dsa2 min read
Running Sum of 1D Array — Prefix Sum Foundation [Amazon Easy]
Compute running (prefix) sum in O(n) time O(1) extra space. The prefix sum pattern is foundational for range queries, subarray problems and 2D matrices.
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Prefix-sum
24 articles
dsa2 min read
Product of Array Except Self — Prefix × Suffix O(n) O(1) [Google, Meta, Amazon]
Compute product of all elements except self without division. O(n) two-pass prefix/suffix approach with O(1) extra space.
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dsa2 min read
Subarray Sum Equals K — Prefix Sum + HashMap O(n) [Google, Meta]
Count subarrays summing to k. Classic prefix sum + HashMap trick: if prefix[j]-prefix[i]=k then prefix[i]=prefix[j]-k. O(n) time.
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dsa1 min read
Shortest Subarray with Sum ≥ K [Hard] — Deque on Prefix Sums
Find the shortest subarray with sum >= K using a monotonic deque on prefix sums, handling negative numbers correctly.
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dsa2 min read
Count of Range Sum [Hard] — Merge Sort on Prefix Sums
Count the number of range sums that lie in [lower, upper] using a merge sort approach on prefix sums.
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dsa1 min read
Count of Range Sum — Merge Sort on Prefix Sums
Count subarrays with sum in [lower, upper] using merge sort on prefix sums for O(n log n) complexity.
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Subarray Sum Equals K [Medium] — Prefix Sum HashMap
Count subarrays with sum exactly k using prefix sums stored in a HashMap to find valid starting positions in O(n).
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Continuous Subarray Sum [Medium] — Prefix Modulo Map
Check if a continuous subarray of length >= 2 sums to a multiple of k using prefix sum modulo k with a HashMap.
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Random Pick with Weight [Medium] — Prefix Sum + Binary Search
Implement weighted random selection by building a prefix sum array and using binary search to find the sampled index.
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dsa2 min read
Make Sum Divisible by P — Prefix Mod + HashMap
Find the smallest subarray to remove so the remaining sum is divisible by p using prefix modular arithmetic.
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Subarray Sum Divisible by K — Prefix Mod HashMap
Count subarrays with sum divisible by k using prefix mod frequencies and the complement map pattern.
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Remove Zero Sum Consecutive Nodes — Prefix Sum Map
Remove consecutive nodes that sum to zero by tracking prefix sums in a map and relinking past zero-sum runs.
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Range Sum Query 2D Immutable — 2D Prefix Sum
Sum of rectangle region. Precompute 2D prefix sums: prefix[i][j] = sum of all cells from (0,0) to (i-1,j-1). Inclusion-exclusion for query.
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dsa1 min read
Max Sum Rectangle No Larger than K — BIT + Prefix
Find max rectangle sum <= k in 2D matrix. Fix row boundaries, compress to 1D array, use prefix sums + BIT/sorted set to find best subarray sum <= k.
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Longest Subarray with Sum ≤ K — Monotonic Queue + Prefix
Find longest subarray with sum <= k. Build prefix sums, use monotonic deque for decreasing prefix sums to efficiently find left boundaries.
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Shortest Subarray with Sum at Least K — Deque + Prefix Sum
Find the shortest subarray with sum >= k using a monotonic deque on prefix sums for O(n) time.
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Path Sum III — Prefix Sum HashMap on Tree
Count paths in a binary tree summing to target (not necessarily root-to-leaf) using a prefix sum frequency map.
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Running Sum of 1D Array [Easy] — Prefix Sum
Compute the running sum of a 1D array where each element is the sum of itself and all previous elements.
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Count Number of Nice Subarrays [Medium] — atMost(k)−atMost(k−1)
Count subarrays with exactly k odd numbers using the at-most(k) minus at-most(k-1) sliding window formula.
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dsa1 min read
Binary Subarrays With Sum [Medium] — Prefix Sum / atMost
Count binary subarrays with exactly the given sum using prefix sum with HashMap or the atMost(k)-atMost(k-1) trick.
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Subarray Sum Divisible by K [Medium] — Prefix Sum Modulo
Count subarrays with sum divisible by k using prefix sum modulo k and a frequency map of remainders.
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dsa2 min read
Count Subarrays Where Median Equals K [Hard] — Prefix Balance
Count subarrays where the median is exactly k by converting the problem to counting balanced prefix sequences around k.
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Shortest Subarray with Sum ≥ K [Hard] — Monotonic Deque on Prefix
Find the shortest subarray with sum >= k, handling negative numbers correctly using a monotonic deque on prefix sums.
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dsa2 min read
Meta — Subarray Sum Equals K (Prefix Sum + HashMap)
Count subarrays with sum equal to k using prefix sums and a hashmap. O(n) time by tracking how many times each prefix sum has occurred.
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