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

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].


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:

Complexity Analysis

Time Complexity: O(N)

Space Complexity: O(N)

  • N - the length of array nums


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;

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