chimera

Breadth-first search — shortest path on unweighted graphs, level-order traversal, and the `visited` discipline that prevents O(2^n) blowups.

Binary search invariants, half-open intervals, and the `lo<hi` template that beats off-by-one bugs.

Depth-first search — recursive vs iterative, recursion-depth gotchas, three-color cycle detection, topological sort.

Dynamic programming — state design, memoization vs tabulation, dimension-reduction, and when DP is the wrong tool.

Pick the right traversal — BFS for unweighted shortest path, Dijkstra for weighted, A* for goal-directed, 0/1-BFS for binary weights.

Greedy algorithms — exchange-argument proofs, when greedy beats DP, classic patterns (interval scheduling, Huffman, scheduling).

Hash maps and sets — when O(1) lookup pays off, hash collisions, frozen keys, and hashing custom types.

Number-theory and bit-twiddling cheat-sheet — gcd, modular exponentiation, sieve, popcount, divisor enumeration, fast prime tests.

Recursion — base case, recursive case, recursion-depth limits, tail vs non-tail, when to convert to iteration.

Sliding window — fixed and variable size, expand-shrink invariant, hash-state-tracking for substring problems.

Sorting — when to call the built-in, when to roll your own (counting / radix / heap), stability, custom comparators.

String algorithms cheat-sheet — KMP, Rabin-Karp rolling hash, Z-array, suffix arrays, anagram patterns, and when to use built-ins.

Two-pointer scans — opposite ends, same direction, fast/slow — for sorted arrays, partitioning, cycle detection.