Assignment/Homework #1 COP-3530, Fall 2015

Instructor: Dr. Antonio L. Bajuelos

Rules & Instructions:

This assignment has 3 problems.

Due date: Thursday, September 10th, 2015 at 4 pm (Eastern Time)

The assignment/homework will be submitted by email to abajuelo@fiu.edu

Your submission must be a ZIP file (not RAR format). Please name your submission

as 1_xxxxxxx.zip, where xxxxxxx is your seven digit Panther ID number).

Please indicate in the subject of your email message the following information:

COP-3530, SECTION U02, ASSIGNMENT #1

Please include the following header in every Java program:

/*******************************************************

Program Number: A1_<problem # (ranging from 1 to 2) >

Purpose/Description: <a brief description of the program>

Author: <your name>

Due date: <mm/dd/yy>

Certification:

I hereby certify that this work is my own and none of it is the work of

any other person.

< your full name >

*******************************************************/

Submissions turned in after the due date and/or which don’t meet the

established formatting rules will not be accepted.

Problem #1.

The Fibonacci sequence {fib}i≥1 is defined recursively as follows:

fib(1) = fib(2) = 1 and, fib(n) = fib(n-1) + fib(n-2) for n ≥ 3.

The numbers in the Fibonacci sequence are called the Fibonacci numbers, for example:

{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…}

Implement a sub-linear time complexity function in Java

int fib(int n)

that returns the nth Fibonacci number.

Problem #2.

(a) Implement a recursive search function in Java

int terSearch(int arr[], int l, int r, int x)

that returns location of x in a given array arr[l…r] if x is present, otherwise -1.

The terSearch search function, unlike the binary search, must consider two dividing points

int d1 = l + (r - l)/3

int d2 = d1 + (r - l)/3

(b) What is the running time complexity of your function? Justify.

Problem #3.

The input is an N by N matrix of nonnegative integers that is already in memory. Each

individual row is increasing from left to right. Each individual column is increasing from top to

bottom. Propose an O(N) wort-case algorithm that decides if a number x is in the matrix.