Execution Performance

1. Execution Performance • Space complexity • Time complexity

2. Space Complexity • The amount of memory that a program needs to run to completion • Instruction space • Data space • Environment space

3. Time Complexity • The amount of computer time a program needs to run to completion • Only attempts to estimate run time • Approaches: • Identify one or more key operations and determine the number of times that they are performed • Determine the total number of steps executed by the program

4. Operation Counts • To estimate the time complexity of a program • Identify one or more operations, such as add, multiply, and compare, and determine how many times each is performed • Select the operations that contribute most to the time complexity

5. Asymptotic Behavior • To predict the growth in run time as the problem size increases • Compare the time complexities of two or more programs

6. Large Problem Size • Asymptotic notation describes the behavior of the time or space complexity for large instance characteristics • The notation f(n) = O(g(n)) means that f(n) is asymptotically smaller than or equal to g(n) • In an asymptotic sense, g(n) is an upper bound for f(n).

7. Common running time (common order of magnitude) The order (in the descending order of efficiency: O(1) < O(logn) < O(n) < O(nlogn) < O(N2) < O(n3) <O(rn)

8. Running Time: T = function(n)

9. Running time in Big O notation Drop constants, coefficients Only care how T changes with input size, N Several categories of running time O(1), O(n), O(N2), O (logn) … etc. Figure 2.9 Table 2.5