/// 343. Integer Break
/// https://leetcode.com/problems/integer-break/description/
/// 暴力搜索
/// 在Leetcode中提交这个版本的代码会超时! (Time Limit Exceeded)
/// 时间复杂度: O(n^n)
/// 空间复杂度: O(n)
public class Solution1 {

    public int integerBreak(int n) {

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

        return breakInteger(n);
    }

    // 将n进行分割(至少分割两部分), 可以获得的最大乘积
    private int breakInteger(int n){

        if(n == 1)
            return 1;

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