2197 - Replace Non-Coprime Numbers in Array (Hard)

Problem Link

https://leetcode.com/problems/replace-non-coprime-numbers-in-array/

Problem Statement

You are given an array of integers nums. Perform the following steps:

1. Find any two adjacent numbers in nums that are non-coprime.
2. If no such numbers are found, stop the process.
3. Otherwise, delete the two numbers and replace them with their LCM (Least Common Multiple).
4. 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 <= 10^5
• 1 <= nums[i] <= 10^5
• The test cases are generated such that the values in the final array are less than or equal to 108.

Approach 1: Simulation

We iterate each number and check if the gcd of this number $x$ and the last element $y$ of $ans$ is non co-prime, i.e. $gcd(x, y) > 1$. If so, replace them with their LCM and keep doing the same process till they are co-prime.

Written by @wingkwong

class Solution {
public:
    vector<int> replaceNonCoprimes(vector<int>& nums) {
        int n = nums.size();
        vector<int> ans;
        for (int i = 0; i < n; i++) {
            // check if the last element of ans
            // and nums[i] are non co-prime
            while (ans.size() && gcd(ans.back(), nums[i]) > 1) {
                // replace them with their LCM
                nums[i] = lcm(ans.back(), nums[i]);
                // delete the last element
                ans.pop_back();
            }
            // insert nums[i] to ans for the next round
            ans.push_back(nums[i]);
        }
        return ans;
    }
};