Added: Find Minimum and Maximum in an Array Using Recursion

Recursion/Minimum and Maximum in Array/README.md

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+# Find Minimum and Maximum in an Array Using Recursion
+
+## Description
+
+This program demonstrates how to find the minimum and maximum elements in an array using a recursive algorithm. It is a useful technique in situations requiring array analysis without relying on iterative loops, showcasing the power of recursion in breaking problems into smaller subproblems.
+
+```
+Example:
+Enter the size of the array: 5
+Enter the elements of the array:
+Element 1: 12
+Element 2: 7
+Element 3: 19
+Element 4: 3
+Element 5: 15
+
+Output:
+The elements of the array:
+12 7 19 3 15
+Minimum element in the array: 3
+Maximum element in the array: 19
+
+```
+
+### Problem Definition
+
+1.  **Given**:
+- An integer array `arr[]` and its size `n`.
+
+2.  **Objective**:
+- Find the smallest (`min`) and largest (`max`) elements in the array using **recursive functions**.
+
+### Algorithm Overview
+
+1. **Base Case**:
+   - If the current index is the last element of the array, return the element as it is the minimum or maximum of the subarray.
+
+2. **Recursive Case**:
+   - For each recursive call:
+    - Compare the current element with the result of the recursive function applied to the rest of the array.
+    - Return the smaller value for the minimum function and the larger value for the maximum function.
+
+3. **Final Output**:
+   - Combine the results from the recursive calls to find the overall minimum and maximum.
+
+### Key Features
+
+- Recursive approach eliminates the need for explicit loops.
+- Minimal additional space required since recursion works in-place.
+- Efficiently processes each element exactly once.
+
+### Time Complexity
+
+- **Best case**: O(n), where `n` is the number of elements in the array, as every element is visited once.
+- **Worst case**: O(n) for the same reason.
+
+### Space Complexity
+
+- O(n) for the recursion stack in the worst case (when the recursion depth equals the number of elements).
+
+## Implementation
+
+The implementation in C includes:
+
+1. **Recursive Functions to Find Minimum and Maximum**
+    - A function `findMin` to recursively find the smallest element in the array.
+    - A function `findMax` to recursively find the largest element in the array.
+
+2. **User Input Handling**:
+    - A dynamic array to accept user-defined input for the size and elements of the array.
+    - A loop to populate the array with user inputs.
+
+3. **Main Function to Demonstrate Usage**:
+    - Accepts input for the array.
+    - Calls the recursive functions to find the minimum and maximum elements.
+    - Displays the results to the user.
+
+## Usage
+
+- Compile the program using a C compiler (e.g., gcc).
+- Run the program and input the size and elements of the array as prompted.
+- Observe the output displaying the minimum and maximum values.

Recursion/Minimum and Maximum in Array/min_max.c

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+#include <stdio.h>
+
+int findMin(int arr[], int n, int index) {
+    // Base case: If we've reached the end of the array
+    if (index == n - 1)
+        return arr[index];
+
+    // Recursive step: Find minimum of the current element and the rest
+    int minRest = findMin(arr, n, index + 1);
+    return (arr[index] < minRest) ? arr[index] : minRest;
+}
+
+int findMax(int arr[], int n, int index) {
+    // Base case: If we've reached the end of the array
+    if (index == n - 1)
+        return arr[index];
+
+    // Recursive step: Find maximum of the current element and the rest
+    int maxRest = findMax(arr, n, index + 1);
+    return (arr[index] > maxRest) ? arr[index] : maxRest;
+}
+
+int main() {
+    int n;
+
+    // Input size of the array
+    printf("Enter the size of the array: ");
+    scanf("%d", &n);
+
+    int arr[n]; // Declare array
+
+    // Input array elements
+    printf("Enter the elements of the array:\n");
+    for (int i = 0; i < n; i++) {
+        printf("Element %d: ", i + 1);
+        scanf("%d", &arr[i]);
+    }
+
+    // Print the array
+    printf("The elements of the array:\n");
+    for (int i = 0; i < n; i++) {
+        printf("%d ",arr[i]);
+    }
+    // Go to next line before printing the maximum and minimum element in the array
+    printf("\n");
+
+    // Find minimum and maximum
+    int min = findMin(arr, n, 0);
+    int max = findMax(arr, n, 0);
+
+    // Print results
+    printf("Minimum element in the array: %d\n", min);
+    printf("Maximum element in the array: %d\n", max);
+
+    return 0;
+}