Problem Statement

Write a program to find the minimum and maximum elements in an array using recursion. You cannot use loops or built-in functions like min() or max(). The solution should recursively compute the minimum and maximum by dividing the problem into smaller subproblems.

Input:

1. A non-empty array of integers, arr.
2. An integer, n, representing the size of the array.

Output:

1. The minimum element in the array.
2. The maximum element in the array.

Examples

Example 1:

Input: arr = [3, 5, 1, 8, -2, 7], n = 6
Output: Minimum element = -1
        Maximum element = 8

Example 2:

Input: arr = [10], n = 1
Output: Minimum element = 10
        Maximum element = 10

Different Approaches

1️⃣ Recursion

Algorithm:

1. Base Case:
   • If the array has only one element, return it as both the minimum and maximum.
2. Recursive Case:
   • Compare the last element of the array with the result of the recursive call on the rest of the array to find the minimum and maximum.

Code:

#include <iostream>
#include <vector>
#include <climits> // For INT_MIN and INT_MAX

using namespace std;

// Recursive function to find the minimum element in the array
int findMin(const vector<int>& arr, int n) {
    // Base case: If there's only one element, return it as the minimum
    if (n == 1) {
        return arr[0];
    }

    // Recursive case: Find the minimum of the rest of the array
    return min(arr[n - 1], findMin(arr, n - 1));
}

// Recursive function to find the maximum element in the array
int findMax(const vector<int>& arr, int n) {
    // Base case: If there's only one element, return it as the maximum
    if (n == 1) {
        return arr[0];
    }

    // Recursive case: Find the maximum of the rest of the array
    return max(arr[n - 1], findMax(arr, n - 1));
}

int main() {
    vector<int> arr = {3, 5, 1, 8, -2, 7}; // Input array
    int n = arr.size(); // Size of the array

    // Find and print the minimum and maximum elements using recursion
    cout << "Minimum element: " << findMin(arr, n) << endl;
    cout << "Maximum element: " << findMax(arr, n) << endl;

    return 0;
}