LeetCode-343. Integer Break [C++][Java]

LeetCode-343. Integer BreakLevel up your coding skills and quickly land a job. This is the best place to expand your knowledge and get prepared for your next interview.https://leetcode.com/problems/integer-break/

题目描述

Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.

Return the maximum product you can get.

Example 1:

Input: n = 2
Output: 1
Explanation: 2 = 1 + 1, 1 × 1 = 1.

Example 2:

Input: n = 10
Output: 36
Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.

Constraints:

• 2 <= n <= 58

解题思路

【C++】

1.动态规划

class Solution {
public:
    int integerBreak(int n) {
        vector<int> dp(n+1);
        dp[1] = 1;
        for(int i = 2; i <= n; i++) {
            for(int j=1; j<i; j++) {
                dp[i] = max(dp[i], max(j*dp[i-j], j*(i-j)));
            }  
        }
        return dp[n];
    }
};

2. 数学归纳法

class Solution {
public:
    int integerBreak(int n) {
        if (n <= 3) {return n-1;}
        int result = 1;
        if (n % 3 == 1) {
            result = 4;
            n -= 4;
        }
		while (n >= 3) {
            result *= 3;
            n -= 3;
        }
        if (n > 0) {result *= n;}
        return result;
    }
};

【Java】

class Solution {
    public int integerBreak(int n) {
        if (n <= 3) {return n-1;}
        int result = 1;
        if (n % 3 == 1) {
            result = 4;
            n -= 4;
        }
		while (n >= 3) {
            result *= 3;
            n -= 3;
        }
        if (n > 0) {result *= n;}
        return result;
    }
}