Project Euler Problem 154

Problem154.java

import java.util.Arrays;

// Project Euler 154
// 479742450
// 59.7 seconds
public class Problem154 {
    private static final int THT = 200000; // Two Hundred Thousand
    private int[] numOf2FactorsInFactorial = new int[THT + 1];
    private int[] numOf5FactorsInFactorial = new int[THT + 1];

    public static void main(String args[]) {
        Problem154 this_ = new Problem154();
        long startTimeMillis = System.currentTimeMillis();
        System.out.println(this_.solve());
        long durationMillis = System.currentTimeMillis() - startTimeMillis;
        System.out.println(durationMillis / 1000 + "."
          	+ (durationMillis % 1000) / 100 + " seconds");
    }

    public  Problem154() {
    	Arrays.fill(numOf2FactorsInFactorial, -1);
    	Arrays.fill(numOf5FactorsInFactorial, -1);
    }

    private int solve() {
    	int answer = 0;
    	int numOf5FactorsInTHTFactorial = numOfPFactorsInFactorial(THT, 5);
	    int numOf2FactorsInTHTFactorial = numOfPFactorsInFactorial(THT, 2);

	    for (int a = 0; a <= THT / 3; a++) {
	    	for (int b = a; b <= (THT - a) / 2; b++) {
	    		int c = THT - a - b;
	    		assert (a <= b);
	    		assert (b <= c);
	    		int numOf5Factors
	    			= numOf5FactorsInTHTFactorial
	    				- numOfPFactorsInFactorial(a, 5)
	    				- numOfPFactorsInFactorial(b, 5)
	    				- numOfPFactorsInFactorial(c, 5);

	    		if (numOf5Factors >= 12) {
		    		int numOf2Factors
		    			= numOf2FactorsInTHTFactorial
		    				- numOfPFactorsInFactorial(a, 2)
		    				- numOfPFactorsInFactorial(b, 2)
		    				- numOfPFactorsInFactorial(c, 2);

		    		if (numOf2Factors >= 12) {
		    			if (a == b || b == c)
		    				answer += 3;
		    			else
		    				answer += 6;
		    		}
	    		}
	    	}
	    }
	    return answer;
    }

    /**
     * @return number of factors of given prime In factorial of n
     */
    private int numOfPFactorsInFactorial(int n, int prime) {
    	if (prime == 2 && numOf2FactorsInFactorial[n] > 0) {
    		return numOf2FactorsInFactorial[n];
    	} else if (prime == 5 && numOf5FactorsInFactorial[n] > 0) {
    		return numOf5FactorsInFactorial[n];
    	}

        int numOfFactors = 0;
        int multiple = 1;
        while (n >= multiple) {
            multiple *= prime;
            numOfFactors += n / multiple;
        }

        if (prime == 2)
        	numOf2FactorsInFactorial[n] = numOfFactors;
        else if (prime == 5)
        	numOf5FactorsInFactorial[n] = numOfFactors;
        return numOfFactors;
    }
}