Find the Maximum Value Permutation of a Graph in C++

In this problem, we are given a graph of N nodes. Our task is to Find the maximum possible value of the minimum value of the modified array.

For the graph we have a permutation of nodes which is the number of induces with minimum 1 node on the left of it sharing a common edge.

Let’s take an example to understand the problem,

Input : N = 4, edge = {{1, 2}, {2, 3}, {3, 4}, {4, 1}}
Output : 3

Solution Approach

A simple solution to the problem is by traversing the tree from one node visiting all its adjacent nodes. We will find the permutation of nodes using the formula of the number of nodes connected to it.

The formula is,

Size of component - 1.

Example

Program to illustrate the working of our solution

#include <bits/stdc++.h>
using namespace std;

int dfs(int x, vector<int> adjMat[], int visited[]){
   int sz = 1;
   visited[x] = 1;
   for (auto ch : adjMat[x])
      if (!visited[ch])
         sz += dfs(ch, adjMat, visited);
   return sz;
}
int maxValPermutationGraph(int n, vector<int> adjMat[]){
   int val = 0;
   int visited[n + 1] = { 0 };
   for (int i = 1; i <= n; i++)
      if (!visited[i])
         val += dfs(i, adjMat, visited) - 1;
   return val;
}
int main(){
   int n = 4;
   vector<int> adjMat[n + 1] = {{1, 2}, {2, 3}, {3, 4}, {4, 1}};
   cout<<"The maximum value permutation of a graph is "<<maxValPermutationGraph(n, adjMat);
   return 0;
}

Output

The maximum value permutation of a graph is 3