Problem Statement

Given an array of size n, write a function to reverse the elements of the array. The task is to reverse the array in-place, which means you should not use extra space for another array.

Examples

Example 1:

Input: arr = [1, 2, 3, 4, 5]
Output: arr = [5, 4, 3, 2, 1]

Example 2:

Input: arr = [1, 2, 1, 3]
Output: arr = [3, 1, 2, 1]

Different Approaches

1️⃣ Recursive Approach

#include<iostream>
using namespace std;

// Function to reverse the array using recursion
void reverseArrayRecursively(int arr[], int left, int right) {
    if (left >= right) {
        return;  // Base case: when left and right pointers meet
    }

    // Swap the elements
    swap(arr[left], arr[right]);

    // Recursively call the function for the next set of elements
    reverseArrayRecursively(arr, left + 1, right - 1);
}

int main() {
    int n;
    cout << "Enter the number of elements in the array: ";
    cin >> n;

    int arr[n];
    cout << "Enter the elements of the array: ";
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
    }

    reverseArrayRecursively(arr, 0, n - 1);

    cout << "Reversed array: ";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;

    return 0;
}

Complexity Analysis:

• Time Complexity: O(n)
  • Each recursive call processes two elements (one from the start and one from the end of the array).
  • The total number of recursive calls is n/2 since every recursive call works on two elements.
  • However, even though there are n/2 recursive calls, we still look at n elements in total. In Big-O notation, constants are ignored, so the overall time complexity is still: O(n).
• Space Complexity: O(n)
  • Each recursive call adds a frame to the call stack. Since there are n/2n/2n/2 recursive calls, the space complexity for the recursion stack grows in proportion to the number of recursive calls.
    • There are n/2 recursive calls, each of which requires a stack frame.
    • Thus, the space complexity is O(n/2)
  • However, in Big-O notation, constants like 1/2 are ignored, so the space complexity is considered: O(n).