RussellAndrewEdson

public class PascalsTriangle {
    private int[][] triangle;
    
    /* Creates a new PascalsTriangle representation with n rows. */
    public PascalsTriangle(int n) {
        triangle = new int[n][n];
        
        // The first column is all 1's.
        for (int i = 0; i < n; i++) {
            triangle[i][0] = 1;

RussellAndrewEdson

def nextRow(row: List[Int]): List[Int] = (row, (0 :: row)).zipped.map(_ + _)

/* Generating 5 rows of Pascal's triangle. */
var pascal = List[List[Int]]( List(1,0,0,0,0) )
for (i <- 1 to 4) {
  pascal = nextRow(pascal.head) :: pascal
}
pascal = pascal.reverse

for (row <- pascal) { 

RussellAndrewEdson

(defn pascal 
  "Returns the number in the given row and column of
  Pascal's triangle."
  [row column]
  (cond (= column 1) 1
        (= column row) 1
        (> column row) 0
        :else (+ (pascal (- row 1) (- column 1))
                 (pascal (- row 1) column)))))

RussellAndrewEdson

(defn fibonacci
  "Returns the nth Fibonacci number using a recursive process."
  [n]
  (cond (= n 0) 0
        (= n 1) 1
        :else (+ (fibonacci (- n 1))
                 (fibonacci (- n 2)))))

RussellAndrewEdson

# Calculates the nth Fibonacci number using an iterative process.
def fibonacci(n):
    (current, next) = (0, 1)

    index = 0
    while (index < n):
        (current, next) = (next, current + next)
        index += 1

    return current

RussellAndrewEdson

(defn fibonacci
  "Returns the nth Fibonacci number using an iterative process."
  [n]
  (loop [current 0N next 1N index 0]
    (if (= index n)
      current
      (recur next (+ current next) (inc index)))))

RussellAndrewEdson

(defn fibonacci
  "Returns the nth Fibonacci number using a logarithmic squaring algorithm."
  [n]
  (let [square (fn [x] (* x x))]
    (loop [current 0N next 1N p 0N q 1N count n]
      (cond (= count 0) current
            (even? count) (recur current
                                 next
                                 (+ (square p) (square q))
                                 (+ (square q) (* 2 p q))

RussellAndrewEdson

# Calculates the nth Fibonacci number using a logarithmic algorithm.
def fibonacci(n):
    # Helper function: returns True if n is an even number.
    even = lambda n: (n % 2 == 0)

    (current, next, p, q) = (0, 1, 0, 1)    

    while (n > 0):
        if (even(n)):
            (p, q) = (p**2 + q**2, q**2 + 2*p*q)

RussellAndrewEdson

(require '[clojure.math.numeric-tower :as math])

(defn fibonacci
  "Returns the nth Fibonacci number by using the Golden Ratio formula."
  [n]
  (let [root-five (math/sqrt 5M)
        golden-ratio (/ (+ 1 root-five) 2)]
    (math/round (bigdec (/ (math/expt golden-ratio n)
                           root-five)))))

RussellAndrewEdson

import java.math.BigInteger;

/** A common interface for the primality tests we'll look at. */
public abstract class PrimalityTest {
    public abstract boolean isPrime(BigInteger n);
    
    public void timedPrimeTest(BigInteger n) {
        System.out.println("Running test: " + getClass().getName());
        System.out.println("n: " + n);
        long startTime = System.currentTimeMillis();