Getting a good grasp of algorithmic problems is crucial for both budding and experienced programmers. In this comprehensive guide, we’ll be examining one such problem commonly found on Leetcode: “Get Maximum in Generated Array.” We’ll go in-depth to explore multiple Pythonic solutions, dissect the logic behind each, and understand their performance implications.

### 1. Problem Statement

You are given an integer `n`

. An array `nums`

of length `n + 1`

is generated in the following way:

`nums[0] = 0`

`nums[1] = 1`

`nums[2 * i] = nums[i]`

when`2 <= 2 * i <= n`

`nums[2 * i + 1] = nums[i] + nums[i + 1]`

when`2 <= 2 * i + 1 <= n`

Return *the maximum integer in the array nums*.

**Constraints**:

`0 <= n <= 100`

### 2. Understanding the Problem

The problem asks us to generate an array following specific rules and then find the maximum element in the array. This is primarily an algorithmic problem that can be solved using array manipulation techniques.

### 3. Brute-Force Approach

The most straightforward way is to follow the problem’s rules to generate the array and then iterate over it to find the maximum element.

Python Code:

```
def getMaximumGenerated(n):
if n == 0:
return 0
elif n == 1:
return 1
nums = [0, 1] # Initial array
for i in range(2, n + 1):
if i % 2 == 0:
nums.append(nums[i // 2])
else:
nums.append(nums[i // 2] + nums[i // 2 + 1])
return max(nums)
```

### 4. Optimized Approaches

#### 4.1 Using Memoization

We can note that we’re doing repeated calculations in generating the array. Memoization could help us store previously calculated results.

Python Code:

```
def getMaximumGenerated(n):
nums = {}
nums[0] = 0
nums[1] = 1
max_val = 0 # To store the maximum value
for i in range(2, n + 1):
if i % 2 == 0:
nums[i] = nums[i // 2]
else:
nums[i] = nums[i // 2] + nums[i // 2 + 1]
max_val = max(max_val, nums[i])
return max_val if n > 0 else 0
```

#### 4.2 Using Dynamic Programming

Dynamic programming can also be applied to solve this problem, though, for this problem, it doesn’t offer significant advantages over other methods.

### 5. Time Complexity Analysis

All the mentioned approaches run in O(n) time complexity.

### 6. Space Complexity Analysis

The space complexity for all approaches is O(n).

### 7. Conclusion

We explored multiple ways to solve the “Get Maximum in Generated Array” problem from Leetcode in Python. We saw that various techniques can be applied to improve the performance of the brute-force approach, but the time complexity remains O(n).