Solution1.java

/// Source : https://leetcode.com/problems/integer-break/description/
/// Author : liuyubobobo
/// Time   : 2017-11-19
import java.util.Arrays;

/// Memory Search
/// Time Complexity: O(n^2)
/// Space Complexity: O(n)
public class Solution1 {

    private int[] memo;

    public int integerBreak(int n) {

        if(n < 1)
            throw new IllegalArgumentException("n should be greater than zero");

        memo = new int[n+1];
        Arrays.fill(memo, -1);

        return breakInteger(n);
    }

    private int breakInteger(int n){

        if(n == 1)
            return 1;

        if(memo[n] != -1)
            return memo[n];

        int res = -1;
        for(int i = 1 ; i <= n - 1 ; i ++)
            res = max3(res, i * (n - i) , i * breakInteger(n - i));
        memo[n] = res;
        return res;
    }

    private int max3(int a, int b, int c){
        return Math.max(a, Math.max(b, c));
    }

    public static void main(String[] args) {

        System.out.println((new Solution1()).integerBreak(2));
        System.out.println((new Solution1()).integerBreak(10));
    }
}