COM S 228 Algorithms and Analysis Instructor: Ying Cai Department of Computer Science Iowa State University Office: 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 cycles This 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 size We 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))
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 >= 1000 void 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