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Code Recursion

# Reverse array using recursion

Reversing an array is a common task in computer programming. In this article, we will explore how to reverse an array using recursion. Recursion is a programming technique where a function calls itself to solve a smaller instance of the same problem.

## Introduction

The problem we are trying to solve is to reverse the elements of a given array. For example, if we have an array [1, 2, 7, 3, 4, 5, 8, 9], after reversing it, the array will be [9, 8, 5, 4, 3, 7, 2, 1]. To achieve this, we will use a recursive function.

## Problem Statement

Given an array of integers, we need to reverse the order of its elements using a recursive approach. The recursive function should take the array and the indices of the front and tail elements as input parameters and reverse the elements between these indices.

## Example

Let's understand the process with a suitable example. Consider the array [1, 2, 3, 4, 5].

1. Initial Array: [1, 2, 3, 4, 5]
2. Swap elements at the front and tail indices: [5, 2, 3, 4, 1]
3. Call the recursive function with front + 1 and tail - 1 as new indices: [5, 4, 3, 2, 1]
4. Swap elements at the front and tail indices: [5, 4, 3, 2, 1] (unchanged)
5. Recursive call with front + 1 and tail - 1: [5, 4, 3, 2, 1] (unchanged)

At this point, the front index becomes greater than the tail index, and the recursion stops. The final reversed array is [5, 4, 3, 2, 1].

## Pseudocode

Let's represent the algorithm in pseudocode:

``````function reverse_array(data[], front, tail):
if front < tail:
swap data[front] with data[tail]
reverse_array(data, front + 1, tail - 1)
```
```

## Algorithm Explanation

The recursive function `reverse_array` takes three parameters: the array `data` and the indices `front` and `tail`. The base case of the recursion is when the `front` index becomes greater than or equal to the `tail` index, in which case the function returns without doing anything.

If the base case is not met, the function swaps the elements at indices `front` and `tail`, effectively reversing the order of the elements between these indices. Then, the function makes a recursive call with `front + 1` and `tail - 1` as the new indices, so the next pair of elements can be swapped, continuing the reversal process.

## Time Complexity

The time complexity of the recursive function depends on the number of recursive calls made. For an array of size `n`, the function makes `n/2` recursive calls, as we halve the problem size in each recursive step. Therefore, the time complexity of the `reverse_array` function is O(`n`), where `n` is the size of the input array.

## Output Explanation

Let's analyze the output of the provided C code:

``````
Before Reverse
1 2 7 3 4 5 8 9
After Reverse
9 8 5 4 3 7 2 1
```
```

The initial array is [1, 2, 7, 3, 4, 5, 8, 9]. After calling the `reverse_array` function, the array is reversed, resulting in [9, 8, 5, 4, 3, 7, 2, 1], which is the expected output.

## Finally

In this article, we explored how to reverse an array using recursion. We presented a recursive function that swaps the front and tail elements iteratively until the entire array is reversed. Recursion provides an elegant way to solve this problem, and the time complexity of the algorithm is linear, making it efficient for arrays of moderate size.

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