Fibonacci
Fibonacci stuff (Base, recursion, for, while)
Base Code
/*
* Creator: Nighthawk Coding Society
* Mini Lab Name: Fibonacci sequence, featuring a Stream Algorithm
*
*/
import java.util.ArrayList;
import java.util.HashMap;
import java.util.stream.Stream;
/* Objective will require changing to abstract class with one or more abstract methods below */
abstract class Fibo {
String name; // name or title of method
int size; // nth sequence
int hashID; // counter for hashIDs in hash map
ArrayList<Long> list; // captures current Fibonacci sequence
HashMap<Integer, Object> hash; // captures each sequence leading to final result
/*
Zero parameter constructor uses Telescoping technique to allow setting of the required value nth
@param: none
*/
public Fibo() {
this(20); // telescope to avoid code duplication, using default as 20
}
/*
Construct the nth fibonacci number
@param: nth number, the value is constrained to 92 because of overflow in a long
*/
public Fibo(int nth) {
this.size = nth;
this.list = new ArrayList<>();
this.hashID = 0;
this.hash = new HashMap<>();
//initialize fibonacci and time mvc
this.init();
}
/*
This Method should be "abstract"
Leave method as protected, as it is only authorized to extender of the class
Make new class that extends and defines init()
Inside references within this class would change from this to super
Repeat process using for, while, recursion
*/
protected abstract void init();
//{
// this.name = "Stream";
// Stream.iterate(new long[]{0, 1}, f -> new long[]{f[1], f[0] + f[1]})
// .limit(this.size)
// .forEach(f -> this.setData(f[0]) );
// }
/*
Number is added to fibonacci sequence, current state of "list" is added to hash for hashID "num"
*/
public void setData(long num) {
list.add(num);
hash.put(this.hashID++, list.clone());
}
/*
Custom Getter to return last element in fibonacci sequence
*/
public long getNth() {
return list.get(this.size - 1);
}
/*
Custom Getter to return last fibonacci sequence in HashMap
*/
public Object getNthSeq(int i) {
return hash.get(i);
}
/*
Console/Terminal supported print method
*/
public void print() {
System.out.println("Init method = " + this.name);
System.out.println("fibonacci Number " + this.size + " = " + this.getNth());
System.out.println("fibonacci List = " + this.list);
System.out.println("fibonacci Hashmap = " + this.hash);
for (int i=0 ; i<this.size; i++ ) {
System.out.println("fibonacci Sequence " + (i+1) + " = " + this.getNthSeq(i));
}
}
/*
Tester class method. If this becomes abstract you will not be able to test it directly ...
Change this method to call "main" class of each of the extended classes
*/
}
Using For Loop
public class FiboForLoop extends Fibo{
// @Override overrides the Fibo init method so a different one can be used instead
@Override
public void init() {
this.name = "For Loop";
// Hardcode for the first two numbers
int fir = 1;
int sec = 1;
this.setData(0);
this.setData(fir);
this.setData(sec);
int amount = this.size - 2;
// for loop used to make the next term be the sum of the previous two terms.
for(int i = 0; i < amount; i++) {
int holder = sec;
sec = sec + fir;
fir = holder;
this.setData(sec);
}
}
static public void main(String[] args){
FiboForLoop forLoop = new FiboForLoop();
forLoop.print();
}
}
FiboForLoop.main(null);
Using While Loop
public class FiboWhileLoop extends Fibo{
// @Override overrides the Fibo init method so a different one can be used instead
@Override
public void init() {
this.name = "While Loop";
// Hardcode for the first two numbers
int fir = 1;
int sec = 1;
this.setData(0);
this.setData(fir);
this.setData(sec);
int amount = this.size - 2;
int i = 0;
// while loop used to make the next term be the sum of teh previous two terms
while(i < amount) {
int holder = sec;
sec = sec + fir;
fir = holder;
this.setData(sec);
i++;
}
}
public static void main(String[] args){
FiboWhileLoop whileLoop = new FiboWhileLoop();
whileLoop.print();
}
}
FiboWhileLoop.main(null);
Using Recursion
public class FiboRecursion extends Fibo{
// @Override overrides the Fibo init method so a different one can be used instead
@Override
public void init() {
this.name = "Recursion";
// Iterating to show the whole sequence
for (int i = 0; i < this.size; i++){
this.setData(Recursively(i));
}
}
public static int Recursively(int size) {
if (size > 2) {
// Calling the function over and over again inside of itself (recursion)
return (Recursively(size - 1) + Recursively(size - 2));
}
// base cases
else if (size == 2) {
return 1;
}
else if (size == 1) {
return 1;
}
else {
return 0;
}
}
public static void main(String[] args){
FiboWhileLoop whileLoop = new FiboWhileLoop();
whileLoop.print();
}
}
FiboRecursion.main(null);
CB Standards:
1.B
Determined how to implement a while loop, for loop, and recursive function to accomplish fibonacci.
4.C
Determined if all 3 algorithms returned the same result through the printed output being the same.
5.A
For and while loops run in O(n) time since they run through the input size once and do a constant amount of operations for each loop. The recursive algorithm takes exponential time, however, since for each term of the sequence, the algorithm needs to recalculate all of the other terms as well due to the nature of recursion.