How do you solve Replace Non-Coprime Numbers in Array on LeetCode?

Replace Non-Coprime Numbers in Array (LeetCode #2197) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Adjacent numbers can be merged if they share common factors.

What is the brute force solution for Replace Non-Coprime Numbers in Array?

The brute force approach for Replace Non-Coprime Numbers in Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves repeatedly scanning the array for adjacent non-coprime pairs and replacing them with their LCM until no such pairs remain. This is straightforward but inefficient due to repeated scans. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Replace Non-Coprime Numbers in Array?

Replace Non-Coprime Numbers in Array uses the following concepts: Array, Math, Stack, Number Theory. The recommended patterns to study are: Stack, Array.

What are the interview tips for Replace Non-Coprime Numbers in Array?

Explain your thought process clearly while coding. Consider edge cases, such as arrays with no non-coprime pairs. Practice similar problems to get comfortable with stack-based approaches.

What are common mistakes when solving Replace Non-Coprime Numbers in Array?

Not checking for adjacent pairs correctly. Failing to handle the stack properly, leading to incorrect results.

#2197

Replace Non-Coprime Numbers in Array

Hard

ArrayMathStackNumber TheoryStackArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a stack to efficiently manage the merging of adjacent non-coprime numbers. By processing the array in a single pass and using the stack to keep track of the current state, we can achieve better performance.

⚙️

Algorithm

5 steps

1Step 1: Initialize an empty stack.
2Step 2: Iterate through each number in the array.
3Step 3: For each number, check if it can be merged with the top of the stack (if the stack is not empty). If they are non-coprime, replace them with their LCM.
4Step 4: If they are coprime, push the current number onto the stack.
5Step 5: Continue until all numbers are processed, then return the stack as the final result.

solution.py13 lines

1# Full working Python code
2import math
3
4def replaceNonCoprime(nums):
5    stack = []
6    for num in nums:
7        while stack and math.gcd(stack[-1], num) > 1:
8            num = stack.pop() * num // math.gcd(stack[-1], num)
9        stack.append(num)
10    return stack
11
12# Example usage
13print(replaceNonCoprime([6,4,3,2,7,6,2]))

ℹ

Complexity note: The time complexity is O(n) because we make a single pass through the array, and each number is pushed and popped from the stack at most once. The space complexity is O(n) due to the stack storing the results.

1Adjacent numbers can be merged if they share common factors.
2Using a stack allows for efficient merging and backtracking.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.