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ZeckendorfsTheorem.java
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ZeckendorfsTheorem.java
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import java.util.Scanner;
import java.util.ArrayList;
//Problem: https://www.reddit.com/r/dailyprogrammer/comments/55zdxx/20161005_challenge_286_intermediate_zeckendorf/
//Formulas from: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html
public class ZeckendorfsTheorem{
static final double PHI = ((Math.sqrt(5)+1)/2);
public static void main(String[] args){
Scanner console = new Scanner(System.in);
ZeckendorfsTheorem zt = new ZeckendorfsTheorem();
int num = console.nextInt();
int[] input = new int[num];
for (int i = 0; i < num && console.hasNextInt(); i++){
input[i] = console.nextInt();
}
for (int i = 0; i < num; i++){
zt.getResult(input[i]);
}
}
void getResult(int num){
int orginalNum = num;
ArrayList<Integer> intList = new ArrayList<>();
while(num != 0){
int fib = getFib(getFloorIndex(num));
intList.add(fib);
num -= fib;
}
//Print out orginalNum and rest of items in intList
System.out.printf("%d = ",orginalNum);
if (intList.size() > 0){
System.out.printf("%d",intList.get(0));
for(int i = 1; i < intList.size(); i++){
System.out.printf(" + %d",intList.get(i));
}
}
System.out.print("\n");
}
//Formulas from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html
int getFloorIndex(int i){
if (i == 3){return 4;}//There is a rounding error for small i.
return (int)Math.floor((Math.log10(i)+Math.log10(5)/2)/Math.log10(PHI));
}
int getFib(int i){
return (int)Math.round(Math.pow(PHI, i)/Math.sqrt(5));
}
}