Concepts6
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.
Bitset Optimization
Bitset optimization exploits word-level parallelism so one CPU instruction processes 64 bits at once on typical 64-bit machines.
NP-Completeness
NP-completeness classifies decision problems that are both in NP and as hard as any problem in NP via polynomial-time reductions.
Complexity Theory
Complexity theory classifies problems by the resources required to solve or verify them, such as time and memory.
Meet in the Middle
Meet-in-the-middle splits a hard exponential search into two halves, enumerates each half, and then combines results efficiently.
Knapsack Problems
Knapsack problems ask how to pick items under a weight (or cost) limit to maximize value or to check if a target sum is reachable.