Graph Theory
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 1220 Accepted Submission(s): 553
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.
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.
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
3212241 1 2
Sample Output
YesNoNo
Source
Recommend
jiangzijing2015
这道题首先因为个人英语水平有限,多次读题没有明白题目样例,以为进行1操作,是要和前面所有的边进行连线,倘若这样想的话,显然只有2个点1条边的情况符合,因为后面只要出现了1操作,就会出现那个点被多条边覆盖。
但是我们想错了,题目说的并不是这样,进行1操作,可以在前面出现的点里添加一条边(可以不添加),显然,前面如果没有出现2,那么1则和2没有什么区别。同时因为题目要求找的是可能出现的完美匹配,因此,1操作变成了,和前面出现操作2的点连边。题目豁然开朗,以下贴上代码。
#include <iostream>
#include <cstdio>
#include <string.h>
#include <math.h>
using namespace std;
int main(){
int t, n, cnt, x;
scanf("%d", &t);
while(t--){
scanf("%d", &n);
cnt = 1;
for(int i = 1; i < n; i++){
scanf("%d", &x);
if(cnt == 0)
cnt++;
else{
if(x == 1)
cnt--;
else
cnt++;
}
}
if(cnt != 0)
puts("No");
else
puts("Yes");
}
return 0;
}