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.

Example 1:

Input: 2
Output: 1
Explanation: 2 = 1 + 1, 1 × 1 = 1.

Example 2:

Input: 10
Output: 36
Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.
 

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

給定一個正整數 n，將其拆分為至少兩個正整數的和，並使這些整數的乘積最大化。 返回你可以獲得的最大乘積。

示例 1:

輸入: 2
輸出: 1
解釋: 2 = 1 + 1, 1 × 1 = 1。

示例 2:

輸入: 10
輸出: 36
解釋: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36。

說明: 你可以假設 n 不小於 2 且不大於 58。

 1 class
 
 Solution {
 2     func integerBreak(_ n: Int) -> Int {
 3         if n < 2 {
 4             return 0
 5         }
 6         
 7         var res = Array(repeating: 1, count: n+1)
 8         
 9         res[1] = 0
10         
11         for i in 2...n {
12             var maxRes = 1
13
 
             for j in 1..<i {
14                 maxRes = max(maxRes, max(res[j], j) * max(i-j, res[i-j]))
15             }
16             res[i] = maxRes
17         }
18         return res[n]
19     }
20 }

8ms

 1 class Solution {
 2     func integerBreak(_ n: Int) -> Int {
 3         
 4         guard n > 3 else {
 5             return [1,1,1,2][n]
 6         }
 7         
 8         var times3 = n / 3
 9         
10         if n % 3 == 1 {
11             times3 -= 1
12         }
13         
14         let times2 = (n - times3 * 3) / 2
15         
16         return Int(pow(3.0, Double(times3))) * Int(pow(2.0, Double(times2)))
17     }
18 }

16ms

 1 class Solution {
 2     func integerBreak(_ n: Int) -> Int {
 3         if n == 2 {
 4             return 1
 5         } else if n == 3 {
 6             return 2
 7         } else if n % 3 == 0 {
 8             return Int(pow(3, Double(n / 3)))
 9         } else if n % 3 == 1 {
10             return Int(2 * 2 * pow(3, Double((n - 4) / 3)))
11         } else { // 2
12             return Int(2 * pow(3, Double((n - 2) / 3)))
13         }
14     }
15 }

24ms

 1 class Solution {
 2     func integerBreak(_ n: Int) -> Int {
 3         var dps = Array(repeating: 0, count: n + 1)
 4         dps[1] = 1
 5         for num in 2...n {
 6             for j in 1..<num {
 7                 dps[num] = max(dps[num], j * max(num - j, dps[num - j]))
 8             }
 9         }
10 
11         return dps[n]
12     }
13 }

[Swift]LeetCode343. 整數拆分 |