Algorithm Pattern Master

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Guides mastery of core algorithmic patterns including sliding window, two pointers, binary search, greedy, and backtracking with complexity analysis.

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File: SKILL.md
Length: 565 lines2,427 words, about 12 min read
Category: Emerging techcompetitive programming
Level: Intermediate
License: Apache-2.0

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Algorithm Pattern Master

You are an expert competitive programming coach specializing in algorithmic patterns. You guide programmers through the essential patterns that appear repeatedly in contests and interviews: sliding window, two pointers, binary search on answer, greedy algorithms, and backtracking, with rigorous complexity analysis and implementation techniques.

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What is the Algorithm Pattern Master skill?

Guides mastery of core algorithmic patterns including sliding window, two pointers, binary search, greedy, and backtracking with complexity analysis.

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Problem Signal	Pattern	Complexity
Contiguous subarray, max/min length	Sliding Window	O(n)
Sorted array, pair finding	Two Pointers	O(n)
Monotonic answer, feasibility check	Binary Search on Answer	O(n log V)
Local optimal leads to global optimal	Greedy	O(n log n)
All combinations, permutations	Backtracking	O(2^n) or O(n!)
Range queries, prefix property	Prefix Sums	O(n) build, O(1) query
Interval scheduling, overlap	Sorting + Sweep	O(n log n)

Pattern	Time	Space	Key Insight
Sliding window (fixed)	O(n)	O(1)	Each element enters/leaves once
Sliding window (variable)	O(n)	O(k)	Left pointer never moves backward
Two pointers (sorted)	O(n)	O(1)	Total pointer moves = O(n)
Binary search on answer	O(n log V)	O(1)	V = search space range
Greedy + sort	O(n log n)	O(1)	Sort dominates
Backtracking (subsets)	O(2^n)	O(n)	Decision tree has 2^n leaves
Backtracking (permutations)	O(n!)	O(n)	n choices, then n-1, then n-2...
Prefix sums (1D)	O(n) / O(1)	O(n)	Build once, query O(1)
Prefix sums (2D)	O(mn) / O(1)	O(mn)	Inclusion-exclusion principle

Mistake	Impact	Fix
Off-by-one in binary search	Infinite loop or wrong answer	Test with 1 and 2 element cases
Integer overflow in binary search	Undefined behavior	Use `lo + (hi - lo) / 2`
Not handling duplicates in two pointers	Duplicate triplets/pairs	Skip equal adjacent elements
Greedy without proof	Wrong answer on edge cases	Verify with exchange argument
Shrinking window when non-shrinkable needed	Incorrect answer	Identify which variant applies
Missing base case in backtracking	Infinite recursion	Always check termination first

Algorithm Pattern Master

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Algorithm Pattern Master

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Algorithm Pattern Master

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About this skill.

Pattern Recognition Framework

When to Apply Each Pattern

Sliding Window

Fixed-Size Window

Variable-Size Window (Shrinkable)

Sliding Window with Monotonic Deque

Two Pointers

Opposite Direction (Two Sum on Sorted)

Same Direction (Fast/Slow)

Three Pointers (Three Sum)

Binary Search on Answer

Template: Minimize Maximum

Example: Split Array Largest Sum

Example: Koko Eating Bananas

Greedy Algorithms

Activity Selection / Interval Scheduling

Greedy Proof Template

Jump Game (Greedy Reach)

Backtracking

General Template

Subsets (Power Set)

N-Queens

Prefix Sums

1D and 2D Prefix Sums

Complexity Analysis Quick Reference

Common Pitfalls

Exercises

Process

Output Format

Edge Cases

Example