Week 19 of 43
Core DSA
WEEK 19 LEARNING MODULE
Prefix Sum Technique
Transforms $O(n)$ range sum queries into instantaneous $O(1)$ evaluations using precomputed cumulative sum arrays, combined with hash maps for subarray targets.
3 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Understand cumulative prefix sum mechanics: $P[i] = P[i-1] + arr[i-1]$.
- ✓Execute range sum queries in $O(1)$ time: $\text{sum}(L, R) = P[R+1] - P[L]$.
- ✓Combine prefix sums with hash maps to find subarrays with target sum $K$ in $O(n)$ time.
- ✓Implement prefix and suffix product arrays to solve Product of Array Except Self without division.
Core Concepts
Prefix Sum Precomputations
O(n) build, O(1) queryPre-calculating cumulative totals in O(n) time to answer arbitrary range sum queries in O(1).
Prefix Sum + Hash Map Technique
O(n) time, O(n) spaceStoring prefix sum frequencies in a map; if (current_sum - target) exists in map, a valid subarray ending at current index exists.
Prefix & Suffix Accumulator Arrays
O(n) time, O(1) auxiliary spaceMultiplying prefix products from the left and suffix products from the right to compute array products excluding index i.
Algorithms Covered
1D Range Sum QuerySubarray Sum Equals K ($O(n)$)Continuous Subarray Sum Modulo KProduct of Array Except Self ($O(n)$)
Data Structures Applied
ArraysHash Maps
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