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:

class Solution {
public:
    int integerBreak(int n) {
        if ( n == 2 ) return 1;
        if ( n == 3 ) return 2;
        int i = n/3, j = n%3;
        if ( j == 0 ) return pow(3, i);
        if ( j == 1 ) return pow(3, i-1) * pow(2, 2);
        if ( j == 2 ) return pow(3, i) * 2;
        return -1;
    }
};

Notes

• Finding: Decompose into as many three as possible.
• Why?
  • For numbers larger than 3, one can always decompose it into smaller numbers to achieve larger product. For example: $$5 = 2 + 3$$ ( $$2*3 = 6$$ is larger than $$5$$).