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Subarray Sum Equals K - Prefix Sums - Leetcode 560

Disclaimer: This is a personal summary and interpretation based on a YouTube video. It is not official material and not endorsed by the original creator. All rights remain with the respective creators.

This document summarizes the key takeaways from the video. I highly recommend watching the full video for visual context and coding demonstrations.

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Problem Statement

The task is to find the number of contiguous subarrays in a given array of integers that sum up to a target value k. The array can include negative numbers, which adds complexity.

Key takeaway: Focus on contiguous segments, and remember that negatives prevent simple sliding window optimizations.

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Brute Force Approach

Check every possible subarray by iterating through all starting and ending points, calculating the sum for each, and counting those that equal k. This runs in O(n²) time due to the n² subarrays.

Key example: For an array like [1, 1, 1] and k=2, you'd check pairs like [1,1] twice (first two and last two).

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Why Sliding Window Doesn't Work

A sliding window or two-pointer approach fails because array elements can be negative. Adding or removing elements doesn't predictably increase or decrease the sum, breaking the monotonicity needed for optimization.

Key takeaway: Negatives mean you can't assume expanding the window always grows the sum positively.

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Optimized Solution Overview

Use a hashmap to track prefix sums and their frequencies for an O(n) solution. The idea is to find subarrays by subtracting prefixes that leave a sum of k.

Key takeaway: Initialize the hashmap with a prefix sum of 0 (count 1) to handle cases where the subarray starts from the beginning.

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Intuition with Prefix Sums

As you iterate, maintain a running sum. For each position, check if (current_sum - k) exists in the hashmap—if so, add its count to the result, as it means there are that many ways to form a subarray ending here that sums to k. Then, update the hashmap with the current sum.

Key example: For [1, -1, 1, 1, 1] and k=3, the hashmap tracks multiple prefixes summing to the same value due to negatives, finding all four subarrays that sum to 3.

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Code Implementation

Initialize result=0, cur_sum=0, and a hashmap with {0: 1}. Loop through the array: add the current number to cur_sum, check if (cur_sum - k) is in the hashmap and add its count to result, then increment the hashmap count for cur_sum.

def subarraySum(nums, k):
    result = 0
    cur_sum = 0
    prefix_sums = {0: 1}
    for num in nums:
        cur_sum += num
        diff = cur_sum - k
        result += prefix_sums.get(diff, 0)
        prefix_sums[cur_sum] = prefix_sums.get(cur_sum, 0) + 1
    return result

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About the summarizer

I'm Ali Sol, a Backend Developer. Learn more: