## Description

Given a list of non-negative numbers and a target integer k, write a function to check if the array has a continuous subarray of size at least 2 that sums up to a multiple of k, that is, sums up to n*k where n is also an integer.

Example 1:

Input: [23, 2, 4, 6, 7],  k=6
Output: True
Explanation: Because [2, 4] is a continuous subarray of size 2 and sums up to 6.


Example 2:

Input: [23, 2, 6, 4, 7],  k=6
Output: True
Explanation: Because [23, 2, 6, 4, 7] is an continuous subarray of size 5 and sums up to 42.


Note:

1. The length of the array won’t exceed 10,000.
2. You may assume the sum of all the numbers is in the range of a signed 32-bit integer.

## Solutions

### 1. Dict+Math

# Time: O(n)
# Space: O(n)
class Solution:
def checkSubarraySum(self, nums: List[int], k: int) -> bool:
n = len(nums)
if k == 0 :
for i in range(1, n):
if nums[i] == nums[i - 1] and nums[i] == 0:
return True
return False
k = abs(k)
if n >= 2 * k:
return True
sum = [0]
for num in nums:
sum.append((sum[-1] + num) % k)

dic = {}
for i in range(len(sum)):
if sum[i] in dic:
if i - dic[sum[i]] >= 2:
return True
else:
dic[sum[i]] = i
return False
# Runtime: 220 ms, faster than 93.30%
# Memory Usage: 13.3 MB, less than 71.43%