Recursive Programs to find Minimum and Maximum elements of array

Given an array of integers arr, the task is to find the minimum and maximum element of that array using recursion.

Examples :

Input: arr = {1, 4, 3, -5, -4, 8, 6};
Output: min = -5, max = 8

Input: arr = {1, 4, 45, 6, 10, -8};
Output: min = -8, max = 45

Recursive approach to find the Minimum element in the array

Approach:

• Get the array for which the minimum is to be found
• Recursively find the minimum according to the following: 
  • Recursively traverse the array from the end
  • Base case: If the remaining array is of length 1, return the only present element i.e. arr[0] 

if(n == 1)
   return arr[0];

• Recursive call: If the base case is not met, then call the function by passing the array of one size less from the end, i.e. from arr[0] to arr[n-1].
• Return statement: At each recursive call (except for the base case), return the minimum of the last element of the current array (i.e. arr[n-1]) and the element returned from the previous recursive call. 

return min(arr[n-1], recursive_function(arr, n-1));

• Print the returned element from the recursive function as the minimum element

Pseudocode for Recursive function:

If there is single element, return it.
Else return minimum of following.
    a) Last Element
    b) Value returned by recursive call
       for n-1 elements.

Below is the implementation of the above approach:

C++

// Recursive C++ program to find minimum

#include <iostream>
using namespace std;

// function to print Minimum element using recursion
int findMinRec(int A[], int n)
{
    // if size = 0 means whole array has been traversed
    if (n == 1)
        return A[0];
    return min(A[n-1], findMinRec(A, n-1));
}

// driver code to test above function
int main()
{
    int A[] = {1, 4, 45, 6, -50, 10, 2};
    int n = sizeof(A)/sizeof(A[0]);
    cout <<  findMinRec(A, n);
    return 0;
}

Java

// Recursive Java program to find minimum
import java.util.*;

class GFG {

    // function to return minimum element using recursion
    public static int findMinRec(int A[], int n)
    {
      // if size = 0 means whole array
      // has been traversed
      if(n == 1)
        return A[0];

        return Math.min(A[n-1], findMinRec(A, n-1));
    }

    // Driver code
    public static void main(String args[])
    {
        int A[] = {1, 4, 45, 6, -50, 10, 2};
        int n = A.length;

        // Function calling
        System.out.println(findMinRec(A, n));
    }
}

//This code is contributed by Niraj_Pandey

Python3

# Recursive python 3 program to
# find minimum

# function to print Minimum element
# using recursion
def findMinRec(A, n):

    # if size = 0 means whole array
    # has been traversed
    if (n == 1):
        return A[0]
    return min(A[n - 1], findMinRec(A, n - 1))

# Driver Code
if __name__ == '__main__':
    A = [1, 4, 45, 6, -50, 10, 2]
    n = len(A)
    print(findMinRec(A, n))

# This code is contributed by
# Shashank_Sharma

C#

// Recursive C# program to find minimum
using System;

class GFG
{

// function to return minimum
// element using recursion
public static int findMinRec(int []A,
                             int n)
{
// if size = 0 means whole array
// has been traversed
if(n == 1)
    return A[0];

    return Math.Min(A[n - 1],
                    findMinRec(A, n - 1));
}

// Driver code
static public void Main ()
{
    int []A = {1, 4, 45, 6, -50, 10, 2};
    int n = A.Length;

    // Function calling
    Console.WriteLine(findMinRec(A, n));
}
}

// This code is contributed by Sachin

PHP

<?php
// Recursive PHP program to find minimum

// function to print Minimum
// element using recursion
function findMinRec($A, $n)
{

    // if size = 0 means whole
    // array has been traversed
    if ($n == 1)
        return $A[0];
    return min($A[$n - 1], findMinRec($A, $n - 1));
}

    // Driver Code
    $A = array (1, 4, 45, 6, -50, 10, 2);
    $n = sizeof($A);
    echo findMinRec($A, $n);

// This code is contributed by akt
?>

Javascript

<script>

// Javascript program to find minimum

// Function to print Minimum
// element using recursion
function findMinRec(A, n)
{

    // If size = 0 means whole
    // array has been traversed
    if (n == 1)
        return A[0];

    return Math.min(A[n - 1],
        findMinRec(A, n - 1));
}

// Driver Code
let A = [ 1, 4, 45, 6, -50, 10, 2 ];
let n = A.length;

document.write( findMinRec(A, n));

// This code is contributed by sravan kumar G

</script>

Output

-50

Recursive approach to find the Maximum element in the array

Approach:

• Get the array for which the maximum is to be found
• Recursively find the maximum according to the following: 
  • Recursively traverse the array from the end
  • Base case: If the remaining array is of length 1, return the only present element i.e. arr[0] 

if(n == 1)
   return arr[0];

• Recursive call: If the base case is not met, then call the function by passing the array of one size less from the end, i.e. from arr[0] to arr[n-1].
• Return statement: At each recursive call (except for the base case), return the maximum of the last element of the current array (i.e. arr[n-1]) and the element returned from the previous recursive call. 

return max(arr[n-1], recursive_function(arr, n-1));

• Print the returned element from the recursive function as the maximum element

Pseudocode for Recursive function:

If there is single element, return it.
Else return maximum of following.
    a) Last Element
    b) Value returned by recursive call
       for n-1 elements.

Below is the implementation of the above approach:

C++

// Recursive C++ program to find maximum
#include <iostream>
using namespace std;

// function to return maximum element using recursion
int findMaxRec(int A[], int n)
{
    // if n = 0 means whole array has been traversed
    if (n == 1)
        return A[0];
    return max(A[n-1], findMaxRec(A, n-1));
}

// driver code to test above function
int main()
{
    int A[] = {1, 4, 45, 6, -50, 10, 2};
    int n = sizeof(A)/sizeof(A[0]);
    cout <<  findMaxRec(A, n);
    return 0;
}

Java

// Recursive Java program to find maximum
import java.util.*;

class GFG {

    // function to return maximum element using recursion
    public static int findMaxRec(int A[], int n)
    {
      // if size = 0 means whole array
      // has been traversed
      if(n == 1)
        return A[0];

        return Math.max(A[n-1], findMaxRec(A, n-1));
    }

    // Driver code
    public static void main(String args[])
    {
        int A[] = {1, 4, 45, 6, -50, 10, 2};
        int n = A.length;

        // Function calling
        System.out.println(findMaxRec(A, n));
    }
}

//This code is contributed by Niraj_Pandey

Python3

# Recursive Python 3 program to
# find maximum

# function to return maximum element
# using recursion
def findMaxRec(A, n):

    # if n = 0 means whole array
    # has been traversed
    if (n == 1):
        return A[0]
    return max(A[n - 1], findMaxRec(A, n - 1))

# Driver Code
if __name__ == "__main__":

    A = [1, 4, 45, 6, -50, 10, 2]
    n = len(A)
    print(findMaxRec(A, n))

# This code is contributed by ita_c

C#

// Recursive C# program to find maximum
using System;

class GFG
{
// function to return maximum
// element using recursion
public static int findMaxRec(int []A,
                             int n)
{
// if size = 0 means whole array
// has been traversed
if(n == 1)
    return A[0];

    return Math.Max(A[n - 1],
                    findMaxRec(A, n - 1));
}

// Driver code
static public void Main ()
{
    int []A = {1, 4, 45, 6, -50, 10, 2};
    int n = A.Length;

    // Function calling
    Console.WriteLine(findMaxRec(A, n));
}
}

// This code is contributed by Sach_Code

PHP

<?php
// Recursive PHP program to find maximum

// function to return maximum
// element using recursion
function findMaxRec($A, $n)
{
    // if n = 0 means whole array
    // has been traversed
    if ($n == 1)
        return $A[0];
    return max($A[$n - 1],
        findMaxRec($A, $n - 1));
}

// Driver Code
$A = array(1, 4, 45, 6, -50, 10, 2);
$n = sizeof($A);
echo findMaxRec($A, $n);

// This code is contributed
// by Akanksha Rai
?>

Javascript

<script>

// Recursive Java program to find maximum

// Function to return maximum element
// using recursion
function findMaxRec(A, n)
{

    // If size = 0 means whole array
    // has been traversed
    if (n == 1)
        return A[0];

    return Math.max(A[n - 1],
        findMaxRec(A, n - 1));
}

// Driver code
let A = [ 1, 4, 45, 6, -50, 10, 2 ];
let n = A.length;

// Function calling
document.write(findMaxRec(A, n));

// This code is contributed by sravan kumar G

</script>

Output

45