in terms of and cwhich are the number of rows and columns in the puzzleand wwhich is the number of wordswhat are the running times of the algorithms described in suppose the word list is presorted show how to use binary search to obtain an algorithm with significantly better running time suppose that line in the binary search routine had the statement low mid instead of low mid would the routine still workimplement the binary search so that only one two-way comparison is performed in each iteration suppose that lines and in algorithm (fig are replaced by algorithm analysis int maxleftsum maxsumrecaleftcenter )int maxrightsum maxsumrecacenterright )would the routine still workthe inner loop of the cubic maximum subsequence sum algorithm performs ( + )( + )/ iterations of the innermost code the quadratic version performs ( )/ iterations the linear version performs iterations what pattern is evidentcan you give combinatoric explanation of this phenomenonreferences analysis of the running time of algorithms was first made popular by knuth in the threepart series [ ][ ]and [ analysis of the gcd algorithm appears in [ another early text on the subject is [ big-ohbig-omegabig-thetaand little-oh notation were advocated by knuth in [ there is still no uniform agreement on the matterespecially when it comes to using (many people prefer to use ()even though it is less expressive additionallyo(is still used in some corners to express lower boundwhen (is called for the maximum subsequence sum problem is from [ the series of books [ ][ ]and [ show how to optimize programs for speed ahoj hopcroftand ullmanthe design and analysis of computer algorithmsaddison-wesleyreadingmass bentleywriting efficient programsprentice hallenglewood cliffsn bentleyprogramming pearlsaddison-wesleyreadingmass bentleymore programming pearlsaddison-wesleyreadingmass knuththe art of computer programmingvol fundamental algorithms ed addison-wesleyreadingmass knuththe art of computer programmingvol seminumerical algorithms ed addison-wesleyreadingmass knuththe art of computer programmingvol sorting and searching ed addisonwesleyreadingmass knuth"big omicron and big omega and big theta,acm sigact news ( ) -