Learn in dependency order

Contiguous memory, O(1) indexing. The substrate every other structure is built on.

Arrays of characters with immutability quirks and a whole family of matching algorithms.

Trade memory for time. Turns most quadratic scans into a single linear pass.

A preprocessing step that unlocks two pointers, greedy and binary search.

Halve the search space every step. Works on any monotonic predicate, not just sorted arrays.

Two indices moving under an invariant. Converts nested loops into one pass.

A contiguous range that grows on the right and shrinks on the left while a condition holds.

Precompute cumulative aggregates so any range query becomes constant time.

Two dimensional grids: traversal orders, rotations and in-place tricks.

Sort by start or end, then sweep. Covers merging, meeting rooms and scheduling.

Pointer surgery. Cheap inserts, no random access, and a favourite whiteboard test.

LIFO and FIFO. Monotonic variants crack the whole next-greater family.

Recursive structure where almost every solution is solve the children, then combine.

Ordering invariant: left is smaller, right is larger. In-order traversal yields sorted output.

Partially ordered complete tree that hands you the extreme element instantly.

Nodes and edges. Most grid, dependency and network questions are graph questions in disguise.

Take the locally best option and prove it never hurts. Short code, hard proofs.

Build a candidate, recurse, undo. The brute force that all DP is an optimisation of.

Prefix tree that makes autocomplete, dictionary and XOR maximisation problems linear.

Primes, GCD, modular arithmetic, combinatorics and the overflow traps around them.

Compose primitives into a structure that hits required time bounds. The bridge to system design.

Overlapping subproblems plus optimal substructure. Write the recursion, then cache it.

Integers as bit vectors. Sets in 32 bits, XOR tricks and subset enumeration.

Segment trees, Fenwick, LCA and SCC. Rare in SDE loops, decisive in competitive rounds.