Isomorphic Trees

★★★★★

3 votes

Algorithms, Graphs, Medium, Minimum Cost Maximum Flow

Details

Problem

You are given two trees. You are allowed to perform an operation several times: attaching a new vertex connect to an existing vertex of a tree. For each vertex A of the first tree and vertex B of second tree, we root the first tree at A and the second tree at B then your task is to find the minimum number of operations needed to make two trees isomorphic.

(Two rooted trees are isomorphic if they are the same size $N$ , and there is a permutation $P$ of $\{1, 2, \dots, N\}$ such that P["root of the first tree"] = "root of the second tree" and there is an edge between $u, v$ in the first tree iff there is an edge between $P[u], P[v]$ in the second tree.)

Input Format

The first line contains two space-separated integers $N, M$ denoting the number of vertices of two trees.

Each of $N - 1$ next lines contains two space-separated integers $u, v$ denoting an edge $(u, v)$ of the first tree.

Each of $M - 1$ next lines contains two space-separated integers $u, v$ denoting an edge $(u, v)$ of the second tree.

Output Format

Output $N$ lines, each line contains $M$ space-separated integers. $j$ -th number in the $i$ -th line contains the answer if we root the first tree at vertex $i$ and the second tree at vertex $j$ .

Constraints

$1 \le N, M \le 50$ .

Sample Input

Sample Output

1 3 3 3
3 1 1 1
3 1 1 1

Time Limit: 3

Memory Limit: 256

Source Limit:

Explanation

First tree:

Second tree:

If we root the first tree at vertex $1$ and the second tree at vertex $1$ , then we must attach a new vertex to vertex $1$ in the first tree to make two trees isomorphic. The cost is $1$ .
If we root the first tree at vertex $1$ and the second tree at vertex $2$ , then we must attach two new vertcies to vertex $2$ or $3$ in the first tree and attach a new vertex to vertex $2$ in the second tree to make two trees isomorphic. The cost is $3$ .

Contributers:

Trung Nguyen

Lewin Gan