Discrete Math CSC151 Analysis of Algorithms

Complexity of Algorithms  In CS it's important to be able to predict how many resources an algorithm will use space (in RAM, on disk) time  Too expensive to implement everything then test it  Too hard to do precise analysis  Want a quick and easy solution

Analysis of a sample program  Linear search start at first item, and compare if it's the right one. Move on to next if not  Searching for 6 in matches!

Analysis of a sample program  Bubble Sort compare each element with its neighbor and swap if they're out of order Pass Pass Pass Pass 4-6 don't change anything.

Analysis of bubble sort  Each comparison requires t1 time  Each exchange requires t2 time  If there are n items, then there are n passes  Pass p requires n-p comparisons  Total time is somewhere between (n-1 + n )*t1 and (n-1 + n )*(t1+t2) time

Analysis of a sample program  Insert Sort take a list of one and add in other elements until they're sorted

Analysis of Insert sort  Each comparison requires t1 time  Each exchange requires t2 time  If there are n items, we must insert n-1 times  Inserting element m requires between 1 and m-1 comparison/exchanges