Subarray Sums Divisible by K

Description

Given an array A of integers, return the number of (contiguous, non-empty) subarrays that have a sum divisible by K.

 

Example 1:

Input: A = [4,5,0,-2,-3,1], K = 5
Output: 7
Explanation: There are 7 subarrays with a sum divisible by K = 5:
[4, 5, 0, -2, -3, 1], [5], [5, 0], [5, 0, -2, -3], [0], [0, -2, -3], [-2, -3]

 

Note:

1. 1 <= A.length <= 30000
2. -10000 <= A[i] <= 10000
3. 2 <= K <= 10000

Solution(javascript)

/** 可以用 Prefix Sum 来解吗
 * https://leetcode.com/problems/subarray-sums-divisible-by-k/discuss/310767/(Python)-Concise-Explanation-and-Proof
 * @param {number[]} A
 * @param {number} K
 * @return {number}
 */
const subarraysDivByK = function (A, K) {
  let sum = 0
  const map = { 0: 1 }
  let count = 0
  for (const num of A) {
    sum += num
    // 注意负数的情况
    const key = ((sum % K) + K) % K
    if (map[key]) {
      count += map[key]
      map[key] += 1
    } else {
      map[key] = 1
    }
  }
  return count
}