Leetcode #2436: Minimum Split Into Subarrays With GCD Greater Than One
In this guide, we solve Leetcode #2436 Minimum Split Into Subarrays With GCD Greater Than One in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an array nums consisting of positive integers. Split the array into one or more disjoint subarrays such that: Each element of the array belongs to exactly one subarray, and The GCD of the elements of each subarray is strictly greater than 1.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Array, Math, Dynamic Programming, Number Theory
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nums = [12,6,3,14,8]
Output: 2
Explanation: We can split the array into the subarrays: [12,6,3] and [14,8].
- The GCD of 12, 6 and 3 is 3, which is strictly greater than 1.
- The GCD of 14 and 8 is 2, which is strictly greater than 1.
It can be shown that splitting the array into one subarray will make the GCD = 1.
Python Solution
class Solution:
def minimumSplits(self, nums: List[int]) -> int:
ans, g = 1, 0
for x in nums:
g = gcd(g, x)
if g == 1:
ans += 1
g = x
return ans
Complexity
The time complexity is , where and are the length of the array and the maximum value in the array, respectively. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.