The “Shuffle the Array” problem is a classic example of a coding challenge that focuses on array manipulation. This problem is relatively straightforward but important for building a strong foundation in array operations and indexing.

In this in-depth article, we’ll explore:

- The Problem Statement
- Initial Thoughts and Simple Approaches
- Further Optimizations
- Python Implementations
- Test Cases and Edge Cases
- Complexity Analysis
- Conclusion

## 1. The Problem Statement

You are given an array `nums`

consisting of `2n`

elements in the form `[x1, x2, ..., xn, y1, y2, ..., yn]`

. Shuffle the array to make it in the form `[x1, y1, x2, y2, ..., xn, yn]`

. Return the shuffled array.

#### Example 1:

Input: `nums = [2, 5, 1, 3, 4, 7], n = 3`

Output: `[2, 3, 5, 4, 1, 7]`

Explanation: We take `[2, 5, 1]`

as x and `[3, 4, 7]`

as y. After shuffling, we get `[2, 3, 5, 4, 1, 7]`

.

#### Example 2:

Input: `nums = [1, 1, 2, 2], n = 2`

Output: `[1, 2, 1, 2]`

## 2. Initial Thoughts and Simple Approaches

The problem is fairly straightforward. The simplest approach would be to create a new array, iterate through the existing arrays x and y, and insert elements in the required order. This approach would use O(n) extra space.

## 3. Further Optimizations

The algorithm can be optimized for space by doing the shuffle in-place, but for clarity, the simple approach often suffices, especially given that the problem doesn’t have tight constraints.

## 4. Python Implementations

### Simple Implementation

```
def shuffle(nums, n):
x, y = nums[:n], nums[n:]
result = []
for i in range(n):
result.extend([x[i], y[i]])
return result
```

### In-Place Implementation (Optimized)

This implementation doesn’t require additional space.

```
def shuffle(nums, n):
for i in range(n):
nums.insert(2 * i + 1, nums.pop(n + i))
return nums
```

## 5. Test Cases and Edge Cases

To validate your solution, you need to consider multiple test cases, including edge cases:

```
# Test 1
assert shuffle([2, 5, 1, 3, 4, 7], 3) == [2, 3, 5, 4, 1, 7]
# Test 2
assert shuffle([1, 1, 2, 2], 2) == [1, 2, 1, 2]
# Test 3 (Edge Case)
assert shuffle([1], 1) == [1]
# Test 4 (Edge Case)
assert shuffle([1, 2], 1) == [1, 2]
```

## 6. Complexity Analysis

### Time Complexity

For the simple implementation, the time complexity is O(n) as we loop through the array once. For the in-place implementation, the insert operation takes O(n) time, making it O(n^2) overall.

### Space Complexity

The simple implementation uses O(n) additional space. The in-place implementation has a space complexity of O(1).

## 7. Conclusion

The “Shuffle the Array” problem from LeetCode is a great starting point for understanding array manipulations and serves as a building block for more complicated problems. Although the problem may not present the most challenging scenario, it’s a valuable exercise in understanding the basic principles of array operations and algorithmic efficiency.