# Continuous Subarray Sum（2 sum）

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 the 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.

分析

2个loop做法：这里**presum**\[j] - presum\[i] 包括j 不包括i,根据题意这里j-i>=2才行。 所以Presum计算的时候坐标后移一位。

自己版本：2个loop

```
class Solution:
    def checkSubarraySum(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: bool
        """

        preSum = list(itertools.accumulate(nums))
        n = len(nums)
        if n< 2: return False
        if n == 2: return preSum[1] == k or (k != 0 and preSum[1] % k == 0)
        if k != 0 and preSum[-1] %k == 0:
            return True
        for i in range(n):
            for j in range(n)[i:]:
                subSum = preSum[j] - preSum[i]
                if j - i >= 2 and (subSum == k or (k != 0 and subSum % k == 0)):
                    return True

        return False
```

2个loop：map的坐标后移一位。补充{0:0} 这样d\[2]-d\[0]就是2个数至少

```
class Solution:
    def checkSubarraySum(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: bool
        """
        sum,d = 0,{0:0}
        for i,e in enumerate(nums):
            sum += e
            d[i+1] = sum
        n = len(nums)
        for i in range(0,n-1):
            for j in range(i+2,n+1):
                subsum = d[j]-d[i]
                if subsum == k or (k != 0 and subsum % k == 0):
                    return True

        return False
```

1个loop : map sum: index. 初始化{0,-1}

其实这里还是2 sum问题。x = presum % k，如果X再次出现，直接隔得就是multiple of k。corner是k=0

还是Index直接相减，留尾去头。i-j>=2

```
class Solution:
    def checkSubarraySum(self, nums, k):
        n= len(nums)
        if k == 0:
            return n >= 2 and sum(nums) == 0

        summ, d = 0, {0: -1}
        for i, v in enumerate(nums):
            summ = (summ + v) % k
            if summ in d:
                if i - d[summ] >= 2:
                    return True
            else:
                d[summ] = i
        return False
```


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