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# Subarray Sum Equals K（2sum and presum）

Given an array of integers and an integer **k**, you need to find the total number of continuous subarrays whose sum equals to **k**.

**Example 1:**

```
Input:
nums = [1,1,1], k = 2

Output:
 2
```

**Note:**

1. The length of the array is in range \[1, 20,000].
2. The range of numbers in the array is \[-1000, 1000] and the range of the integer **k** is \[-1e7, 1e7].

分析：

本题只能two sum思想，不能用two pointers，因为可能有负数，所以当前的sum可能和前面好几个sum的diff == K. 用Map才能准确记录前面多少个subsum = cursum - K.(含有负数抵消的情况）

```
PrefixSum + Dictionary
> Time Complexity O(N)
> Space Complexity O(N)
```

这里没有presum数组，只有sum累积

这里map存个数 map\[sum]=count

对map和ret都是+=1不是=！！！！！

PYTHON MAP:MAP.GET(KEY,0)

```
 if we know SUM[0, i - 1] and SUM[0, j], then we can easily get SUM[i, j]. 因为不包含前数，所以Map[0]=1
```

```
import collections

class Solution:
    def subarraySum(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: int
        """
        if not nums:
            return 0
        ret = 0
        n = len(nums)

        map = collections.defaultdict(int)
        map[0] = 1 #因为前面总是不包含，所以需要map[0]补足？
        sum=0
        for i in range(n):
            sum+=nums[i]
            if sum - k in map:
                ret += map[sum- k]#+= 不是 =
            map[sum] += 1 #+= 不是 =
        return ret
```


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