Concepts7
Complexity Analysis Quick Reference
Use an operation budget of about 10^8 simple operations per second on typical online judges; always multiply by the time limit and number of test files if known.
Debugging Strategies for CP
Systematic debugging beats guesswork: always re-read the statement, re-check constraints, and verify the output format before touching code.
Small-to-Large Principle
Small-to-large means always merge the smaller container into the larger one to keep total work low.
Breadth-First Search (BFS)
Breadth-First Search (BFS) explores a graph level by level, visiting all vertices at distance d from the source before any at distance d+1.
0-1 BFS
0-1 BFS is a shortest path algorithm specialized for graphs whose edge weights are only 0 or 1.
Prefix Sum and Difference Array
Prefix sums precompute running totals so any range sum [l, r] can be answered in O(1) time as prefix[r] - prefix[l-1].
Sorting Algorithms
Sorting arranges items into a chosen order so that searching, grouping, and further algorithms become faster and simpler.