Algorithms

Parsing nested structures, simulations that interact with the previous element, monotonic stacks, greedy deletion for the smallest string, and a lazy-deletion Max Stack

Circular queues, zigzag iterators, FIFO matching with cancellation, and the data structure combinations that design problems keep using

GCD, primality tests, the sieve of Eratosthenes / linear sieve / smallest prime factor (SPF), connecting numbers by prime factors with Union-Find, and splitting an array by the last occurrence of prime factors

Merge sort templates, where to count in inversion-style problems, the linked list version, and common mistakes

Combinatorial counting (pairs, ways to split), building the k-th permutation digit by digit, geometry (nearest point, law of cosines, triangle inequality), problems that become formulas after sorting or an observation, plus carry arithmetic, base conversion and fast exponentiation

One-dimensional DP, state-machine DP, DP with a monotonic deque, interval scheduling DP after sorting, deduplicated subsequence counting, and DP-tagged problems where an observation or greedy is faster

Interval DP (choose the last step / merge equal ends), partition DP into k segments, palindrome tables plus partitioning, and memoizing the whole state when it is too tangled to split

heapq basics, Top-K, lazy deletion, two heaps, k-way merge, sweep line, and Dijkstra

Sort then scan, intervals sorted by right end, left and right passes, pairing and parity invariants, adjacent differences, and “remove what exceeds the average”, each with why greedy is correct

Lower / upper bound, binary search on the answer, k-th smallest, integer roots, and why the two interval styles must not be mixed

Connected components, grid flood fill, multi-source BFS, state-space BFS, shortest cycles, and recursion depth in DFS

The choose, recurse, undo template for subsets, permutations, constrained placement, grid search, and pruning