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# subarray-sum-equals-k

## Problem Description

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

## Solution

Usually when see subarray sum relate problem, preSum should come to your mind. calculate all subarray sum = k, using map to keep track of number of times presum already appear, for each presum, check whether presum - k in map or not:
• if `map.containsKey(presum - k)`, meaning presum already appear before, `count+=map.get(presum-k);`
• then add/update map, `map.put(presum, map.getOrDefault(presum, 0) + 1)`
after sum the whole array, return count.
For example:
Subarray Sum Equals K

### Complexity Analysis

Time Complexity: `O(N)`
Space Complexity: `O(N)`
• N - the length of array nums

### Code

class Solution {
public int subarraySum(int[] nums, int k) {
int count = 0;
int preSum = 0;
Map<Integer, Integer> map = new HashMap<>();
map.put(0, 1);
for (int num : nums) {
preSum += num;
if (map.containsKey(preSum - k)) {
count += map.get(preSum- k);
}
map.put(preSum, map.getOrDefault(preSum, 0) + 1);
}
return count;
}
}