Array operations II manipulating arrays and measuring performance

D. Goforth, COSC 3106, fall Operations on arrays  searching – most common collection operation in computer science search for a value in a collection may succeed or fail basis of all data operations

D. Goforth, COSC 3106, fall Search algorithm int size; double[] data; … int search ( double x ) { for( int index = 0; index < size; index++ ) if ( data[index] == x ) return index; return -1; // signal for “not found” }

D. Goforth, COSC 3106, fall Intelligent searching  if data in the array is in order, the search can be more efficient K K

D. Goforth, COSC 3106, fall Binary search  data must be sorted  search is faster K K

BinarySearch algorithm int size; double[] data; int binarysearch ( double x ) { int low = 0, high = size-1, middle; while (low <= high ) { middle = ( low + high ) / 2; if ( data[middle] == x ) return middle; if ( data[middle] > x ) high = middle – 1; else low = middle + 1; } return -1; // signal for “not found” }

D. Goforth, COSC 3106, fall Sorting data in arrays  for binary search, data must be in order algorithms for sorting data by swapping positions

D. Goforth, COSC 3106, fall Basic swap operation int size; double[] data; double temp; temp = data[4]; data[4] = data[7]; data[7] = temp; temp data 1 2 3

D. Goforth, COSC 3106, fall Selection sort algorithm  find minimum item in array  swap minimum item with first item  repeat to find second item, third, etc. temp data minimum

Selection sort algorithm int size; double[] data; void selectionSort () { for ( int i = 0; i < size-1; i++ ) { int minIndex = i; for ( int j = i+1; j < size; j++ ) if ( data[j] < data[minIndex] ) minIndex = j; double temp = data[minIndex]; data[minIndex] = data[j]; data[j] = temp; }

D. Goforth, COSC 3106, fall Insertion sort algorithm  compare first, second items; rearrange if necessary  place third item properly with first second  repeat for all other items temp data sorted

Insertion sort algorithm int size; double[] data; void insertionSort () { for ( int i = 1; i < size; i++ ) { double temp = data[i]; int j = i-1; while (j >= 0 && data[j] > temp ) { data[j+1] = data[j]; j--; } data[j+1] = temp; }

D. Goforth, COSC 3106, fall Fast search: is it worth the sort?  tradeoff: slow linear search fast binary search BUT extra effort and time to sort data  good tradeoff if ‘many’ searches sort

D. Goforth, COSC 3106, fall Measuring performance of algorithms  performance in time (and space) time – execution time of method space – extra memory used in execution  performance due to coding comparing algorithms (not hardware speed)  dominant performance factor: dependence on collection size

D. Goforth, COSC 3106, fall Measuring performance – predicting algorithm efficiency  count number of executions of statements  watch number increase as collection size increases  what is rate of increase? Performance project

D. Goforth, COSC 3106, fall Performance categories – Big O  approximate measure of rate of increase in execution time with size of collection (or other factors) useful to compare algorithms e.g. – sort algorithms works with ‘random factor’ algorithms e.g. – search, insertion sort

D. Goforth, COSC 3106, fall Performance – big O notation  categories describe performance as approximate function of size linear function O(n) quadraticO(n 2 ) perf n n