Integer Break Python Solution with Tests

lcpy gen -n 343   # by problem number
lcpy gen -s integer_break   # by problem name

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.

class Solution:
    # Time: O(n^2)
    # Space: O(n)
    def integer_break(self, n: int) -> int:
        dp = [0] * (n + 1)
        dp[1] = 1

        for target in range(2, n + 1):
            for part in range(1, target):
                dp[target] = max(dp[target], part * (target - part), part * dp[target - part])

        return dp[n]