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}<b_{i}<=n $ ) 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
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3
3
1 2
3 4
1 4
样例输出 #1
2
1
0
样例 #2
样例输入 #2
5 7
1 5 1
2 5 1
3 5 1
4 5 1
1 2 2
2 3 2
3 4 2
5
1 5
5 1
2 5
1 5
1 4
样例输出 #2
1
1
1
1
2
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
#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
#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;
}