leetcode题库

//定理：将一个数拆解为两个数时：(n/2)*(n-n/2)可得到最大乘积，拆解成大于两个数时，最大乘积为：max(i*f(n-i)),1<i<n/2
class Solution {
   // 动态规划
    public int integerBreak(int n) {
        if (n <= 3) return n - 1;
        int[] dp = new int[n + 1];
        //初始化,1,2,3特殊处理
        dp[1] = 1;
        dp[2] = 2;
        dp[3] = 3;
        for (int i = 4; i <= n; i++) {
            for (int j = 1; j <= i / 2; j++) {
                dp[i] = Math.max(dp[i], dp[j] * dp[i - j]);
            }
        }
        return dp[n];
    }
}