Graph Theory HDU - 6029 留着练英语
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, ..., nn}. You have to consider every vertice from left to right (i.e. from vertice 2 to nn). At vertice ii, 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−1i−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.
Let the set of vertices be {1, 2, 3, ..., nn}. You have to consider every vertice from left to right (i.e. from vertice 2 to nn). At vertice ii, 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−1i−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.
InputThe first line of the input contains an integer T(1≤T≤50)T(1≤T≤50), denoting the number of test cases.
In each test case, there is an integer n(2≤n≤100000)n(2≤n≤100000) in the first line, denoting the number of vertices of the graph.
The following line contains n−1n−1 integers a2,a3,...,an(1≤ai≤2)a2,a3,...,an(1≤ai≤2), denoting the decision on each vertice.OutputFor 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
Graph Theory
HDU - 6029
#include<iostream> #include<cstdio> #include<cstring> #include<string> #include<algorithm> #include<cmath> #include<utility> #include<set> #include<vector> #include<map> #include<queue> #include<stack> #define maxn 110 #define INF 0x3f3f3f3f #define LL long long #define ULL unsigned long long #define E 1e-8 #define mod 100000000 using namespace std; #define raf(i,k,n) for(int i=k;i<=n;i++) //Oo0Oooo00ooOoo00oO int a[100005]; int main() { int t,n,i,j,s,flag; cin>>t; while(t--) { memset(a,0,sizeof(a)); s=0,flag=1; cin>>n; for(i=1; i<n; i++) cin>>a[i]; if(n%2!=0){cout<<"No"<<endl; continue;} for(i=n-1; i>=0; i--) { if(a[i]==1) s++; else { s--; if ( s < 0 ) {flag=0;break;} } } if(flag) cout<<"Yes"<<endl; else cout<<"No"<<endl; } }