matrix recall that the product ab is defined so that [ [jwhat is the running time of your methodc- suppose each row of an array consists of ' and ' such thatin any row of all the ' come before any ' also suppose that the number of ' in row is at least the number in row for , assuming is already in memorydescribe method running in (ntime (not ( )for counting the number of ' in - describe recursive method for computing the nth harmonic numberprojects - implement prefixaverages and prefixaverages from section and perform an experimental analysis of their running times visualize their running times as function of the input size with log-log chart - perform careful experimental analysis that compares the relative running times of the methods shown in code fragments notes the big-oh notation has prompted several comments about its proper use [ knuth [ defines it using the notation (no( ( ))but says this "equalityis only "one way we have chosen to take more standard view of equality and view the big-oh notation as setfollowing brassard [ the reader interested in studying average-case analysis is referred to the book by vitter and flajolet [ we found the story about archimedes in [ for some additional mathematical toolsplease refer to appendix