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Find smallest and largest element from square matrix diagonals
  • Last Updated : 12 Feb, 2021

Given a square matrix of order n*n, find the smallest and largest elements from both diagonals of the given matrix. 
Examples: 

Input : matrix = {
            {1, 2, 3, 4, -10},
            {5, 6, 7, 8, 6},
            {1, 2, 11, 3, 4},
            {5, 6, 70, 5, 8},
            {4, 9, 7, 1, 5}};
Output :
Principal Diagonal Smallest Element:  1
Principal Diagonal Greatest Element :11
Secondary Diagonal Smallest Element: -10
Secondary Diagonal Greatest Element: 11

The idea behind solving this problem is, First check traverse matrix and reach all diagonals element(for principle diagonal i == j and secondary diagonal i+j = size_of_matrix-1) and compare diagonal element with min and max variable and take new min and max values. and same thing for secondary diagonals.
Here is implementation of above approach: 
Example 1: With O(n^2) Complexity:  

C++




// CPP program to find smallest and
// largest elements of both diagonals
#include<bits/stdc++.h>
using namespace std;
 
// Function to find smallest and largest element
// from principal and secondary diagonal
void diagonalsMinMax(int mat[5][5])
{
    // take length of matrix
    int n = sizeof(*mat) / 4;
    if (n == 0)
        return;
 
    // declare and initialize variables
    // with appropriate value
    int principalMin = mat[0][0],
        principalMax = mat[0][0];
    int secondaryMin = mat[n - 1][0],
        secondaryMax = mat[n - 1][0];
 
    for (int i = 1; i < n; i++)
    {
        for (int j = 1; j < n; j++)
        {
 
            // Condition for principal
            // diagonal
            if (i == j)
            {
 
                // take new smallest value
                if (mat[i][j] < principalMin)
                {
                    principalMin = mat[i][j];
                }
 
                // take new largest value
                if (mat[i][j] > principalMax)
                {
                    principalMax = mat[i][j];
                }
            }
 
            // Condition for secondary
            // diagonal
            if ((i + j) == (n - 1))
            {
 
                // take new smallest value
                if (mat[i][j] < secondaryMin)
                {
                    secondaryMin = mat[i][j];
                }
 
                // take new largest value
                if (mat[i][j] > secondaryMax)
                {
                    secondaryMax = mat[i][j];
                }
            }
        }
    }
 
    cout << ("Principal Diagonal Smallest Element: ")
        << principalMin << endl;
    cout << ("Principal Diagonal Greatest Element : ")
        << principalMax << endl;
 
    cout << ("Secondary Diagonal Smallest Element: ")
        << secondaryMin << endl;
    cout << ("Secondary Diagonal Greatest Element: ")
        << secondaryMax << endl;
}
 
// Driver code
int main()
{
    // Declare and initialize 5X5 matrix
    int matrix[5][5] = {{ 1, 2, 3, 4, -10 },
                        { 5, 6, 7, 8, 6 },
                        { 1, 2, 11, 3, 4 },
                        { 5, 6, 70, 5, 8 },
                        { 4, 9, 7, 1, -5 }};
    diagonalsMinMax(matrix);
}
 
// This code is contribuuted by
// Shashank_Sharma


Java




// Java program to find
// smallest and largest elements of both diagonals
 
public class GFG {
    // Function to find smallest and largest element from
    // principal and secondary diagonal
    static void diagonalsMinMax(int[][] mat)
    {
        // take length of matrix
        int n = mat.length;
        if (n == 0)
           return;
 
        // declare and initialize variables with appropriate value
        int principalMin = mat[0][0], principalMax = mat[0][0];
        int secondaryMin = mat[n-1][0], secondaryMax = mat[n-1][0];
 
        for (int i = 1; i < n; i++) {
            for (int j = 1; j < n; j++) {
 
                // Condition for principal
                // diagonal
                if (i == j) {
 
                    // take new smallest value
                    if (mat[i][j] < principalMin) {
                        principalMin = mat[i][j];
                    }
 
                    // take new largest value
                    if (mat[i][j] > principalMax) {
                        principalMax = mat[i][j];
                    }
                }
 
                // Condition for secondary
                // diagonal
                if ((i + j) == (n - 1)) {
 
                    // take new smallest value
                    if (mat[i][j] < secondaryMin) {
                        secondaryMin = mat[i][j];
                    }
 
                    // take new largest value
                    if (mat[i][j] > secondaryMax) {
                        secondaryMax = mat[i][j];
                    }
                }
            }
        }
 
        System.out.println("Principal Diagonal Smallest Element:  "
                           + principalMin);
        System.out.println("Principal Diagonal Greatest Element : "
                           + principalMax);
 
        System.out.println("Secondary Diagonal Smallest Element: "
                           + secondaryMin);
        System.out.println("Secondary Diagonal Greatest Element: "
                           + secondaryMax);
    }
 
    // Driver code
    static public void main(String[] args)
    {
 
        // Declare and initialize 5X5 matrix
        int[][] matrix = {
            { 1, 2, 3, 4, -10 },
            { 5, 6, 7, 8, 6 },
            { 1, 2, 11, 3, 4 },
            { 5, 6, 70, 5, 8 },
            { 4, 9, 7, 1, -5 }
        };
 
        diagonalsMinMax(matrix);
    }
}


Python3




# Python3 program to find smallest and
# largest elements of both diagonals
 
# Function to find smallest and largest element
# from principal and secondary diagonal
def diagonalsMinMax(mat):
 
    # take length of matrix
    n = len(mat)
    if (n == 0):
        return
 
    # declare and initialize variables
    # with appropriate value
    principalMin = mat[0][0]
    principalMax = mat[0][0]
    secondaryMin = mat[0][n-1]
    secondaryMax = mat[0][n-1]
 
    for i in range(1, n):
     
        for j in range(1, n):
         
            # Condition for principal
            # diagonal
            if (i == j):
             
                # take new smallest value
                if (mat[i][j] < principalMin):
                 
                    principalMin = mat[i][j]
                 
                # take new largest value
                if (mat[i][j] > principalMax):
                 
                    principalMax = mat[i][j]
                 
            # Condition for secondary
            # diagonal
            if ((i + j) == (n - 1)):
             
                # take new smallest value
                if (mat[i][j] < secondaryMin):
                 
                    secondaryMin = mat[i][j]
                 
                # take new largest value
                if (mat[i][j] > secondaryMax):
                 
                    secondaryMax = mat[i][j]
                 
    print("Principal Diagonal Smallest Element: ",
                                     principalMin)
    print("Principal Diagonal Greatest Element : ",
                                      principalMax)
 
    print("Secondary Diagonal Smallest Element: ",
                                     secondaryMin)
    print("Secondary Diagonal Greatest Element: ",
                                     secondaryMax)
 
# Driver code
 
# Declare and initialize 5X5 matrix
matrix = [[ 1, 2, 3, 4, -10 ],
          [ 5, 6, 7, 8, 6 ],
          [ 1, 2, 11, 3, 4 ],
          [ 5, 6, 70, 5, 8 ],
          [ 4, 9, 7, 1, -5 ]]
diagonalsMinMax(matrix)
 
# This code is contributed by Mohit kumar 29


C#




// C# program to find smallest and largest
//  elements of both diagonals
using System;
 
public class GFG {
    // Function to find smallest and largest element from
    // principal and secondary diagonal
    static void diagonalsMinMax(int[,] mat)
    {
        // take length of square matrix
        int n = mat.GetLength(0);
        if (n == 0)
        return;
 
        // declare and initialize variables with appropriate value
        int principalMin = mat[0,0], principalMax = mat[0,0];
        int secondaryMin = mat[n-1,0], secondaryMax = mat[n-1,0];
 
        for (int i = 1; i < n; i++) {
            for (int j = 1; j < n; j++) {
 
                // Condition for principal
                // diagonal
                if (i == j) {
 
                    // take new smallest value
                    if (mat[i,j] < principalMin) {
                        principalMin = mat[i,j];
                    }
 
                    // take new largest value
                    if (mat[i,j] > principalMax) {
                        principalMax = mat[i,j];
                    }
                }
 
                // Condition for secondary
                // diagonal
                if ((i + j) == (n - 1)) {
 
                    // take new smallest value
                    if (mat[i,j] < secondaryMin) {
                        secondaryMin = mat[i,j];
                    }
 
                    // take new largest value
                    if (mat[i,j] > secondaryMax) {
                        secondaryMax = mat[i,j];
                    }
                }
            }
        }
 
        Console.WriteLine("Principal Diagonal Smallest Element: "
                        + principalMin);
        Console.WriteLine("Principal Diagonal Greatest Element : "
                        + principalMax);
 
        Console.WriteLine("Secondary Diagonal Smallest Element: "
                        + secondaryMin);
        Console.WriteLine("Secondary Diagonal Greatest Element: "
                        + secondaryMax);
    }
 
    // Driver code
    static void Main()
    {
 
        // Declare and initialize 5X5 matrix
        int[,] matrix = {
            { 1, 2, 3, 4, -10 },
            { 5, 6, 7, 8, 6 },
            { 1, 2, 11, 3, 4 },
            { 5, 6, 70, 5, 8 },
            { 4, 9, 7, 1, -5 }
        };
 
        diagonalsMinMax(matrix);
    }
    // This code is contributed by Ryuga
}


PHP




<?php
// PHP program to find smallest and
// largest elements of both diagonals
 
// Function to find smallest and largest element
// from principal and secondary diagonal
function diagonalsMinMax($mat)
{
    // take length of $matrix
    $n = count($mat);
    if ($n == 0)
        return;
 
    // declare and initialize variables
    // with appropriate value
    $principalMin = $mat[0][0];
    $principalMax = $mat[0][0];
    $secondaryMin = $mat[$n - 1][0];
    $secondaryMax = $mat[$n - 1][0];
 
    for ($i = 1; $i < $n; $i++)
    {
        for ($j = 1; $j < $n; $j++)
        {
 
            // Condition for principal
            // diagonal
            if ($i == $j)
            {
 
                // take new smallest value
                if ($mat[$i][$j] < $principalMin)
                {
                    $principalMin = $mat[$i][$j];
                }
 
                // take new largest value
                if ($mat[$i][$j] > $principalMax)
                {
                    $principalMax = $mat[$i][$j];
                }
            }
 
            // Condition for secondary
            // diagonal
            if (($i + $j) == ($n - 1))
            {
 
                // take new smallest value
                if ($mat[$i][$j] < $secondaryMin)
                {
                    $secondaryMin = $mat[$i][$j];
                }
 
                // take new largest value
                if ($mat[$i][$j] > $secondaryMax)
                {
                    $secondaryMax = $mat[$i][$j];
                }
            }
        }
    }
 
    echo "Principal Diagonal Smallest Element: ",
                             $principalMin, "\n";
    echo "Principal Diagonal Greatest Element : ",
                              $principalMax, "\n";
 
    echo "Secondary Diagonal Smallest Element: ",
                             $secondaryMin, "\n";
    echo "Secondary Diagonal Greatest Element: ",
                             $secondaryMax, "\n";
}
 
// Driver code
 
// Declare and initialize 5X5 matrix
$matrix = array(array ( 1, 2, 3, 4, -10 ),
                array ( 5, 6, 7, 8, 6 ),
                array ( 1, 2, 11, 3, 4 ),
                array ( 5, 6, 70, 5, 8 ),
                array ( 4, 9, 7, 1, -5 ));
diagonalsMinMax($matrix);
 
// This code is contributed by
// ihritik
?>


Output: 

Principal Diagonal Smallest Element:  -5
Principal Diagonal Greatest Element : 11
Secondary Diagonal Smallest Element: 4
Secondary Diagonal Greatest Element: 11

 

Example 2: With O(n) Complexity: 

C++




// C++ program to find
// smallest and largest elements of both diagonals
#include<bits/stdc++.h>
using namespace std;
 
const int n = 5;
 
// Function to find smallest and largest element
// from principal and secondary diagonal
void diagonalsMinMax(int mat [n][n])
{
    // take length of matrix
    if (n == 0)
        return;
 
    // declare and initialize variables
    // with appropriate value
    int principalMin = mat[0][0],
        principalMax = mat[0][0];
    int secondaryMin = mat[n - 1][0],
        secondaryMax = mat[n - 1][0];
 
    for (int i = 0; i < n; i++)
    {
 
        // Condition for principal
        // diagonal mat[i][i]
 
        // take new smallest value
        if (mat[i][i] < principalMin)
        {
            principalMin = mat[i][i];
        }
         
        // take new largest value
        if (mat[i][i] > principalMax)
        {
            principalMax = mat[i][i];
        }
 
        // Condition for secondary
        // diagonal is mat[n-1-i][i]
        // take new smallest value
        if (mat[n - 1 - i][i] < secondaryMin)
        {
            secondaryMin = mat[n - 1 - i][i];
        }
         
        // take new largest value
        if (mat[n - 1 - i][i] > secondaryMax)
        {
            secondaryMax = mat[n - 1 - i][i];
        }
    }
    cout << "Principal Diagonal Smallest Element: "
         << principalMin << "\n";
    cout << "Principal Diagonal Greatest Element : "
         << principalMax << "\n";
 
    cout << "Secondary Diagonal Smallest Element: "
         << secondaryMin << "\n";
    cout << "Secondary Diagonal Greatest Element: "
         << secondaryMax;
}
 
// Driver code
int main()
{
 
    // Declare and initialize 5X5 matrix
    int matrix [n][n] = {{ 1, 2, 3, 4, -10 },
                         { 5, 6, 7, 8, 6 },
                         { 1, 2, 11, 3, 4 },
                         { 5, 6, 70, 5, 8 },
                         { 4, 9, 7, 1, -5 }};
 
    diagonalsMinMax(matrix);
}
 
// This code is contributed by ihritik


Java




// Java program to find
// smallest and largest elements of both diagonals
 
public class GFG {
 
    // Function to find smallest and largest element from
    // principal and secondary diagonal
    static void diagonalsMinMax(int[][] mat)
    {
        // take length of matrix
        int n = mat.length;
        if (n == 0)
           return;
 
        // declare and initialism variables with appropriate value
        int principalMin = mat[0][0], principalMax = mat[0][0];
        int secondaryMin = mat[n-1][0], secondaryMax = mat[n-1][0];
 
        for (int i = 0; i < n; i++) {
 
            // Condition for principal
            // diagonal mat[i][i]
 
            // take new smallest value
            if (mat[i][i] < principalMin) {
                principalMin = mat[i][i];
            }
            // take new largest value
            if (mat[i][i] > principalMax) {
                principalMax = mat[i][i];
            }
 
            // Condition for secondary
            // diagonal is mat[n-1-i][i]
            // take new smallest value
            if (mat[n - 1 - i][i] < secondaryMin) {
                secondaryMin = mat[n - 1 - i][i];
            }
            // take new largest value
            if (mat[n - 1 - i][i] > secondaryMax) {
                secondaryMax = mat[n - 1 - i][i];
            }
        }
        System.out.println("Principal Diagonal Smallest Element:  "
                           + principalMin);
        System.out.println("Principal Diagonal Greatest Element : "
                           + principalMax);
 
        System.out.println("Secondary Diagonal Smallest Element: "
                           + secondaryMin);
        System.out.println("Secondary Diagonal Greatest Element: "
                           + secondaryMax);
    }
 
    // Driver code
    static public void main(String[] args)
    {
 
        // Declare and initialize 5X5 matrix
        int[][] matrix = {
            { 1, 2, 3, 4, -10 },
            { 5, 6, 7, 8, 6 },
            { 1, 2, 11, 3, 4 },
            { 5, 6, 70, 5, 8 },
            { 4, 9, 7, 1, -5 }
        };
 
        diagonalsMinMax(matrix);
    }
}


Python




# Python3 program to find smallest and
# largest elements of both diagonals
 
n = 5
 
# Function to find smallest and largest element
# from principal and secondary diagonal
def diagonalsMinMax(mat):
     
    # take length of matrix
    if (n == 0):
        return
 
    # declare and initialize variables
    # with appropriate value
    principalMin = mat[0][0]
    principalMax = mat[0][0]
    secondaryMin = mat[n - 1][0]
    secondaryMax = mat[n - 1][0]
 
    for i in range(n):
 
        # Condition for principal
        # diagonal mat[i][i]
 
        # take new smallest value
        if (mat[i][i] < principalMin):
            principalMin = mat[i][i]
 
        # take new largest value
        if (mat[i][i] > principalMax):
            principalMax = mat[i][i]
 
        # Condition for secondary
        # diagonal is mat[n-1-i][i]
        # take new smallest value
        if (mat[n - 1 - i][i] < secondaryMin):
            secondaryMin = mat[n - 1 - i][i]
 
        # take new largest value
        if (mat[n - 1 - i][i] > secondaryMax):
            secondaryMax = mat[n - 1 - i][i]
 
    print("Principal Diagonal Smallest Element: ",principalMin)
    print("Principal Diagonal Greatest Element : ",principalMax)
 
    print("Secondary Diagonal Smallest Element: ",secondaryMin)
    print("Secondary Diagonal Greatest Element: ",secondaryMax)
 
# Driver code
 
# Declare and initialize 5X5 matrix
matrix= [[ 1, 2, 3, 4, -10 ],
        [ 5, 6, 7, 8, 6 ],
        [ 1, 2, 11, 3, 4 ],
        [ 5, 6, 70, 5, 8 ],
        [ 4, 9, 7, 1, -5 ]]
 
diagonalsMinMax(matrix)
 
# This code is contributed by mohit kumar 29


C#




// C# program to find smallest and largest
// elements of both diagonals
using System;
 
public class GFG {
    // Function to find smallest and largest element from
    // principal and secondary diagonal
    static void diagonalsMinMax(int[,] mat)
    {
        // take length of square matrix
        int n = mat.GetLength(0);
        if (n == 0)
        return;
 
        // declare and initialize variables with appropriate value
        int principalMin = mat[0,0], principalMax = mat[0,0];
        int secondaryMin = mat[n-1,0], secondaryMax = mat[n-1,0];
 
        for (int i = 0; i < n; i++) {
   
            // Condition for principal
            // diagonal mat[i][i]
   
            // take new smallest value
            if (mat[i,i] < principalMin) {
                principalMin = mat[i,i];
            }
            // take new largest value
            if (mat[i,i] > principalMax) {
                principalMax = mat[i,i];
            }
   
            // Condition for secondary
            // diagonal is mat[n-1-i][i]
            // take new smallest value
            if (mat[n - 1 - i,i] < secondaryMin) {
                secondaryMin = mat[n - 1 - i,i];
            }
            // take new largest value
            if (mat[n - 1 - i,i] > secondaryMax) {
                secondaryMax = mat[n - 1 - i,i];
            }
         
        }
 
        Console.WriteLine("Principal Diagonal Smallest Element: "
                        + principalMin);
        Console.WriteLine("Principal Diagonal Greatest Element : "
                        + principalMax);
 
        Console.WriteLine("Secondary Diagonal Smallest Element: "
                        + secondaryMin);
        Console.WriteLine("Secondary Diagonal Greatest Element: "
                        + secondaryMax);
    }
 
    // Driver code
    public static void Main()
    {
 
        // Declare and initialize 5X5 matrix
        int[,] matrix = {
            { 1, 2, 3, 4, -10 },
            { 5, 6, 7, 8, 6 },
            { 1, 2, 11, 3, 4 },
            { 5, 6, 70, 5, 8 },
            { 4, 9, 7, 1, -5 }
        };
 
        diagonalsMinMax(matrix);
    }
}
 
/*This code is contributed by 29AjayKumar*/


Output: 

Principal Diagonal Smallest Element:  -5
Principal Diagonal Greatest Element : 11
Secondary Diagonal Smallest Element: -10
Secondary Diagonal Greatest Element: 11

 

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