LeetCode-in-Java

3618. Split Array by Prime Indices

Medium

You are given an integer array nums.

Split nums into two arrays A and B using the following rule:

• Elements at prime indices in nums must go into array A.
• All other elements must go into array B.

Return the absolute difference between the sums of the two arrays: |sum(A) - sum(B)|.

Note: An empty array has a sum of 0.

Example 1:

Input: nums = [2,3,4]

Output: 1

Explanation:

• The only prime index in the array is 2, so nums[2] = 4 is placed in array A.
• The remaining elements, nums[0] = 2 and nums[1] = 3 are placed in array B.
• sum(A) = 4, sum(B) = 2 + 3 = 5.
• The absolute difference is |4 - 5| = 1.

Example 2:

Input: nums = [-1,5,7,0]

Output: 3

Explanation:

• The prime indices in the array are 2 and 3, so nums[2] = 7 and nums[3] = 0 are placed in array A.
• The remaining elements, nums[0] = -1 and nums[1] = 5 are placed in array B.
• sum(A) = 7 + 0 = 7, sum(B) = -1 + 5 = 4.
• The absolute difference is |7 - 4| = 3.

Constraints:

• 1 <= nums.length <= 105
• -109 <= nums[i] <= 109

Solution

public class Solution {
    public long splitArray(int[] nums) {
        int n = nums.length;
        boolean[] isPrime = sieve(n);
        long sumA = 0;
        long sumB = 0;
        for (int i = 0; i < n; i++) {
            if (isPrime[i]) {
                sumA += nums[i];
            } else {
                sumB += nums[i];
            }
        }
        return Math.abs(sumA - sumB);
    }

    // Sieve of Eratosthenes to find all prime indices up to n
    private boolean[] sieve(int n) {
        boolean[] isPrime = new boolean[n];
        if (n > 2) {
            isPrime[2] = true;
        }
        for (int i = 3; i < n; i += 2) {
            isPrime[i] = true;
        }
        if (n > 2) {
            isPrime[2] = true;
        }
        for (int i = 3; i * i < n; i += 2) {
            if (isPrime[i]) {
                for (int j = i * i; j < n; j += i * 2) {
                    isPrime[j] = false;
                }
            }
        }
        isPrime[0] = false;
        if (n > 1) {
            isPrime[1] = false;
        }
        return isPrime;
    }
}

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