Introduction

In this blog post, we will explore how to solve the LeetCode problem "2197" 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 array of integers nums. Perform the following steps: Find any two adjacent numbers in nums that are non-coprime. If no such numbers are found, stop the process. Otherwise, delete the two numbers and replace them with their LCM (Least Common Multiple). Repeat this process as long as you keep finding two adjacent non-coprime numbers. Return the final modified array. It can be shown that replacing adjacent non-coprime numbers in any arbitrary order will lead to the same result. The test cases are generated such that the values in the final array are less than or equal to 108. Two values x and y are non-coprime if GCD(x, y) > 1 where GCD(x, y) is the Greatest Common Divisor of x and y. Example 1: Input: nums = [6,4,3,2,7,6,2] Output: [12,7,6] Explanation: - (6, 4) are non-coprime with LCM(6, 4) = 12. Now, nums = [12,3,2,7,6,2]. - (12, 3) are non-coprime with LCM(12, 3) = 12. Now, nums = [12,2,7,6,2]. - (12, 2) are non-coprime with LCM(12, 2) = 12. Now, nums = [12,7,6,2]. - (6, 2) are non-coprime with LCM(6, 2) = 6. Now, nums = [12,7,6]. There are no more adjacent non-coprime numbers in nums. Thus, the final modified array is [12,7,6]. Note that there are other ways to obtain the same resultant array. Example 2: Input: nums = [2,2,1,1,3,3,3] Output: [2,1,1,3] Explanation: - (3, 3) are non-coprime with LCM(3, 3) = 3. Now, nums = [2,2,1,1,3,3]. - (3, 3) are non-coprime with LCM(3, 3) = 3. Now, nums = [2,2,1,1,3]. - (2, 2) are non-coprime with LCM(2, 2) = 2. Now, nums = [2,1,1,3]. There are no more adjacent non-coprime numbers in nums. Thus, the final modified array is [2,1,1,3]. Note that there are other ways to obtain the same resultant array. Constraints: 1 <= nums.length <= 105 1 <= nums[i] <= 105 The test cases are generated such that the values in the final array are less than or equal to 108.

Explanation

Here's an efficient solution to the problem:

• Core Idea: Use a stack to efficiently maintain the processed array. Iterate through the input array. For each number, check if it's non-coprime with the top of the stack. If so, calculate their LCM, replace the top of the stack with the LCM, and repeat the check. If not, push the number onto the stack.

• GCD & LCM: Implement helper functions for calculating the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) to avoid redundancy and improve readability.

• Runtime & Storage Complexity: O(N * log(MAX_VALUE)), O(N) where N is the length of the input array and MAX_VALUE is the maximum value of numbers in the array.

Code

    def gcd(a, b):
    """Calculates the Greatest Common Divisor of two numbers."""
    while b:
        a, b = b, a % b
    return a

def lcm(a, b):
    """Calculates the Least Common Multiple of two numbers."""
    return (a * b) // gcd(a, b)

def replaceNonCoprime(nums):
    """Replaces adjacent non-coprime numbers with their LCM."""
    stack = []
    for num in nums:
        while stack and gcd(stack[-1], num) > 1:
            num = lcm(stack[-1], num)
            stack.pop()
        stack.append(num)
    return stack