LeetCode 2584: Split the Array to Make Coprime Products Solution

Master LeetCode problem 2584 (Split the Array to Make Coprime Products), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2584. Split the Array to Make Coprime Products

Hard

Array Hash Table Math Number Theory

Problem Explanation

Explanation

To solve this problem, we need to iterate through all possible splits of the array and check if the product of the elements on the left side and the product of the elements on the right side are coprime. We can calculate the products efficiently using prefix and suffix arrays.

Create an array leftProduct where leftProduct[i] stores the product of elements from index 0 to i.
Create an array rightProduct where rightProduct[i] stores the product of elements from index i+1 to n-1.
Iterate through each possible split position i.
Check if gcd of leftProduct[i] and rightProduct[i] is 1. If it is 1, return i as the result.
If no valid split is found, return -1.

Time Complexity: O(n) where n is the number of elements in the input array
Space Complexity: O(n) for storing leftProduct and rightProduct arrays

Solution Code

class Solution {
    public int splitArray(int[] nums) {
        int n = nums.length;
        int[] leftProduct = new int[n];
        int[] rightProduct = new int[n];
        
        leftProduct[0] = nums[0];
        rightProduct[n-1] = nums[n-1];
        
        for (int i = 1; i < n; i++) {
            leftProduct[i] = leftProduct[i-1] * nums[i];
        }
        
        for (int i = n-2; i >= 0; i--) {
            rightProduct[i] = rightProduct[i+1] * nums[i];
        }
        
        for (int i = 0; i < n-1; i++) {
            if (gcd(leftProduct[i], rightProduct[i+1]) == 1) {
                return i;
            }
        }
        
        return -1;
    }
    
    private int gcd(int a, int b) {
        while (b != 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
}

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