Brute2Best · DSA Pattern Mastery (30 Core Patterns)

The 30 Core DSA Patterns: Pattern-Based Problem Solving & Questions

Stop memorising disconnected LeetCode problems. Learn to solve the unseen: every question is taught as an unbroken chain of reasoning — discover the repeated work, define the invariant, and write verified C++23 code.

Overall DSA Progress440 Total

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30 Core Patterns122 Sub-patterns

The 6-Step Thinking Blueprint

Full Blueprint & Decision Tree

01

Recognise

Which words & constraints point to a pattern?

02

Brute force

What is the obvious slow solution?

03

Repeated work

What does brute force recompute again & again?

04

State + validity

What invariant do I maintain, and when is it valid?

05

Transitions

When do I move which pointer, and why is it safe?

06

Code + test

Write modern C++23, dry-run edge cases & compare.

Algorithmic Mental Model

6-Step Thinking Blueprint & Clue Tree

Recognise → brute force → repeated work → state → transitions → test, plus the visual clue-to-pattern decision tree.

Featured Guided Lesson

Arrays & Hashing

Use a hash map or set to remember what you have already seen, so you never search the array twice.

Categories:Arrays & Strings5 Stacks & Intervals4 Linked Lists2 Trees3 Heaps3 Graphs4 Recursion & Greedy2 Dynamic Programming6 Math & Bits1

Arrays & Strings

(5 patterns)

Arrays & Hashing

When to use:"Have I seen X before?", pairs that add up to a target, grouping things that look alike, counting occurrences.

4 sub-patternsOpen

Two Pointers

When to use:Sorted array, pairs/triplets with a target, comparing from both ends, compacting an array in place.

4 sub-patternsOpen

Sliding Window

When to use:Contiguous subarray / substring + longest, shortest, maximum, count, or "of size K".

6 sub-patternsOpen

Prefix Sum

When to use:Range sums, "subarray sum equals K" (especially with negatives), equal counts, divisible by K.

5 sub-patternsOpen

Binary Search

When to use:Sorted data, "minimum X such that…", "maximum X such that…", rotated arrays, answers that are monotonic (if X works, X+1 also works).

4 sub-patternsOpen

Stacks & Intervals

(4 patterns)

Stack

When to use:Matching pairs, nested structure, undo, evaluating expressions, "the last one wins".

3 sub-patternsOpen

Monotonic Stack

When to use:Next/previous greater or smaller element, spans, histogram areas, "for each element, how far does it dominate?"

5 sub-patternsOpen

Intervals

When to use:Input is [start, end] pairs; overlap, merge, insert, meeting rooms, free time, minimum removals.

4 sub-patternsOpen

Cyclic Sort

When to use:Numbers in range 1..n or 0..n, find missing / duplicate / both, O(1) extra space.

3 sub-patternsOpen

Linked Lists

(2 patterns)

Linked List — Fast & Slow

When to use:Cycle detection, middle of list, "n-th from end", two lists meeting, repeating sequences.

3 sub-patternsOpen

Linked List — Reversal

When to use:Reverse whole / part / every k nodes, reorder, palindrome check, numbers stored as lists.

4 sub-patternsOpen

Trees

(3 patterns)

Tree BFS

When to use:Level order, per-level max/average, right side view, minimum depth, nodes at distance k.

4 sub-patternsOpen

Tree DFS

When to use:Paths, heights, diameters, validating structure, ancestors, anything "for every subtree".

6 sub-patternsOpen

Trie

When to use:Many words + prefix search, autocomplete, word dictionary with wildcards, maximum XOR.

3 sub-patternsOpen

Heaps

(3 patterns)

Heap — Top K

When to use:"K largest / smallest / most frequent / closest", kth element, streaming top-K.

4 sub-patternsOpen

Two Heaps

When to use:Running median, sliding median, choosing from two pools (available vs locked).

3 sub-patternsOpen

K-way Merge

When to use:K sorted lists/arrays, kth smallest across sorted rows, smallest range covering all lists.

3 sub-patternsOpen

Graphs

(4 patterns)

Graph BFS / DFS

When to use:Grid of cells, islands, regions, "minimum steps", transformations between states, connected components.

6 sub-patternsOpen

Topological Sort

When to use:Prerequisites, dependencies, build order, "can all courses be finished?", ordering letters from sorted words.

4 sub-patternsOpen

Union-Find (DSU)

When to use:Edges arrive one by one, "are these connected?", merge equivalent items, count components, extra edge creating a cycle.

4 sub-patternsOpen

Shortest Paths (Weighted)

When to use:Weighted edges, "minimum cost / time / effort", at most K stops, negative weights, all-pairs distances.

3 sub-patternsOpen

Recursion & Greedy

(2 patterns)

Backtracking

When to use:"All subsets / permutations / combinations", place items under rules (N-Queens, Sudoku), find a path in a grid.

7 sub-patternsOpen

Greedy

When to use:Maximise count / minimise cost with a natural "best next step", sorting makes the choice obvious, reachability.

6 sub-patternsOpen

Dynamic Programming

(6 patterns)

DP — 1D Linear

When to use:"Number of ways", "maximum/minimum up to i", choices at each step that depend on the previous one or two.

3 sub-patternsOpen

DP — Kadane / Subarray

When to use:Maximum (or minimum) sum/product of a contiguous subarray, stock buy/sell, circular arrays.

4 sub-patternsOpen

DP — Knapsack

When to use:Pick a subset to hit a target sum / capacity, partition into two groups, count the ways to reach an amount.

4 sub-patternsOpen

DP — Longest Increasing Subsequence

When to use:Longest chain where each item must be bigger/fit inside the previous one (numbers, pairs, envelopes, words).

3 sub-patternsOpen

DP — Grid

When to use:Move only right/down, count paths, minimum path cost, largest square of 1s.

2 sub-patternsOpen

DP — Strings

When to use:Longest common subsequence, edit distance, palindromes, matching with wildcards, interleaving.

4 sub-patternsOpen

Math & Bits

(1 patterns)

Bit Manipulation

When to use:"Every element appears twice except…", power of two, counting set bits, subsets as bitmasks, O(1) space tricks.

4 sub-patternsOpen