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10/2/20

Root the Tree codechef lunchtime solution| codechef lunchtime problem editorial

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

Problem Statement->

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) such that it is possible to reach all vertices of the graph from r by moving along the directed edges.

You are given a directed tree with N vertices (numbered 1 through 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 denoting the number of test cases. The description of T test cases follows.
  • The first line of each test case contains a single integer N.
  • Each of the next N1 lines contains two space-separated integers u and v denoting that there is a directed edge from u to 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

  • 1N104
  • 1u,vN
  • the graph described on the input is a directed tree
  • the sum of N over all test cases does not exceed 105

Subtasks

Subtask #1 (20 points): for each edge, u=1 or 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 to vertex 2 and insert an edge from 3 to 1. Then, the graph becomes a rooted directed tree with vertex 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.

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 .

Root the Tree codechef lunchtime solution| codechef lunchtime problem editorial


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->


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