1524. Number of Sub-arrays With Odd Sum

Problem

Given an array of integers arr, return **the number of subarrays with an *odd* sum**.

Since the answer can be very large, return it modulo 10^9 + 7.

  Example 1:

Input: arr = [1,3,5]
Output: 4
Explanation: All subarrays are [[1],[1,3],[1,3,5],[3],[3,5],[5]]
All sub-arrays sum are [1,4,9,3,8,5].
Odd sums are [1,9,3,5] so the answer is 4.

Example 2:

Input: arr = [2,4,6]
Output: 0
Explanation: All subarrays are [[2],[2,4],[2,4,6],[4],[4,6],[6]]
All sub-arrays sum are [2,6,12,4,10,6].
All sub-arrays have even sum and the answer is 0.

Example 3:

Input: arr = [1,2,3,4,5,6,7]
Output: 16

  Constraints:

• 1 <= arr.length <= 10^5

• 1 <= arr[i] <= 100

Solution (Java)

class Solution {
    public int numOfSubarrays(int[] arr) {
        int number = arr[0] % 2 == 0 ? 0 : 1;
        long res = number;
        for (int i = 1; i < arr.length; i++) {
            if (arr[i] % 2 != 0) {
                number = i - number + 1;
            }
            res += number;
        }
        long mod = 1_000_000_007;
        return (int) (res % mod);
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).