Pay attention to cost of computation (usually time and space)

Running time of programs depends on “size” of problem input

Doubling Hypothesis is the question “What is the effect on running time if input size is doubled?”

Two kinds of running time analysis:

• Empirical analysis
  • Run your program on differently-sized input sets, each set of input twice as big as the previous set
  • Plot a graph or make a table of running times
  • Guess the doubling effect
• Mathematical analysis
  • Look for nested loops
  • Make rough calculation (use only leading term)
  • Develop approximate expressions

The notation g(n) ~ f(n) means g(n)/f(n)→1 as n → ∞

The notation ~f(n) means all functions g such that g(n)/f(n)→1 as n → ∞

For many programs, the running time satisfies the relationship T(n) ~ cf(n) where c is a constant and f is a function known as the order of growth of the running time.

Typical f are

• 1 — constant
  
• log n — logarithmic
  
• n — linear
  
• n log n — linearithmic
  
• n² — quadratic
  
• n³ — cubic
  
• aⁿ — exponential

• how data (both primitive & reference data) are implemented in java
• the storage space used for each primitive type
• how objects like arrays are initialialized at object construction time