343. Integer Break

Given a positive integer n, break it into the sum of at least two positive integers and maximize the product of those integers. Return the maximum product you can get.

For example, given n= 2, return 1 (2 = 1 + 1); given n= 10, return 36 (10 = 3 + 3 + 4).

Note: You may assume that n is not less than 2 and not larger than 58.

Solution: Trying to split the number into two parts by cutting at every possible point, and collect the maximum result. The value from each part can be gotten from DP. The number can be not split at all, except the input n itself, because it is required by the problem.

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