COM S 228Algorithms and Analysis

Instructor: Ying Cai

Department of Computer ScienceIowa State Universityyingcai@iastate.eduOffice: Atanasoff 201

Algorithm

An algorithm is a strategy for solving a problem, independent of the actual implementation

Which algorithms are faster Implement both algorithms and measure them with a stopwatch or count CPU cyclesThis approach has several problems The system may be running other applications, which share the same CPU

Many other factors impact the speed Memory swapping Garbage collection

Both must be implemented, which is often not practical

It is unclear how the algorithms scale when you give a faster CPU

Time Complexity (Run Time)The time complexity of an algorithm is a function that describes the number of basic execution steps in terms of the input sizeWe express time complexity using Big-O notation

Algorithm: Sequential Search

Basic idea

Pseudocode

The running time of the sequential search depends on the particular values in A. If v is the first item, it takes one step; If v is not present, which is the worst case, it takes T(n) = 3n+3. The worst-case time complexity of this algorithm is O(n), or “big-O of N”

Notion of O(f(n))

Notion of O(f(n))

Notion of O(f(n))

Array Equality Revisited

Algorithm 1

In the worst case, this algorithm needs to search the entire array B for A[i]

Array Equality Revisited

Algorithm Analysis in Practice

In practice, algorithm analysis is seldom done at the level of detail as we have done so far

Example 1

void printAll(int[] array) {

for (int i=0; i< array.length; i++)

{System.out.println(array[i]);

}}

Example 2

// assuming array.length >= 1000void sumDouble(double [] array) {

double sum = 0.0;for (int i=0; i< 1000; i++) {

sum = sum + i;}

}

Example 3

for (int i =0; i< array.length; i++) {

method1(); // take O(n)method2(); // takes O(n2)

}

Example 4

Practical Implication of Asymptotic Analysis

Computation Time