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Find count of pair of nodes at even distance

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Given a connected acyclic graph with N nodes and N-1 edges, find out the pair of nodes that are at even distance from each other.

Examples: 

Input:
3
1 2 
2 3
Output: 1
Explanation:
    1
   /
  2
 /
3
Input:
5
1 2
2 3
1 4
4 5
Output: 4

Approach:  

  • Assume a graph is having 6 levels (0 to 5) level 0, 2, 4 are at even distance but level 1, 3, 5 are also at even distance as their difference is 2 which is even so we have to take care of both the conditions i.e count both levels even and odd.
  • The given problem can be solved by performing dfs traversal
  • Choose any source node as root and perform dfs traversal and maintain the visited 
    array for performing dfs and dist array to calculate distance from the root
  • now traverse the distance array and keep count of even level and odd level
  • Calculate total as ((even_count * (even_count-1)) + (odd_count * (odd_count-1))/2

Below is the implementation of above approach:  

C++




// C++ program to find
// the count of nodes
// at even distance
#include <bits/stdc++.h>
using namespace std;
 
// Dfs function to find count of nodes at
// even distance
void dfs(vector<int> graph[], int node, int dist[],
                                    bool vis[], int c)
{
    if (vis[node]) {
        return;
    }
    // Set flag as true for current
    // node in visited array
    vis[node] = true;
 
    // Insert the distance in
    // dist array for current
    // visited node u
    dist[node] = c;
 
    for (int i = 0; i < graph[node].size(); i++) {
        // If its neighbours are not vis,
        // run dfs for them
        if (!vis[graph[node][i]]) {
            dfs(graph, graph[node][i], dist, vis, c + 1);
        }
    }
}
 
int countOfNodes(vector<int> graph[], int n)
{
    // bool array to
    // mark visited nodes
    bool vis[n + 1] = { false };
 
    // Integer array to
    // compute distance
    int dist[n + 1] = { 0 };
 
    dfs(graph, 1, dist, vis, 0);
 
    int even = 0, odd = 0;
 
    // Traverse the distance array
    // and count the even and odd levels
    for (int i = 1; i <= n; i++) {
        if (dist[i] % 2 == 0) {
            even++;
        }
        else {
            odd++;
        }
    }
 
    int ans = ((even * (even - 1)) + (odd * (odd - 1))) / 2;
 
    return ans;
}
 
// Driver code
int main()
{
 
    int n = 5;
    vector<int> graph[n + 1] = { {},
                                 { 2 },
                                 { 1, 3 },
                                 { 2 } };
 
    int ans = countOfNodes(graph, n);
    cout << ans << endl;
 
    return 0;
}


Java




// Java program to find the count of
// nodes at even distance
import java.util.*;
 
class GFG
{
 
// Dfs function to find count of nodes at
// even distance
static void dfs(Vector<Integer> graph[],
                   int node, int dist[],
                   boolean vis[], int c)
{
    if (vis[node])
    {
        return;
    }
     
    // Set flag as true for current
    // node in visited array
    vis[node] = true;
 
    // Insert the distance in
    // dist array for current
    // visited node u
    dist[node] = c;
 
    for (int i = 0; i < graph[node].size(); i++)
    {
        // If its neighbours are not vis,
        // run dfs for them
        if (!vis[graph[node].get(i)])
        {
            dfs(graph, graph[node].get(i),
                        dist, vis, c + 1);
        }
    }
}
 
static int countOfNodes(Vector<Integer> graph[],
                                         int n)
{
    // bool array to
    // mark visited nodes
    boolean []vis = new boolean[n + 1];
 
    // Integer array to
    // compute distance
    int []dist = new int[n + 1];
 
    dfs(graph, 1, dist, vis, 0);
 
    int even = 0, odd = 0;
 
    // Traverse the distance array
    // and count the even and odd levels
    for (int i = 1; i <= n; i++)
    {
        if (dist[i] % 2 == 0)
        {
            even++;
        }
        else
        {
            odd++;
        }
    }
    int ans = ((even * (even - 1)) +
                (odd * (odd - 1))) / 2;
 
    return ans;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 5;
    Vector<Integer> []graph = new Vector[n + 1];
    for(int i = 0; i< n + 1; i++)
    {
        graph[i] = new Vector<Integer>();
    }
     
    graph[0] = new Vector<Integer>();
    graph[1] = new Vector(Arrays.asList(2));
    graph[2] = new Vector<Integer>(1, 3);
    graph[3] = new Vector<Integer>(2);
    int ans = countOfNodes(graph, n);
    System.out.println(ans);
}
}
 
// This code is contributed by 29AjayKumar


Python3




# Python3 program to find
# the count of nodes
# at even distance
 
# Dfs function to find count of
# nodes at even distance
def dfs(graph, node, dist, vis, c) :
 
    if (vis[node]) :
        return;
     
    # Set flag as true for current
    # node in visited array
    vis[node] = True;
 
    # Insert the distance in
    # dist array for current
    # visited node u
    dist[node] = c;
 
    for i in range(len(graph[node])) :
        # If its neighbours are not vis,
        # run dfs for them
        if (not vis[graph[node][i]]) :
            dfs(graph, graph[node][i],
                    dist, vis, c + 1);
 
def countOfNodes(graph, n) :
 
    # bool array to
    # mark visited nodes
    vis = [False] * (n + 1);
 
    # Integer array to
    # compute distance
    dist = [0] * (n + 1);
 
    dfs(graph, 1, dist, vis, 0);
 
    even = 0; odd = 0;
 
    # Traverse the distance array
    # and count the even and odd levels
    for i in range(1, n + 1) :
        if (dist[i] % 2 == 0) :
            even += 1;
     
        else :
            odd += 1;
 
    ans = ((even * (even - 1)) +
            (odd * (odd - 1))) // 2;
 
    return ans;
 
# Driver code
if __name__ == "__main__" :
 
    n = 5;
    graph = [[], [ 2 ], [ 1, 3 ], [ 2 ]];
 
    ans = countOfNodes(graph, n);
    print(ans);
 
# This code is contributed by kanugargng


C#




// C# program to find the count of
// nodes at even distance
using System;
using System.Collections.Generic;
     
class GFG
{
 
// Dfs function to find count of
// nodes at even distance
static void dfs(List<int> []graph,
                int node, int []dist,
                bool []vis, int c)
{
    if (vis[node])
    {
        return;
    }
     
    // Set flag as true for current
    // node in visited array
    vis[node] = true;
 
    // Insert the distance in
    // dist array for current
    // visited node u
    dist[node] = c;
 
    for (int i = 0; i < graph[node].Count; i++)
    {
        // If its neighbours are not vis,
        // run dfs for them
        if (!vis[graph[node][i]])
        {
            dfs(graph, graph[node][i],
                    dist, vis, c + 1);
        }
    }
}
 
static int countOfNodes(List<int> []graph,
                                    int n)
{
    // bool array to
    // mark visited nodes
    bool []vis = new bool[n + 1];
 
    // int array to
    // compute distance
    int []dist = new int[n + 1];
 
    dfs(graph, 1, dist, vis, 0);
 
    int even = 0, odd = 0;
 
    // Traverse the distance array
    // and count the even and odd levels
    for (int i = 1; i <= n; i++)
    {
        if (dist[i] % 2 == 0)
        {
            even++;
        }
        else
        {
            odd++;
        }
    }
    int ans = ((even * (even - 1)) +
                (odd * (odd - 1))) / 2;
 
    return ans;
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 5;
    List<int> []graph = new List<int>[n + 1];
    for(int i = 0; i< n + 1; i++)
    {
        graph[i] = new List<int>();
    }
     
    graph[0] = new List<int>{};
    graph[1] = new List<int>{2};
    graph[2] = new List<int>{1, 3};
    graph[3] = new List<int>{2};
    int ans = countOfNodes(graph, n);
    Console.WriteLine(ans);
}
}
 
// This code is contributed by Rajput-Ji


Javascript




<script>
 
// JavaScript program to find the count of
// nodes at even distance
     
// Dfs function to find count of
// nodes at even distance
function dfs(graph, node, dist, vis, c)
{
    if (vis[node])
    {
        return;
    }
     
    // Set flag as true for current
    // node in visited array
    vis[node] = true;
 
    // Insert the distance in
    // dist array for current
    // visited node u
    dist[node] = c;
 
    for (var i = 0; i < graph[node].length; i++)
    {
        // If its neighbours are not vis,
        // run dfs for them
        if (!vis[graph[node][i]])
        {
            dfs(graph, graph[node][i],
                    dist, vis, c + 1);
        }
    }
}
 
function countOfNodes(graph, n)
{
    // bool array to
    // mark visited nodes
    var vis = Array(n+1).fill(false);
 
    // int array to
    // compute distance
    var dist = Array(n+1).fill(0);
 
    dfs(graph, 1, dist, vis, 0);
 
    var even = 0, odd = 0;
 
    // Traverse the distance array
    // and count the even and odd levels
    for (var i = 1; i <= n; i++)
    {
        if (dist[i] % 2 == 0)
        {
            even++;
        }
        else
        {
            odd++;
        }
    }
    var ans = ((even * (even - 1)) +
                (odd * (odd - 1))) / 2;
 
    return ans;
}
 
// Driver code
var n = 5;
var graph = Array.from(Array(n+1), ()=>Array());
 
graph[1] = [2];
graph[2] = [1, 3];
graph[3] = [2];
var ans = countOfNodes(graph, n);
document.write(ans);
 
 
</script>


Output:  

6

Time Complexity: O(V+E)
 



Last Updated : 13 Sep, 2021
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