Runtime Analysis

1
Runtime Analysis

• CSC 172
• SPRING 2004
• LECTURE 4

2
General

• Project is Due Friday visit the writing center
• Slides are on
• http//www.cs.rochester.edu/pawlicki/CSC172SP04
• Start reading Weiss Chapter 6 (this week next)

3
BEST PICTURE?

• The Lord of the Rings The Return of the King
• Lost in Translation
• Master and Commander The Far Side of the World
• Mystic River
• Seabiscuit

4
Runtime of programs

• Measure some size of the input
• the value of some integer
• The length of a string or array

5
Program Analysis

• Basis cases (simple statements) constant time
• Assignments
• Break, continue, return
• System.in.println()
• Induction
• Loops
• Branching (if, if-else)
• Blocks .

6
Blocks

• Blocks Running time bound is the sum of the
  bounds of the consitutents
• Use summation law to drop from the sum any term
  that is Big-Oh of another term

7
Conditionals

• Bound is O(1)larger of the bounds for the then
  and else clauses
• O(1) for the cost of the test

8
Loops

• Bound is usually the maximum number of times
  around the loop times the bound on the body of
  the loop.
• We must include O(1) for the increment and test
  each time around a loop
• The possibility exists that the loop executes 0
  times, this costs O(1) for the initialization and
  the first test

9
Structure Tree

• Nodes are complex statements
• Children are constituent statements

10

• public String int2bin(int n)
• String rval
• while (ngt0)
• if((n2) 1)
• rval 0
• else
• rval 1
• n/2
• return rval

1 2 3 4 5 6 7 8 9
O(log2n)
1-9
O(1)
O(1)
O(log2n)
2-8
9
1
log2n times
3-7
O(1)
O(1)
O(1)
3-6
7
O(1) max
6
4
O(1)
O(1)
11
Reductions

• Use summation law to drop from the sum any term
  that is Big-Oh of another
• O(1) O(1) O(1)
• O(1) O(log2i) O(1) O(log2i)
• Looping
• O(1) log2i O(log2i)