1)The Complete Array Algorithms Roadmap: 12 Patterns from Beginner to Expert (2026 Guide)

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Arrays are the “Bread and Butter” of coding. Every interview starts here.

But most candidates fail not because they don’t know loop syntax, but because they use Brute Force ($O(N^2)$) instead of Pattern Logic ($O(N)$).

To clear top-tier interviews, you must stop thinking about “Loops” and start thinking about “Pointers and Windows.” This guide covers the 12 Essential Array Patterns that map to 90% of LeetCode problems.

Part 1: The “Pointer” Patterns (Navigation)

How to move through an array efficiently.

1. Two Pointers (Converging)

  • The Scenario: “Find a pair that sums to Target X” or “Reverse the array.”
  • The Logic: One pointer at Start, one at End. Move them toward each other based on a condition.
  • Complexity: $O(N)$.

2. Fast & Slow Pointers (Tortoise & Hare)

  • The Scenario: “Find the Duplicate Number” (Read-only array) or “Cycle Detection.”
  • The Logic: Use array values as indices. Fast moves 2 steps, Slow moves 1 step.
  • Why: This solves the “Duplicate” problem in $O(N)$ time and $O(1)$ space without modifying the array.

Part 2: The “Window” Patterns (Sub-arrays)

Focusing on a specific chunk of the array.

3. Sliding Window (Fixed & Variable)

  • The Scenario: “Max sum of subarray of size K” or “Smallest subarray with sum > S.”
  • The Logic:
    • Add element to the right (expand).
    • Remove element from the left (shrink) if condition is broken.
  • Trigger: “Contiguous Subarray”, “Longest Substring.”

4. Kadane’s Algorithm (Max Subarray Sum)

  • The Scenario: “Find the contiguous subarray with the largest sum.”
  • The Logic:
    • Carry the current_sum.
    • If current_sum becomes negative, reset it to 0 (because a negative prefix never helps).
    • Update max_so_far.

Part 3: The “Pre-Computation” Pattern (Range Queries)

Answering “How many?” or “What is the sum?” instantly.

5. Prefix Sum Array

  • The Scenario: “Calculate sum of elements between index L and R multiple times.”
  • The Logic: Create an auxiliary array where P[i] = Sum(0...i).
    • Sum(L, R) = P[R] - P[L-1].
  • Complexity: Query takes $O(1)$.

Part 4: The “Sorting” Patterns (Ordering)

Sorting without std::sort.

6. Dutch National Flag (Sort Colors)

  • The Scenario: “Sort an array of 0s, 1s, and 2s in one pass.”
  • The Logic: Use 3 pointers: Low (for 0s), Mid (for 1s), High (for 2s).
    • 0? Swap to Low.
    • 1? Leave it (Mid++).
    • 2? Swap to High.

7. Cyclic Sort (Missing/Duplicate)

  • The Scenario: “Array contains numbers 1 to N. Find the missing/duplicate.”
  • The Logic: Put number x at index x-1.
    • If nums[i] != nums[nums[i]-1], swap them.
    • Do this until everyone is in their “chair.”
  • Trigger: “Numbers from 1 to N.”

Part 5: The “Voting” Pattern (Counting)

Finding the leader without a Hash Map.

8. Moore’s Voting Algorithm

  • The Scenario: “Find the Majority Element (appears > N/2 times).”
  • The Logic:
    • Assume first number is leader. Count = 1.
    • If next number is same, Count++. If different, Count--.
    • If Count == 0, pick new leader.
  • Why: The majority element will survive the “cancellations.”

Part 6: The “Search” Pattern (Dividing)

Navigating sorted or rotated data.

9. Binary Search (Standard & Rotated)

  • The Scenario: “Find target in Rotated Sorted Array.”
  • The Logic: Find which half is sorted. Check if target lies in that range. If yes, go there. If no, go to the other half.

Part 7: The “Matrix” Patterns (2D Arrays)

Don’t get lost in the grid.

10. Rotate Image (In-place)

  • The Scenario: “Rotate a Matrix 90 degrees clockwise.”
  • The Logic:
    1. Transpose the matrix (swap [i][j] with [j][i]).
    2. Reverse every row.

11. Spiral Matrix

  • The Scenario: “Print matrix in spiral order.”
  • The Logic: Maintain 4 boundaries: Top, Bottom, Left, Right.
    • Move Right, Move Down, Move Left, Move Up.
    • Shrink boundaries after every pass.

12. Search in 2D Matrix (Staircase Search)

  • The Scenario: Rows are sorted, Columns are sorted. Find target.
  • The Logic: Start at Top-Right corner.
    • If Target < Current, go Left.
    • If Target > Current, go Down.

The Professor’s Cheat Code Sheet

Stick this table at the bottom. It maps the Constraint to the Algorithm.

If the problem mentions…Use this AlgorithmComplexity
Sorted Array + Target SumTwo Pointers$O(N)$
Contiguous Subarray + Max/MinSliding Window$O(N)$
Contains Negatives + Max SumKadane’s Algo$O(N)$
Range Sum Queries (L to R)Prefix Sum$O(1)$ Query
Numbers range 1 to NCyclic Sort$O(N)$
Majority (> N/2)Moore’s Voting$O(N)$
Sort 0s, 1s, 2sDutch National Flag$O(N)$
Rotated Sorted ArrayBinary Search$O(\log N)$
Matrix + Sorted Rows/ColsStaircase Search$O(N+M)$

Professor’s Advice for Teaching This

“Students, Arrays are not just about for loops.

  1. Level 1: Master Two Pointers and Sliding Window. This clears 60% of interviews.
  2. Level 2: Master Kadane’s and Cyclic Sort. This clears Product Company rounds.
  3. Level 3: Master Moore’s Voting and Matrix Manipulation. This makes you ‘Google Ready’.”

The Complete Array Algorithms Roadmap: 12 Patterns from Beginner to Expert (2026 Guide)

Array Algorithms for Interview Kadane’s Algorithm Explained Sliding Window vs Two Pointers Dutch National Flag Problem

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