DSA · THE PATH

The Path

Novice → Studied → Expert · the 22 mental models behind senior DSA reasoning

22mental models

58problems

0/22complete

I

NOVICEfoundations

II

STUDIEDpatterns

III

EXPERTmastery

PHASE 1

PHASE 2

PHASE 3

01currently studyingArrays & StringsThink about in-place manipulation — how do you rewrite an array without extra space?Read the fundamentals →

344Reverse String

026Remove Duplicates from Sorted Array

088Merge Sorted Array +1 more

02upcomingHash Maps & SetsTrading space for time — find what you need in O(1) by remembering what you've seen.Read the fundamentals →

217Contains Duplicate

387First Unique Character in a String

001Two Sum +1 more

03upcomingTwo PointersTwo pointers converge — eliminate the need for nested loops by moving inward together.Read the fundamentals →

027Remove Element

167Two Sum II - Input Array Is Sorted

011Container With Most Water +1 more

04upcomingSliding WindowExpand your window until it's invalid, then shrink from the left. The window remembers what you've seen.Read the fundamentals →

643Maximum Average Subarray I

003Longest Substring Without Repeating Characters

05upcomingLinked ListsPointer manipulation — you can restructure any linked list in-place if you can visualize the pointer dance.Read the fundamentals →

206Reverse Linked List

021Merge Two Sorted Lists

141Linked List Cycle

06upcomingStack & QueueLIFO vs FIFO — when the order you process things determines correctness, reach for a stack or queue.Read the fundamentals →

232Implement Queue using Stacks

020Valid Parentheses

155Min Stack +1 more

07upcomingRecursion & Backtracking IntroTrust the recursion. At each step, make a choice, explore, then undo it. The decision tree writes itself.Read the fundamentals →

509Fibonacci Number

08upcomingBinary SearchEliminate half the search space every step. You don't search — you shrink until only one answer remains.Read the fundamentals →

704Binary Search

035Search Insert Position

278First Bad Version +1 more

09upcomingBinary TreesEvery tree problem is a conversation between a node and its subtrees. Trust the recursion to handle the children.Read the fundamentals →

226Invert Binary Tree

10upcomingBinary Search TreesThe BST property gives you direction — at every node you know exactly which subtree to enter.Read the fundamentals →

11upcomingHeaps & Priority QueuesA heap always has the answer at the top — maintain sorted order dynamically without re-sorting everything.Read the fundamentals →

12upcomingGraphs - Fund. + DFSGraphs are tree recursion with 4 neighbors instead of 2 — master the representation first, then let DFS loose.Read the fundamentals →

200Number of Islands

695Max Area of Island

133Clone Graph +3 more

13upcomingGraph Traversal — BFSBFS explores level by level — if you need the shortest path in an unweighted graph, BFS finds it first.Read the fundamentals →

14upcomingAdvanced Graph AlgorithmsTopological sort orders dependencies. Union-Find groups components. Dijkstra finds the cheapest path.Read the fundamentals →

15upcomingBacktracking Deep DiveNow you add constraints. The mountain climber knows which paths lead nowhere and prunes them early.Read the fundamentals →

16upcomingDynamic Programming — 1DCache overlapping subproblems. If you've solved it before, don't solve it again — look it up.Read the fundamentals →

17upcomingDynamic Programming — 2DTwo-dimensional state: the answer at grid[i][j] depends on previously computed cells. Build bottom-up.Read the fundamentals →

18upcomingGreedy AlgorithmsMake the locally optimal choice at every step. When the greedy choice is provably safe, you never need to look back.Read the fundamentals →

19upcomingIntervalsSort by start time. Then decide: does this interval overlap with the last? Merge, skip, or insert.Read the fundamentals →

20upcomingTriesA trie is a tree where each path spells a word. Share prefixes, branch at differences.Read the fundamentals →

21upcomingMath & GeometryMatrix problems reward in-place thinking. Identify the transformation pattern before touching any cell.Read the fundamentals →

22upcomingBit ManipulationXOR cancels duplicates. AND masks bits. Shift multiplies or divides by two. Think in binary.Read the fundamentals →