Algorithmic Paradigms

Sizing the search space, subsets and permutations, backtracking, pruning, meet in the middle, and iterative deepening.

Proving a greedy choice with exchange arguments, choosing the sort key, and cases where greedy fails.

Merge sort as the template, counting inversions, closest pair, and Karatsuba.

Choosing states and transitions, memoization vs bottom-up, and counting the state space.

Knapsack, coin change, LIS, edit distance and LCS, interval DP, bitmask DP, and tree DP.

Rolling arrays, loop order, monotonic deque and prefix-max transitions, and when not to optimize.

Monotone predicates, feasibility checks, integer and floating-point loops, and minimize-the-maximum problems.

Sorting events, interval merging and overlap, maximum concurrency, segment intersection, and coordinate compression.