The problem “Create Target Array in the Given Order” is a great example of array manipulation and index management in Python. Though it seems straightforward at first glance, this problem can teach you a lot about efficient data structure use, and can also offer a sneak peek into how programming puzzles often have more than one valid solution. In this article, we’ll walk through various approaches to solving this problem, and analyze their time and space complexities.

## Table of Contents

- Understanding the Problem Statement
- Initial Thoughts and Pseudocode
- The Brute-Force Approach
- Using List Insert Method
- Using Dynamic Array/Slicing
- Time and Space Complexity Analysis
- Testing and Edge Cases
- Conclusion

## 1. Understanding the Problem Statement

The problem asks you to create a target array by following a given order. You’ll have two arrays, `nums`

and `index`

, with the same length. For each index-value pair `(i, x)`

in arrays `index`

and `nums`

, you have to insert the value `x`

at the ith position in the target array.

### Constraints and Assumptions:

`1 <= nums.length, index.length <= 100`

`nums.length == index.length`

`0 <= nums[i] <= 100`

`0 <= index[i] <= i`

## 2. Initial Thoughts and Pseudocode

You need to initialize an empty array and then go through each pair `(i, x)`

from `index`

and `nums`

to insert `x`

into the `i`

th position in the target array.

Pseudocode:

```
1. Initialize an empty array called target
2. For each pair (i, x) in arrays index and nums:
- Insert x at index i in the target array
3. Return target
```

## 3. The Brute-Force Approach

One simple way is to manually shift all the elements every time you insert a new element at an index.

```
def createTargetArray(nums, index):
target = []
for i in range(len(nums)):
target = target[:index[i]] + [nums[i]] + target[index[i]:]
return target
```

## 4. Using List Insert Method

Python provides a built-in method called `insert`

for lists which allows us to insert an element at a specific index in a more readable way.

```
def createTargetArray(nums, index):
target = []
for i in range(len(nums)):
target.insert(index[i], nums[i])
return target
```

## 5. Using Dynamic Array/Slicing

Python lists are dynamic arrays behind the scenes. The slicing operation itself is quite efficient and can be used for this problem. We showed this method in the brute-force approach.

## 6. Time and Space Complexity Analysis

**Brute-Force/Slicing Method**: O(n^2) time complexity, because the slice operation`[a:b]`

takes`O(b-a+1) = O(n)`

time. O(n) space complexity.**Using List Insert Method**: O(n^2) time complexity and O(n) space complexity, as list insert operation takes O(n) time.

## 7. Testing and Edge Cases

Make sure to test your code with several edge cases:

- Cases where
`nums`

contains duplicate values. - Cases where
`index`

is in descending order. - Cases where
`nums`

and`index`

have length 1.

## 8. Conclusion

Though the problem “Create Target Array in the Given Order” looks simple at first glance, it serves as a good practice for array manipulation in Python. This problem also highlights how different approaches can be employed to solve the same problem, and how Python’s built-in functions can simplify the code. Understanding the underlying time and space complexities is important to assess the efficiency of the different approaches.