O(n) time and O(n) space using Prefix Sum and Hashtable.

Author: 149ps

974. Subarray Sums Divisible by K/974. Subarray Sums Divisible by K.py

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+"""
+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 <= A.length <= 30000
+-10000 <= A[i] <= 10000
+2 <= K <= 10000
+"""
+class Solution:
+    def subarraysDivByK(self, A: List[int], K: int) -> int:
+        hmap,total,result = {},0,0
+        for num in A:
+            hmap[total] = hmap.get(total,0) + 1
+            total += num
+            total %= K
+            if hmap.get(total):
+                result += hmap[total]
+        return result