Introduction

In this blog post, we will explore how to solve the LeetCode problem "1646" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer n. A 0-indexed integer 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​​​. Example 1: Input: n = 7 Output: 3 Explanation: According to the given rules: nums[0] = 0 nums[1] = 1 nums[(1 2) = 2] = nums[1] = 1 nums[(1 2) + 1 = 3] = nums[1] + nums[2] = 1 + 1 = 2 nums[(2 2) = 4] = nums[2] = 1 nums[(2 2) + 1 = 5] = nums[2] + nums[3] = 1 + 2 = 3 nums[(3 2) = 6] = nums[3] = 2 nums[(3 2) + 1 = 7] = nums[3] + nums[4] = 2 + 1 = 3 Hence, nums = [0,1,1,2,1,3,2,3], and the maximum is max(0,1,1,2,1,3,2,3) = 3. Example 2: Input: n = 2 Output: 1 Explanation: According to the given rules, nums = [0,1,1]. The maximum is max(0,1,1) = 1. Example 3: Input: n = 3 Output: 2 Explanation: According to the given rules, nums = [0,1,1,2]. The maximum is max(0,1,1,2) = 2. Constraints: 0 <= n <= 100

Explanation

Here's the solution:

• Key Idea: Utilize dynamic programming to efficiently calculate nums[i] based on previously computed values, as the problem definition lends itself well to this approach. We only need to keep track of the maximum value encountered so far to avoid iterating through the entire array at the end.
• Optimization: Instead of storing the entire nums array, we can optimize space by keeping track of the current maximum value and updating it as we generate the array elements. This is because the problem only requires the maximum value, not the entire array.

• Base Cases: Handle the base cases n = 0 and n = 1 separately for efficiency and correctness.

• Complexity:

  • Runtime Complexity: O(n)
  • Storage Complexity: O(1)

Code

    def getMaximumGenerated(n: int) -> int:
    """
    You are given an integer n. A 0-indexed integer 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.
    """
    if n == 0:
        return 0
    if n == 1:
        return 1

    nums = [0] * (n + 1)
    nums[0] = 0
    nums[1] = 1
    max_num = 1

    for i in range(1, (n // 2) + 1):
        if 2 * i <= n:
            nums[2 * i] = nums[i]
            max_num = max(max_num, nums[2 * i])
        if 2 * i + 1 <= n:
            nums[2 * i + 1] = nums[i] + nums[i + 1]
            max_num = max(max_num, nums[2 * i + 1])

    return max_num