algorithm analysis totalsum for in rangen rowsum[ (an (bfor in rangen rowsum[irowsum[imatrix[ ,jtotalsum totalsum matrix[ , for in rangen for in rangen figure markup for version one of the matrix summing algorithm(ashows all operations marked with the appropriate time and (bshows only the non-constant time steps choosing the function the function (nused to categorize particular algorithm is chosen to be the dominant term within (nthat isthe term that is so large for big values of nthat we can ignore the other terms when computing big- value for examplein the expression log the term dominates the other terms since for > we have log < log < which leads to time-complexity of ( nowconsider the function ( and assume it is the polynomial that represents the exact number of instructions required to execute some algorithm for small values of (less than )the constant value dominates the functionbut what happens as gets largersay the term becomes the dominant termwith the other two becoming less significant in computing the final result classes of algorithms we will work with many different algorithms in this textbut most will have time-complexity selected from among common set of functionswhich are listed in table and illustrated graphically in figure algorithms can be classified based on their big- function the various classes are commonly named based upon the dominant term logarithmic algorithm is