2307 Replace Non Coprime Numbers In Array

Replace Non-Coprime Numbers in Array

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.

class Solution:
    def replaceNonCoprimes(self, nums):
        stack = []
        for num in nums:
            while stack and math.gcd(stack[-1], num) > 1:
                top = stack.pop()
                num = (top * num) // math.gcd(top, num) 
            stack.append(num)
        return stack