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 :
// 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 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 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# 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 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. ?> |
<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> |
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