560. Subarray Sum Equals K

https://leetcode.com/problems/subarray-sum-equals-k/

Problem

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

Constraints:

• 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

1. $O(N^2)$ using prefix sum

class Solution {
public:
    int subarraySum(vector<int>& nums, const int k) {
        int prefix[nums.size() + 1];
        prefix[0] = 0;
        int count = 0;
        for (int i = 1; i <= nums.size(); ++i) prefix[i] = prefix[i - 1] + nums[i - 1];
        for (int i = 1; i <= nums.size(); ++i) {
            for (int j = i; j <= nums.size(); ++j) {
                if (prefix[j] - prefix[i - 1] == k) ++count;
            }
        }
        return count;
    }
};

2. $O(N)$ using hash map

class Solution {
public:
    int subarraySum(vector<int>& nums, const int k) {
        int sum = 0;
        int count = 0;
        unordered_map<int, int> counter;
        counter.reserve(nums.size());
        counter[0] = 1;
        for (int i = 0; i < nums.size(); ++i) {
            sum += nums[i];
            if (counter.find(sum - k) != counter.end()) count += counter[sum - k];
            ++counter[sum];
        }
        return count;
    }
};

• #hash

• #veryimportant

• #prefix