SUNY Geneseo Department of Computer Science

Conditionals and Logic

Previous Lecture

Misc

Hand out Lab 3

Java clock function = System.currentTimeMillis()

• See Sect. 4.7
• Digression:
  • "Static" members = data or methods associated with class, not an object
    • Named as class.member
  • System is a library class
    • Automatically imported into every program
  • currentTimeMillis is a static method in System
  • out is a static variable in System
    • Handles println, print, etc. messages
  • Also public static void main(...)

Questions?

Conditionals and Logic

Sections 5.1 through 5.5

Terminology and format

• Test
• Action done if true
• Alternative, done if test is false

Testing or fundamental logic

• And
• Or (either or both)
• Exclusive Or (one or the other)
• Negation
  • Is !!p equivalent to p in Java programs?
  • Meanings (semantics) are the same
  • !!p has two operations to perform
  • (!!p == p) will always be true
• Implication (like modus ponens)

Boolean algebra

• Complex truth tables and proofs
• Math rules -- commutativity, associativty, etc.

Correctness

• Proof by cases

Analysis of conditionals

• Time has to be bounded -- best and worst cases
  • And average (not really for this course though)
• Empirical issues -- selecting data to force into worst case, best case, average (tricky)

Examples

The generic search (e.g., search array A of n elements for value x)

• loop until either A[i] = x or i >= n
• But Java (and many other languages) have "while", not "until" -- how do you change the loop?
  • loop while !( either A[i] = x or i >= n )
  • loop while A[i] != x or i < n
  • oops - loop while A[i] != x and i < n
  • DeMorgan's law

Is a point on a cylinder?

• x² + z² = 1 and 0 <= y <= 1
  • or y = 0 and x² + z² < 1
  • or y = 1 and x² + z² < 1
• Lots of places in this expression to write the logic differently -- factoring common terms out of some expressions (distributive law), replacing explicit logic with conditional statements, etc.

Next

Introduction to Recursion

Read Sec. 6.1

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