cout << "No" << endl; } } } return 0; }