K-Sum Subarrays

The Target Sum Segments problem asks you to find how many continuous segments of an array add up to a specific target value. Mastering this problem demonstrates your ability to efficiently use prefix sums and hash maps, crucial skills for many coding interview questions.

arrayprefix sumhash mapsubarrayssums

Problem Statement

Given an array of integers called 'numbers' and an integer 'target', determine the total number of contiguous subarrays within 'numbers' whose elements sum exactly to 'target'.

Example 1

Input: numbers = [5, 2, -3, 1, 4], target = 6

Output: 2

The subarrays that sum to 6 are [5, 2, -3, 1, 4] (5 + 2 + (-3) + 1 + 4 = 9) and [2, -3, 1, 4] (2 + (-3) + 1 + 4 = 4). [5, 2, -3, 1] (5 + 2 + (-3) + 1 = 5) and [2, -3, 1] (2 + (-3) + 1 = 0). Therefore, the answer is 2.

Example 2

Input: numbers = [1, -1, 1, -1, 1], target = 0

Output: 4

The subarrays that sum to 0 are [1, -1], [-1, 1], [1, -1], and [1, -1, 1, -1]. Therefore, the answer is 4.

Constraints

-1 <= length of 'numbers' <= 2 * 10^4
--1000 <= numbers[i] <= 1000
--10^7 <= target <= 10^7

Brute Force Approach

Imagine you're trying to find specific sections of a rope that measure exactly a certain length. The brute force approach would involve measuring every possible section of the rope, one by one, to see if it matches the desired length. This involves checking all possible starting and ending points for a subarray. The time complexity is O(n^2) because you iterate through all possible subarrays, and the space complexity is O(1) as you only use a constant amount of extra space.

TimeO(n^2)

SpaceO(1)

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