Question

I am learning JAVA myself and I am learning about memoization now. But i am kind of losing my way…

Does anyone has some sample code about how to compute the Combination in Java by using recursion and using memoization to accelerate the algorithm?

Like a way to compute C5,3 = 5*4*3/3*2*1 = 10? but using recursion?

Answer 1

Lets do it with an example 20 choose 5

Since 20 choose 5 is defined as 20! / ( 5! * (20-5)! )

We could use memoization to store those factorial computations so we don’t have to continually re-compute them under our recursion.

So:

    //STORING FACTORIAL COMPUTATIONS
    private Map<Integer,Long> factorialMap = new HashMap<Integer,Long>();


    public Long getFactorial(int number) {

        //CHECK IF I ALREADY COMPUTED THIS FACTORIAL
        Long val = factorialMap.get(number);
        if(val != null) {
            //GOT IT!
            return val;
        } else {
            //NEED TO COMPUTE!
            val = getFactorialRecursive(number);
            //STORING IT TO SAVE COMPUTATION FOR LATER
            factorialMap.put(number, val);
            return val;
        }
    }

    //RECURSIVE FUNCTION TO COMPUTE FACTORIAL
    public Long getFactorialRecursive(int number) {
        if(number < 2) {
            return 1L;
        } else {
            return number * getFactorialRecursive(number-1);
        }
    }


    //ACTUAL CALL TO "20 choose 5"
    public Long combination(int fromVal, int chooseVal) {
        return getFactorial(fromVal)/(getFactorial(chooseVal)*getFactorial(fromVal-chooseVal));
    }