First 100 of Fibonacci

Question: Write a function that computes the list of the first 100 Fibonacci numbers.

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Use BigInteger

Java's int type is a 32-bit sized primitive type that has a maximum of 2,147,483,647. Since our fibonacci sequence values will be bigger than this, we have to use a BigInteger class. BigInteger is implemented using an int[], so the maximum is 232Integer.MAX_VALUE.

A naive approach

We could naively use a recursion method, but for each call that would branch out another 2 recursive calls. Effectively, this would have a O(2n) runtime.

static BigInteger fibSlow(int n) {
    if (n == 1 || n == 2) {
        return 1;
    } else {
        return fib(n-1) + fib(n-2);


Thus, we need to store the already-calculated elements into a list, then retrieve it when needed. The process of storing and retrieving already-calculated values is termed memoization.

import java.util.ArrayList;
import java.math.BigInteger;

public class Fibonacci100 {

	static ArrayList<BigInteger> fib100 = new ArrayList<>();

	public static void main(String[] args) {

		for (BigInteger n : fib100) {

	static BigInteger fib(int n) {

		if (n >= fib100.size()) {
			fib100.add(n, fib(n-1).add(fib(n-2)));

		return fib100.get(n);




Upper bound to a BigInteger

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