Java Solution for Integer Break Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe problem is to break a given integer n into the sum of at least two positive integer
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe problem is to break a given integer n into the sum of at least two positive integers and maximize the product of those integers.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\nThe approach used here is dynamic programming. The idea is to maintain an array dp where dp[i] represents the maximum product that can be obtained by breaking the number i into at least two positive integers.\n\nTo compute dp[i], we iterate over all possible ways of breaking i into two positive integers j and i-j, and calculate the product of dp[j] and dp[i-j]. We take the maximum of this product and dp[i] to update dp[i].\n\nThe final answer is dp[n].\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\nThe outer loop iterates n-1 times, and the inner loop iterates i times for each iteration of the outer loop. Therefore, the time complexity is O(n^2).\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nWe use an array dp of size n+1. Therefore, the space complexity is O(n).\n\n# Code\n```\nclass Solution {\n    public int integerBreak(int n) {\n        int[] dp = new int[n+1];\n        for(int i=1; i<n; i++)\n        {\n            for(int j=1; j<i+1; j++)\n            {\n                if(i+j<=n)\n                {\n                    dp[i+j]=Math.max(Math.max(dp[i],i)*Math.max(dp[j],j), dp[i+j]);\n                }\n            }\n        }\n        return dp[n];\n    }\n}\n```
['Java']