Combinations using memoization in java

Question

I'm making a program that calculates a combination given two numbers, ex:

java Combination 5 3 

would give an answer of 10.

I have a method that looks like this:

public static int choose(int n, int k) {   // chooses k elements out of n total
  if (n == 0 && k > 0)
      return 0;
  else if (k == 0 && n >= 0)
      return 1;
  else return choose(n - 1, k - 1) + choose(n - 1, k);

How would I be able to use memoization for this in order to make it calculate faster with larger numbers?

Answer 1

You might be better off using a more efficient formula: http://en.wikipedia.org/wiki/Binomial_coefficient#Multiplicative_formula

If you want to use this formula, then this is a way to memoize (sans the typos I might have):

private static Map<Pair<Integer, Integer>, Long> cache = new HashMap<>(); // you'll need to implement pair

public static int choose(int n, int k) {
... // the base cases are the same as above.
} else if (cache.contains(new Pair<>(n, k)) {
    return cache.get(new Pair<>(n, k));
} else {
    Long a = cache.get(new Pair<>(n - 1, k - 1));
    if (a == null) { a = choose(n - 1, k - 1); }
    Long b = cache.get(new Pair<>(n - 1, k));
    if (b == null) { b = choose(n - 1, k); }

    cache.put(new Pair<>(n, k), a + b);
    return a + b;
}