chap algorithm analysis further reading pioneering works on algorithm analysis include the art of computer programming by donald knuth [knu knu ]and the design and analysis of computer algorithms by ahohopcroftand ullman [ahu the alternate definition for ohm comes from [ahu the use of the notation " (nis in ( ( ))rather than the more commonly used " (no( ( )) derive from brassard and bratley [bb ]though certainly this use predates them good book to read for further information on algorithm analysis techniques is compared to whatby gregory rawlins [raw bentley [ben describes one problem in numerical analysis for whichbetween and the complexity of the best known algorithm had decreased from ( to ( for problem of size this is roughly equivalent to the speedup achieved from all advances in computer hardware during the same time period while the most important aspect of program efficiency is the algorithmmuch improvement can be gained from efficient coding of program as cited by frederick brooks in the mythical man-month [bro ]an efficient programmer can often produce programs that run five times faster than an inefficient programmereven when neither takes special efforts to speed up their code for excellent and enjoyable essays on improving your coding efficiencyand ways to speed up your code when it really matterssee the books by jon bentley [ben ben ben the situation described in example arose when we were working on the project reported on in [su as an interesting asidewriting correct binary search algorithm is not easy knuth [knu notes that while the first binary search was published in the first bug-free algorithm was not published until bentley ("writing correct programsin [ben ]has found that of the computer professionals he tested could not write bug-free binary search in two hours exercises for each of the five expressions of figure give the range of values of for which that expression is most efficient graph the following expressions for each expressionstate the range of values of for which that expression is the most efficient log log /