Hello World! An Invitation to Computer Science

Lecture slides on algorithms applied to lists

Thursday, January 31, 2008

Key ideas from last time

• pseudocode: what and why
• sequential operations: "straight-line" instructions
    computation: variable assignment, primitive arithmetic operations
    input/output (with details abstracted away)
• conditional operations for decision making
• iterative operations for specifying lots of work in small space
    with power comes responsibility - algorithms may not halt!
• bottom-up reductionism: complex algorithms constructed from simpler pieces

Division via repeated subtraction

  input dividend, divisor
  quotient ← 0
  remainder ← dividend
  while remainder &ge divisor:
    remainder ← remainder - divisor
    quotient ← quotient + 1
  output quotient, remainder

Algorithms that operate on lists

• "real" algorithms rarely operate on just one or two pieces of data


• analogy: consecutively numbered mailboxes

  McNulty	Kema	Lester	Bunk
  1	2	3	4



• analogy: playing cards

Adding numbers on a list

  input n; L1, L2, ... Ln
  sum ← 0
  i ← 1
  while i ≤ n:
    sum ← sum + Li
    i ← i + 1
  output sum

Sequential search

  input n; L1, L2,  ... Ln; x
  found ← false
  i ← 1
  while not found and i ≤ n:
    if Li = x:
      found ← true
    else:  
      i ← i + 1
  output found

Observe: Boolean variables and conjunction

Finding largest item on a list

  input n; L1, L2,  ... Ln
  max ← L1
  i ← 2
  while i ≤ n:
    if Li > max:
      max ← Li
    i ← i + 1
  output max

Why do we assume n > 0 and start i at 2?

Where analogies break down

• solving problems on computers differs from solving in physical-world
• throwing away v. overwriting
• moving v. copying
• digital copies are perfect and close to free

Pattern matching

• important concept throughout computer science
• can be used on numbers, DNA, text, images, and more
• algorithm in 2.3.4 is simple (not very efficient)
• "nested" loops
• algorithmic development employs abstraction and top-down design
• eventually need to get very specific
    "cannot assume common sense in a computer system"