Key ideas from last time

• what computer science is not
• instead, c.s. is the study of algorithms
• algorithm: well-ordered sequence of unambiguous,
  effectively computable operations... (that halts!)
• algorithm can be formalized, transmitted to computing agent
  that does not understand problem
• abstraction: black-box analogy

Pseudocode for expressing algorithms

• why not natural language?
  • too verbose
  • does not visually indicate structure
  • context-dependent
  • inherently ambiguous
• why not concrete programming language?
  • too much emphasis on syntax
  • for human reader, requires familiarity with quirks of p.l.

Pseudocode is a compromise

1. natural language ⇒ pseudocode ("algorithm discovery")
2. pseudocode ⇒ programming language

• import of readability / ease of visualization
• pseudocode not formal: be consistent, but tune
  depending on kind of problem and intended audience
• why is it unrealistic to program in pseudocode?

Sequential operations

• computation: "assignment" of arithmetic expression to variable
• mailbox analogy for variables
• assume standard arithmetic ops are "primitive"
• examples:

    f ← 9c/5 + 32
    i ← i + 1
  



• input/output: need not be numeric nor of same kind
• abstraction again: we ignore details of input/output

Example: Compute average of 3 values

  get input values x, y, z
  sum ← x + y + z
  avg ← sum / 3
  print avg

Conditional operations

• decisions rather than straight-line calculations
• compound: refers to other, simpler ops
• if-then-else (sometimes we ignore else)

  get input value n
  if n divided by 2 has no remainder then
    print "even!"
  else
    print "odd!"

• "else" may be on its own line for visual formatting

Iterative operations

• repetition - where computation gets interesting
• without loops - algorithms must halt!
• with loops - even small ones might not
• loop also compound; in fact it contains conditional
  or else it must be infinite

  get input value n
  p ← 1
  i ← 1
  while i ≤ n:
    p ← p * i
    i ← i + 1
  output value p

Bottom-up reductionism

• believe it or not: that's all there is!
• from basic arithmetic, conditional, and iterative ops:
  any algorithm can be constructed
• challenge yourself to find counterexample