0343 - Integer Break

0343 - Integer Break

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.

Examples

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

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

Constraints

• 2 <= n <= 58

Java Solution (Dynammic Programming)

class Solution {
    public int integerBreak(int n) {
        int[] dp = new int[n+1];
        dp[0] = 0;
        dp[1] = 1;
        for(int i = 2; i <= n; i++) 
            for(int j = 1; j < i; j++) 
                dp[i] = Math.max(dp[i], (Math.max(j,dp[j]) * Math.max(i-j,dp[i-j])));
    
        return dp[n];
    }
}