[LeetCode] 560.Subarray Sum Equals K_Medium tag: Array, Subarray, prefix Sum

Posted 2021-06-18

Given an array of integers nums and an integer k, return the total number of continuous subarrays whose sum equals to k.

 

Example 1:

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

Example 2:

Input: nums = [1,2,3], k = 3
Output: 2

 

Constraints:

• 1 <= nums.length <= 2 * 104
• -1000 <= nums[i] <= 1000
• -107 <= k <= 107

 

Ideas:

1. brute force     T: O(n ^2), S: O(1)

class Solution:
    def subarraySum(self, nums: List[int], target: int) -> int:
        n, count = len(nums), 0
        for i in range(n):
            for j in range(i, n):
                curSum = sum(nums[i: j + 1])
                if curSum == target:
                    count += 1
        return count

 

2. 参考Prefix Sum & Dictionary Time and Space O(n) for -- Find a number of continuous subarrays/submatrices/tree paths that sum to target     T: O(n), S: O(n)

class Solution:
    def subarraySum(self, nums: List[int], target: int) -> int:
        count, curSum, d = 0, 0, collections.Counter()
        for num in nums:
            curSum += num
            if curSum == target:
                count += 1
            count += d[curSum - target]
            d[curSum] += 1
        return count