A typical CS style DP based solution:
class Solution(object):
def __init__(self):
self.hm = {} def integerBreak(self, n):
if n in self.hm:
return self.hm[n]
ret = 0
for i in range(1, n//2 + 1):
v1 = self.integerBreak(i)
v2 = self.integerBreak(n - i)
ret = max(ret, v1 * v2, v1 * (n - i), i * v2, i * (n - i))
self.hm[n] = ret
return ret
But there's a Math based solution:
https://leetcode.com/discuss/98249/easy-to-understand-c-with-explanation
In which: "For any integer p strictly greater than 4, it has the property such that 3 * (p - 3) > p, which means breaking it into two integers 3 and p - 3 makes the product larger while keeping the sum unchanged"