PATTERN 3: Prefix / Suffix / Precomputation

D

Qubits of DPK

April 11, 2026

Core DSA

Core Idea (lock this sentence)

“Precompute partial results so repeated work disappears.”
If a brute-force solution recomputes the same thing again and again,
this pattern is screaming at you.

How to Recognize This Pattern (VERY IMPORTANT)

You should think Prefix / Suffix when you see:
  • Repeated range queries
  • Subarray / substring problems
  • “For every index, compute something”
  • Constraints like O(N^2) TLE but O(N) possible

30 MUST-DO INTERVIEW PROBLEMS

(10 Easy → 10 Medium → 10 Hard)

EASY (1–10): Learn to Precompute

Goal: get used to building arrays that help later
  1. #
    Range Sum Query – Immutable – LC 303
  2. #
    Left and Right Sum Differences – LC 2574
  3. #
    Find the Highest Altitude – LC 1732
  4. #
    Find the Middle Index – LC 1991
  5. #
    XOR Queries of a Subarray – LC 1310
  6. #
    Product of Array Except Self – LC 238
  7. #
    Squares of a Sorted Array – LC 977
  8. #
    Running Sum to Find Target – LC 1413
  9. #
    Check if All 1's Are at Least Length K Apart – LC 1893
  10. #
    Find Pivot Index (Prefix view) – LC 724
After these:
Prefix/suffix arrays should feel obvious, not special.

️ MEDIUM (11–20): Real Interview Usage

Write English explanation first.
  1. #
    Count Subarrays with Sum = K – LC 560
  2. #
    Contiguous Array (Equal 0s and 1s) – LC 525
  3. #
    Trapping Rain Water – LC 42
  4. #
    Largest Subarray with 0 Sum – GFG
  5. #
    Maximum Score of a Good Subarray – LC 1793
  6. #
    Count Number of Nice Subarrays – LC 1248
  7. #
    Minimum Value to Get Positive Step by Step Sum – LC 1413
  8. #
    Maximum Sum of Two Non-Overlapping Subarrays – LC 1031
  9. #
    Maximum Number of Occurrences of a Substring – LC 1297
  10. #
    Maximum Sum Obtained of Any Permutation – LC 1589
Interviewers test:
Can you convert brute force to prefix logic cleanly?

HARD (21–30): Prefix + Multiple States

These build mental toughness.
  1. #
    Count of Range Sum – LC 327
  2. #
    Maximum Average Subarray II – LC 644
  3. #
    Number of Submatrices That Sum to Target – LC 1074
  4. #
    Range Sum Query 2D – Immutable – LC 304
  5. #
    Shortest Subarray with Sum at Least K – LC 862
  6. #
    Split Array Largest Sum – LC 410
  7. #
    Count Subarrays With Fixed Bounds – LC 2444
  8. #
    Maximum Sum of 3 Non-Overlapping Subarrays – LC 689
  9. #
    Subarrays With K Different Integers – LC 992
  10. #
    Count Subarrays With Median K – LC 2488
These require:
  • Multiple prefix states
  • Careful variable tracking
  • No panic under complexity

What You Should Realize After These 30

You should instinctively say:
  • “Let me build a prefix array”
  • “This avoids recomputation”
  • “Now range queries are O(1)”
If you’re still looping inside loops → repeat this pattern.

Common Mistakes (Interview Killers)

  • Building prefix array but not using it
  • Off-by-one errors
  • Forgetting prefix[0] = 0 concept
  • Mixing prefix and sliding window blindly

INTERVIEW REVISION CARD — Pattern 3

1️⃣ Pattern in One Line

"Precompute partial results upfront so repeated range queries become O(1)."

2️⃣ Recognize It When...

  • Same subarray/range computed multiple times
  • "For every index, compute something using previous elements"
  • Trigger words: "subarray sum", "range query", "difference array", "cumulative"
  • O(N²) brute force but O(N) is possible

3️⃣ Don't Confuse With...

  • Hashing (P2) → when you need existence/frequency, not cumulative values
  • Sliding Window (P4) → when window shrinks/expands, not precomputed
  • DP (P13) → when choices are involved, not just precomputation

4️⃣ Approach in 3 Steps

  1. #
    Build prefix array: prefix[i] = prefix[i-1] + arr[i-1]
  2. #
    Answer range [l, r] = prefix[r+1] - prefix[l]
  3. #
    Remember: prefix[0] = 0 always

5️⃣ Invariant to Maintain

"prefix[i] always represents the sum/product of all elements from index 0 to i-1."

6️⃣ Complexity to Justify

  • Build: O(N) time, O(N) space
  • Query: O(1) per query
  • Why: Precomputation eliminates repeated scanning

7️⃣ Edge Cases to Always Check

  • prefix[0] = 0 (empty prefix)
  • Off-by-one in range [l, r]
  • Negative numbers in prefix sum
  • Integer overflow for large arrays
  • Single element array

8️⃣ One Line to Say in Interview

"I'll precompute a prefix array in O(N) so each range query is answered in O(1), avoiding repeated scanning."

Pattern 3 is now LOCKED

Chamber Portal

EASY PROBLEM SOLUTIONS

Chamber Portal

MEDIUM PROBLEM SOLUTIONS

Chamber Portal

HARD PROBLEM SOLUTIONS