notes11 - Goal of Asymptotle Analysis Find out how an...

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Find out how an algorithm behaves in the worst case and when n -> (infinity) The function O(f(n)) should be as small as possible example 7n -b is O(n) bust also O(n^2) or O(n^3) but we choose O(n) because it better discribes 7n-b process drop the lowest order terms and construct functions from the function: 7n-3 -> O(n) 8n^2 * log(n)+5n^2+n -> O(n^2log(n)) special cases: O(log n)->logarithmic time O(n)->linear time O(n^2)->quadratic time O(n^k)->polynomial time O(a^n)->exponential time (n>0) Bubble Sort: void bubblesort (int n, int* array){ for(int i=0;i<n-1;i++){ for(int j=0;j<n-i-1;j++){ int tmp = array[j]; array[j]=arrray[j++]; array[j+1]=tmp; } } } } -assume the operations check the array values and swap is done in O(1) In the worst case the swap and if statements are exectuted in (n-1)*n/2 = n^2/2- n/2=O(n^2) operations. Execution times Bubble sort: O(n^2) Heap sort O(n log(n)) Merge sort O(n log(n)) Stacks 2 basic methods: push(0) push items to top of the stack
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This note was uploaded on 02/02/2012 for the course CS 251 taught by Professor Staff during the Fall '08 term at Purdue University.

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notes11 - Goal of Asymptotle Analysis Find out how an...

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