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Practice SetLesson 071 min read

Prefix Sums — Practice Problems

November 05, 2026

// How to use this set

Work these in order: easy (Range Sum Query, Find Pivot Index, Minimum Value to Get Positive Step by Step Sum) → medium (Subarray Sum Equals K, Product of Array Except Self, Contiguous Array, Subarray Sums Divisible by K, Continuous Subarray Sum, Range Sum Query 2D, Maximum Size Subarray Sum Equals k). The recurring trick is a hash map of prefix-sum → first index (or count), so a subarray property becomes an O(1) lookup. Every solution below was run and tested.

Ten problems that drill the prefix-sum pattern from Lesson 7. The big idea keeps coming back: precompute running totals so any range question becomes a subtraction, and store prefix sums in a hash map so “find a subarray with property X” collapses to a lookup. Each solution here was actually run and tested.

How to practise. For each problem, first decide what the prefix sum means (a running total? a running balance of +1/−1? a running sum mod k?) and what you need to store (just the array, or a map of sum → index / count). Try it yourself for ~20 minutes, then read the approach, close the page, and re-solve from memory the next day.

The 10 problems

  1. 1Range Sum Query - Immutable (LeetCode 303)EasyAnswer many range-sum queries on a fixed array: build a prefix array once, then each query is one subtraction.arrow_forward
  2. 2Find Pivot Index (LeetCode 724)EasyFind the first index where left sum equals right sum: keep a running left sum, right = total - left - x.arrow_forward
  3. 3Minimum Value to Get Positive Step by Step Sum (LeetCode 1413)EasySmallest start value keeping a running sum at least 1: find the lowest prefix sum and lift it to exactly 1.arrow_forward
  4. 4Subarray Sum Equals K (LeetCode 560)MediumCount subarrays summing to k: each is a difference of prefix sums, so count earlier prefixes equal to s − k.arrow_forward
  5. 5Product of Array Except Self (LeetCode 238)MediumProduct of all other elements at each index without division: multiply a prefix product by a suffix product.arrow_forward
  6. 6Contiguous Array (LeetCode 525)MediumLongest subarray with equal 0s and 1s: count 0 as -1, then find the farthest-apart repeat of a running sum.arrow_forward
  7. 7Subarray Sums Divisible by K (LeetCode 974)MediumCount subarrays whose sum is divisible by k: two prefix sums with the same remainder mod k bound one.arrow_forward
  8. 8Continuous Subarray Sum (LeetCode 523)MediumSubarray of length ≥ 2 summing to a multiple of k? Store each remainder's first index and check the gap.arrow_forward
  9. 9Range Sum Query 2D - Immutable (LeetCode 304)MediumSum any sub-rectangle of a fixed matrix in O(1): a 2-D prefix sum plus inclusion–exclusion on four corners.arrow_forward
  10. 10Maximum Size Subarray Sum Equals k (LeetCode 325)MediumLongest subarray summing to k: store each prefix sum's earliest index and look up current - k.arrow_forward
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