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An examination of Program 7 means that it takes less time to sort n numbers that are already in nondecreasing order than when they are not. 3. What computer is the program going to be run on? The time is less on a fast computer and more on a slow one. 4. What programming language and compiler will be used? These influence the quality of the computer code generated for the algorithm. To resolve the first two question, we ask for the worst case or average time as a function on instance size. The worst case size for any instance size n is defined as TW (n) = max{t(I ) | I is an instance of size n}.

Using the first possibility, we can decompose the instance (10,18,8,12,9) into any of the following pairs of instances: (a) (b) (c) (d) (10,18,8,12) (9) (10) (18,8,12,9) (10,18,8,9) (12) (10,18,12,9) (8) and so on. Suppose we choose the first option. Having decomposed the initial instance into two, we must sort the two instances and then combine the two-sorted sequences into one. When (10,18,8,12) is sorted, the result is (8,10,12,18). Since the second sequence is of size 1, it is already in sorted order.

Usually good algorithm Algorithm that generally provides optimal solutions using a small amount of computing resources. At other time, the resources required may be prohibitively large. IN ORDER to get a computer to solve a problem, it is necessary to provide it with a sequence of instructions that if followed faithfully will result in the desired solution. This sequence of instructions is called a computer algorithm. , a programming language), it is called a program. The topic of computer algorithms deals with methods of developing algorithms as well as methods of analyzing algorithms to determine the amount of computer resources (time and memory) required by them to solve a problem and methods of deriving lower bounds on the resources required by any algorithm to solve a specific problem.