CF505B Mr. Kitayuta‘s Colorful Graph

Mr. Kitayuta's Colorful Graph

题面翻译

给出一个 n n n 个点， m m m 条边的无向图，每条边上是有颜色的。有 q q q 组询问

对于第 i i i 组询问，给出点对 u i , v i u_i,v_i ui,vi。求有多少种颜色 c c c 满足：有至少一条 u i u_i ui 到 v i v_i vi 路径，满足该路径上的所有边的颜色都为 c c c

输入格式

第一行两个整数 n , m n,m n,m 分别表示点的个数和边的个数

接下来 m m m 行，每行三个整数 x i , y i , c i x_i,y_i,c_i xi,yi,ci，表示有一条连接点 x i , y i x_i,y_i xi,yi 的边，且该边的颜色为 c i c_i ci

接下来一行一个整数 q q q，表示询问的个数

接下来 q q q 行，每行两个整数 u i , v i u_i,v_i ui,vi，表示一组询问

输出格式

对于每一组询问，在单独的一行输出一个整数，表示满足上述要求的颜色种数

说明与提示

2 ≤ n ≤ 100 2 \le n \le 100 2≤n≤100
1 ≤ m , q ≤ 100 1 \le m,q \le 100 1≤m,q≤100
1 ≤ x i , y i , u i , v i ≤ n 1\le x_i,y_i,u_i,v_i \le n 1≤xi,yi,ui,vi≤n
1 ≤ c i ≤ m 1 \le c_i \le m 1≤ci≤m

感谢 @_Wolverine 提供的翻译

题目描述

Mr. Kitayuta has just bought an undirected graph consisting of $n$ vertices and $m$ edges. The vertices of the graph are numbered from 1 to $n$ . Each edge, namely edge $i$ , has a color $c_{i}$ , connecting vertex $a_{i}$ and $b_{i}$ .

Mr. Kitayuta wants you to process the following $q$ queries.

In the $i$ -th query, he gives you two integers --- $u_{i}$ and $v_{i}$ .

Find the number of the colors that satisfy the following condition: the edges of that color connect vertex $u_{i}$ and vertex $v_{i}$ directly or indirectly.

输入格式

The first line of the input contains space-separated two integers --- $n$ and $m$ ( $2\<=n\<=100,1\<=m\<=100$ ), denoting the number of the vertices and the number of the edges, respectively.

The next $m$ lines contain space-separated three integers --- $a_{i}$ , $b_{i}$ ( $1\<=a_{i}\ ) and c_{i} ( 1\<=c_{i}\<=m ). Note that there can be multiple edges between two vertices. However, there are no multiple edges of the same color between two vertices, that is, if i≠j , (a_{i},b_{i},c_{i})≠(a_{j},b_{j},c_{j}) .$

The next line contains a integer --- $q$ ( $1\<=q\<=100$ ), denoting the number of the queries.

Then follows $q$ lines, containing space-separated two integers --- $u_{i}$ and $v_{i}$ ( $1\<=u_{i},v_{i}\<=n$ ). It is guaranteed that $u_{i}≠v_{i}$ .

输出格式

For each query, print the answer in a separate line.

样例 #1

样例输入 #1

复制代码

样例输出 #1

复制代码

2
1
0

样例 #2

样例输入 #2

复制代码

样例输出 #2

复制代码

提示

Let's consider the first sample.

The figure above shows the first sample. - Vertex $1$ and vertex $2$ are connected by color $1$ and $2$ .

Vertex $3$ and vertex $4$ are connected by color $3$ .
Vertex $1$ and vertex $4$ are not connected by any single color.

思路

（1）并查集

一个二维并查集，一个记录颜色，一个记录点。

（2）Floyed

普通Floyed加一维颜色。数据只有100四维循环不会T。

AC code

（1）并查集

cpp 复制代码

#include<bits/stdc++.h>

using namespace std;

int fa[1000][1000];
int n, m, t;

int find(int x, int i) 
{
	if (fa[x][i] == x) return x;
	return fa[x][i] = find(fa[x][i], i); 
}

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= m; j++)
			fa[i][j] = i; 
	for (int i = 1; i <= m; ++i)
	{
		int u, v, z;
		cin >> u >> v >> z;
		fa[find(u, z)][z] = find(v,z); 
	}
	
	cin >> t;
	while (t--)
	{
		int u, v, ans = 0;
		cin >> u >> v;
		for(int i = 1; i <= m;i++)
			if (find(u,i) == find(v,i)) ans++; 
		cout << ans << endl;
	}
	return 0;
}

（2）Floyed

cpp 复制代码

#include<bits/stdc++.h>

using namespace std;

int a[101][101][101];

int main()
{
	int n, m;
	cin >> n >> m;
	for(int i = 1; i <= m; i++)
	{
		int u, v, q;
		cin >> u >> v >> q;
		a[u][v][q] = 1;
		a[v][u][q] = 1;
	}
	for (int k = 1; k <= n; k++)
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++)
				for (int c = 1; c <= m; c++)
					if (a[i][k][c] == 1 && a[k][j][c] == 1)
						a[i][j][c] = 1;
	int q;
	cin >> q;
	for (int i = 1; i <= q; i++)
	{
		int u, v;
		cin >> u >> v;
		int sum = 0;
		for(int j = 1; j <= m; j++)
			if(a[u][v][j] == 1)
				sum++;
		cout << sum << endl;
	}
	return 0;
}