Question

Need an anylasis explaing the code: Let a and n be both nonnegative integers. Consider the problem of calculating the nth power of a: an.

 Present a brute-force algorithm for the calculation and show the number of multiplications performed overall.

 Develop a recursive reduce-by-one algorithm for the calculation, establish and solve the recurrence relation for the number of multiplications performed overall.

 Develop a transform-and-conquer algorithm for the calculation. Describe your idea used in the transformation. Evaluate your algorithm to determine the number of multiplications performed overall.

Test your algorithms in Java at

http://codingbat.com/prob/p158888

Compare the results of your three solutions and assess which does more or less work.

Submission Requirement:

 Submit your algorithms in Java as an attachment in a text document on Blackboard. Your method should use the signature as follows:

public int powerN(int base, int n) {

}

 Submit your analysis in a typed document as an attachment in pdf or Microsoft Word format on Blackboard online before the due time.