Root the Tree codechef lunchtime solution| codechef lunchtime problem editorial

 Root the Tree codechef lunchtime solution| codechef lunchtime problem editorial-

Problem Statement->

A directed tree is a directed graph such that if all edges were undirected, this graph would be a tree. A rooted directed tree is a directed tree in which there is one vertex (the root, let's denote it by r$r$) such that it is possible to reach all vertices of the graph from r$r$ by moving along the directed edges.

You are given a directed tree with N$N$ vertices (numbered 1$1$ through N$N$). You may perform the following operation on it any number of times (including zero):

• Choose some edge which currently exists in the graph.
• Remove this edge.
• Add a new edge in such a way that the graph becomes a directed tree again.

What is the smallest number of operations which need to be performed in order to make the directed tree rooted?

Input

• The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
• The first line of each test case contains a single integer N$N$.
• Each of the next N−1$N-1$ lines contains two space-separated integers u$u$ and v$v$ denoting that there is a directed edge from u$u$ to v$v$ in the tree.

Output

For each test case, print a single line containing one integer ― the smallest number of operations we need to perform to create a rooted directed tree.

Constraints

• 1≤N≤104$1\le N\le {10}^4$
• 1≤u,v≤N$1\le u,v\le N$
• the graph described on the input is a directed tree
• the sum of N$N$ over all test cases does not exceed 105${10}^5$

Subtasks

Subtask #1 (20 points): for each edge, u=1$u=1$ or v=1$v=1$ (the graph is a directed star)

Subtask #2 (80 points): original constraints

Example Input

2
3
1 2
3 2
3
1 2
2 3

Example Output

1
0

Explanation

Example case 1: We can delete the edge from vertex 3$3$ to vertex 2$2$ and insert an edge from 3$3$ to 1$1$. Then, the graph becomes a rooted directed tree with vertex 3$3$ as the root. However, there are many other possible solutions.

Example case 2: The graph is already a rooted directed tree; the root is vertex 1$1$.

Problem link-https://www.codechef.com/LTIME88B/problems/ROOTTREE

solution->

According to this problem we have given a graph and we have to convert this graph to a rooted directed tree means every node should have only one incoming edge and 1 outgoing edge.

 So my solution approach says that we will store the frequency of incoming edge of each vertex and 

if I found incoming edge frequency greater then 1 so will delete this edge and add to the new node so my final answer will increase by ans+=freq[i]-1;

after doing the same for all vertex I will get my final answer.

my code is mentioned below. Please check it .

wait there is no need of creating any 2D boolean array sorry for that so delete that part of code.

Root the Tree codechef lunchtime code solution->