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Microsoft PowerPoint – CS332-Lec20-ann BU CS 332 – Theory of Computation Lecture 20: • Time/Space Hierarchies • Complexity Class P Reading: Sipser Ch 9.1, 7.2 Mark Bun April 7, 2021 Last Time • Asymptotic notation • Analyzing time / space usage of Turing machines  (algorithms) • Multi‐tape TMs can solve problems faster than single‐ tape TMs 4/7/2021 CS332 ‐ Theory of Computation 2 Time complexity Time complexity of a TM (algorithm) = maximum number of  steps it takes on a worst‐case input Formally: Let  . A TM  runs in time  if on  every input  ,  halts on  within at most  steps A language  if there exists a basic single‐tape  (deterministic) TM  that  1) Decides  , and 2) Runs in time  4/7/2021 CS332 ‐ Theory of Computation 3 […]

PowerPoint Presentation BU CS 332 – Theory of Computation Lecture 18: • Asymptotic Notation • Time/Space Complexity Reading: Sipser Ch 7.1, 8.0 Mark Bun April 5, 2021 Where we are in CS 332 4/5/2021 CS332 – Theory of Computation 2 Automata Computability Complexity Previous unit: Computability theory What kinds of problems can / can’t computers

COMP20007 Design of Algorithms Brute Force Methods Lars Kulik Lecture 5 Semester 1, 2021 1 Brute Force Algorithms Straightforward problem solving approach, usually based directly on the problem’s statement. Exhaustive search for solutions is a prime example. • Selection sort • String matching • Closest pair • Exhaustive search for combinatorial solutions • Graph traversal

COMP2100/COMP6442 Algorithms Part III – Lecture 7] Kin Chau [ Sid Chi 1 What is Dynamic Programming • Dynamic programming (DP) is a general technique • Powerful algorithmic design technique using recursion and memorization • A class of seemingly exponential-time problems may have a polynomial-time solution via DP • Particularly for optimization (min/max) problems (e.g.,