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Remove all outgoing edges except edge with minimum weight

Last Updated : 13 Dec, 2022
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Given a directed graph having n nodes. For each node, delete all the outgoing edges except the outgoing edge with minimum weight. Apply this deletion operation for every node and then print the final graph remaining where each node of the graph has at most one outgoing edge and that too with minimum weight.

Note: Here, the graph is stored as Adjacency Matrix for ease.

Examples :

Input : Adjacency Matrix of input graph :
  | 1  2  3  4
---------------
1 | 0  3  2  5
2 | 0  2  4  7  
3 | 1  2  0  3
4 | 5  2  1  3

Output : Adjacency Matrix of output graph :
  | 1  2  3  4
---------------
1 | 0  0  2  0
2 | 0  2  0  0  
3 | 1  0  0  0
4 | 0  0  1  0

For every row of the adjacency matrix of the graph keep the minimum element (except zero) and make the rest of all zero. Do this for every row of the input matrix. Finally, print the resultant Matrix.

Example :

C++




// CPP program for minimizing graph
#include <bits/stdc++.h>
 
using namespace std;
 
// Utility function for
// finding min of a row
int minFn(int arr[])
{
    int min = INT_MAX;
 
    for (int i = 0; i < 4; i++)
        if (min > arr[i])
            min = arr[i];
    return min;
}
 
// Utility function for minimizing graph
void minimizeGraph(int arr[][4])
{
    int min;
 
    // Set empty edges to INT_MAX
    for (int i = 0; i < 4; i++)
        for (int j = 0; j < 4; j++)
            if (arr[i][j] == 0)
                arr[i][j] = INT_MAX;
 
    // Finding minimum of each row
    // and deleting rest of edges
    for (int i = 0; i < 4; i++) {
 
        // Find minimum element of row
        min = minFn(arr[i]);
 
        for (int j = 0; j < 4; j++) {
            // If edge value is not min
            // set it to zero, also
            // edge value INT_MAX denotes that
            // initially edge value was zero
            if (!(arr[i][j] == min) || (arr[i][j] == INT_MAX))
                arr[i][j] = 0;
            else
                min = 0;
        }
    }
 
    // Print result;
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < 4; j++)
            cout << arr[i][j] << " ";
        cout << "\n";
    }
}
 
// Driver Program
int main()
{
    // Input Graph
    int arr[4][4] = { 1, 2, 4, 0,
                      0, 0, 0, 5,
                      0, 2, 0, 3,
                      0, 0, 0, 0 };
 
    minimizeGraph(arr);
 
    return 0;
}


Java




// Java program for
// minimizing graph
import java.io.*;
import java.util.*;
import java.lang.*;
 
class GFG {
 
    // Utility function for
    // finding min of a row
    static int minFn(int arr[])
    {
        int min = Integer.MAX_VALUE;
 
        for (int i = 0;
             i < arr.length; i++)
            if (min > arr[i])
                min = arr[i];
        return min;
    }
 
    // Utility function
    // for minimizing graph
    static void minimizeGraph(int arr[][])
    {
        int min;
 
        // Set empty edges
        // to INT_MAX
        for (int i = 0;
             i < arr.length; i++)
            for (int j = 0;
                 j < arr.length; j++)
                if (arr[i][j] == 0)
                    arr[i][j] = Integer.MAX_VALUE;
 
        // Finding minimum of each
        // row and deleting rest
        // of edges
        for (int i = 0;
             i < arr.length; i++) {
 
            // Find minimum
            // element of row
            min = minFn(arr[i]);
 
            for (int j = 0;
                 j < arr.length; j++) {
                // If edge value is not
                // min set it to zero,
                // also edge value INT_MAX
                // denotes that initially
                // edge value was zero
                if ((arr[i][j] != min) || (arr[i][j] == Integer.MAX_VALUE))
                    arr[i][j] = 0;
                else
                    min = 0;
            }
        }
 
        // Print result;
        for (int i = 0;
             i < arr.length; i++) {
            for (int j = 0;
                 j < arr.length; j++)
                System.out.print(arr[i][j] + " ");
            System.out.print("\n");
        }
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Input Graph
        int arr[][] = { { 1, 2, 4, 0 },
                        { 0, 0, 0, 5 },
                        { 0, 2, 0, 3 },
                        { 0, 0, 0, 0 } };
 
        minimizeGraph(arr);
    }
}


Python3




# Python3 program for minimizing graph
 
# Utility function for finding min of a row
def minFn(arr):
 
    minimum = float('inf')
     
    for i in range(0, len(arr)):
        if minimum > arr[i]:
            minimum = arr[i]
    return minimum
 
# Utility function for minimizing graph
def minimizeGraph(arr):
 
    # Set empty edges to INT_MAX
    n=len(arr)
    for i in range(0, n):
        for j in range(0, n):
            if arr[i][j] == 0:
                arr[i][j] = float('inf')
 
    # Finding minimum of each row
    # and deleting rest of edges
    for i in range(0, n):
         
        # Find minimum element of row
        minimum = minFn(arr[i])
         
        for j in range(0, n):
             
            # If edge value is not min
            # set it to zero, also
            # edge value INT_MAX denotes that
            # initially edge value was zero
            if ((not(arr[i][j] == minimum)) or
                    (arr[i][j] == float('inf'))):
                arr[i][j] = 0
            else:
                minimum = 0
         
    # Print result
    for i in range(0, n):
        for j in range(0, n):
            print(arr[i][j], end = " ")
        print()
 
# Driver Code
if __name__ == "__main__":
     
    # Input Graph
    arr = [[1, 2, 4, 0],
           [0, 0, 0, 5],
           [0, 2, 0, 3],
           [0, 0, 0, 0]]
     
    minimizeGraph(arr)
     
# This code is contributed by
# Rituraj Jain


C#




// C# program for
// minimizing graph
using System;
 
class GFG {
 
    // Utility function for
    // finding min of a row
    static int minFn(int[] arr)
    {
        int min = int.MaxValue;
 
        for (int i = 0;
             i < arr.Length; i++)
            if (min > arr[i])
                min = arr[i];
        return min;
    }
 
    // Utility function
    // for minimizing graph
    static void minimizeGraph(int[, ] arr)
    {
        int min;
 
        // Set empty edges
        // to INT_MAX
        for (int i = 0;
             i < arr.GetLength(0); i++)
            for (int j = 0;
                 j < arr.GetLength(1); j++)
                if (arr[i, j] == 0)
                    arr[i, j] = int.MaxValue;
 
        // Finding minimum of each
        // row and deleting rest
        // of edges
        for (int i = 0; i < arr.GetLength(0); i++) {
 
            // Find minimum
            // element of row
            min = minFn(GetRow(arr, i));
 
            for (int j = 0;
                 j < arr.GetLength(1); j++) {
                // If edge value is not
                // min set it to zero,
                // also edge value INT_MAX
                // denotes that initially
                // edge value was zero
                if ((arr[i, j] != min) || (arr[i, j] == int.MaxValue))
                    arr[i, j] = 0;
                else
                    min = 0;
            }
        }
 
        // Print result;
        for (int i = 0;
             i < arr.GetLength(0); i++) {
            for (int j = 0;
                 j < arr.GetLength(1); j++)
                Console.Write(arr[i, j] + " ");
            Console.Write("\n");
        }
    }
 
    public static int[] GetRow(int[, ] matrix, int row)
    {
        var rowLength = matrix.GetLength(1);
        var rowVector = new int[rowLength];
 
        for (var i = 0; i < rowLength; i++)
            rowVector[i] = matrix[row, i];
 
        return rowVector;
    }
 
    // Driver Code
    public static void Main(String[] args)
    {
        // Input Graph
        int[, ] arr = { { 1, 2, 4, 0 },
                        { 0, 0, 0, 5 },
                        { 0, 2, 0, 3 },
                        { 0, 0, 0, 0 } };
 
        minimizeGraph(arr);
    }
}
 
// This code contributed by Rajput-Ji


PHP




<?php
// PHP program for minimizing graph
 
// Utility function for finding
// min of a row
function minFn($arr)
{
    $min = PHP_INT_MAX;
     
    for ($i = 0; $i < 4; $i++)
        if ($min > $arr[$i])
            $min = $arr[$i];
    return $min;
}
 
// Utility function for minimizing graph
function minimizeGraph($arr)
{
    $min;
     
    // Set empty edges to INT_MAX
    for ($i = 0; $i < 4; $i++)
        for ($j = 0; $j < 4; $j++)
            if ($arr[$i][$j] == 0)
                $arr[$i][$j] = PHP_INT_MAX;
 
    // Finding minimum of each row
    // and deleting rest of edges
    for ($i = 0; $i < 4; $i++)
    {
         
        // Find minimum element of row
        $min = minFn($arr[$i]);
         
        for ($j = 0; $j < 4; $j++)
        {
            // If edge value is not min
            // set it to zero, also
            // edge value INT_MAX denotes that
            // initially edge value was zero
            if (!($arr[$i][$j] == $min) ||
                 ($arr[$i][$j] == PHP_INT_MAX))
                $arr[$i][$j] = 0;
            else
                $min = 0;
        }
    }
     
    // Print result;
    for ($i = 0; $i < 4; $i++)
    {
        for ($j = 0; $j < 4; $j++)
            echo $arr[$i][$j], " ";
        echo "\n";
    }
}
 
// Driver Code
 
// Input Graph
$arr = array(array(1, 2, 4, 0),
             array(0, 0, 0, 5),
             array(0, 2, 0, 3),
             array(0, 0, 0, 0));
 
minimizeGraph($arr);
 
// This code is contributed by ajit.
?>


Javascript




<script>
 
// Javascript program for minimizing graph
 
// Utility function for
// finding min of a row
function minFn(arr)
{
    var min = 1000000000;
 
    for (var i = 0; i < 4; i++)
        if (min > arr[i])
            min = arr[i];
    return min;
}
 
// Utility function for minimizing graph
function minimizeGraph(arr)
{
    var min;
 
    // Set empty edges to INT_MAX
    for (var i = 0; i < 4; i++)
        for (var j = 0; j < 4; j++)
            if (arr[i][j] == 0)
                arr[i][j] = 1000000000;
 
    // Finding minimum of each row
    // and deleting rest of edges
    for (var i = 0; i < 4; i++) {
 
        // Find minimum element of row
        min = minFn(arr[i]);
 
        for (var j = 0; j < 4; j++) {
            // If edge value is not min
            // set it to zero, also
            // edge value INT_MAX denotes that
            // initially edge value was zero
            if (!(arr[i][j] == min) || (arr[i][j] == 1000000000))
                arr[i][j] = 0;
            else
                min = 0;
        }
    }
 
    // Print result;
    for (var i = 0; i < 4; i++) {
        for (var j = 0; j < 4; j++)
            document.write( arr[i][j] + " ");
        document.write( "<br>");
    }
}
 
// Driver Program
// Input Graph
var arr = [ [1, 2, 4, 0],
                  [0, 0, 0, 5],
                  [0, 2, 0, 3],
                  [0, 0, 0, 0 ]];
minimizeGraph(arr);
 
// This code is contributed by noob2000.
</script>


Output

1 0 0 0 
0 0 0 5 
0 2 0 0 
0 0 0 0 

Time Complexity: O(n^2) 
Auxiliary Space: O(1) as it is using constant space for variables, and space for input adjacency matrix is not considered



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