560. Subarray Sum Equals K

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].

 

Approach #1: Math. [Java]

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

　　

Anslysis:

The key to solve this problem is SUM[i, j]. So if we know SUM[0, i-1] ans SUM[0, j], then we can easily get SUM[i, j]. To achieve this, we just need to go through the array, calculate the current sum and save number of all seen preSum to a HashMap.

Time complexity O(n), Space complexity O (n).

 

Reference:

https://leetcode.com/problems/subarray-sum-equals-k/discuss/102106/Java-Solution-PreSum-%2B-HashMap