Lecture Notes for ENGR 213 - Discrete Structures-Comp Appl with Wang at Christopher Newport (CNU)

Notes Information

Material Type:Class Note
Class:ENGR 213 - Discrete Structures-Comp Appl
University:Christopher Newport University
  • Either...or
  • Contrapositive
  • Proposition
  • Propositional
  • Exclusive Or
  • Conjunction
  • Definitions
  • Necessary Condition
  • Consequence
  • Sufficient Condition
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Logic, Sets Section 1.1 Logic Logic 2 Introduction Applications of discrete mathematics: Formal Languages (computer languages) Digital Circuits Compiler Design Data Structures Computability Algorithm Design Relational Database Theory Complexity Theory (counting) Logic 3 Example (counting) The Traveling Salesman Problem, important in Circuit design Many other CS problems Given: n cities c 1 , c 2 , . . . , c n Distance between city i and j, d ij Find the shortest tour. Logic 4 Example (cont) Assume a very fast PC: 1 flop = 1 nanosecond = 10 -9 sec. = 1,000,000,000 ops/sec = 1 GHz. A tour requires n-1 additions. How many different tours? Choose the first city n ways, the second city n-1 ways, the third city n-2 ways, etc. Logic 5 Example (cont) # tours = n (n-1) (n-2) . . . .(2) (1) = n! (Combinations) Total number of additions = (n-1) n! (Rule of Product) If n=8, T(n) = 7.8! = 282,240 flops < 1/...

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