Remember the story of Little Match Girl? By now, you know exactly what matchsticks the little match girl has, please find out a way you can make one square by using up all those matchsticks. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.

Your input will be several matchsticks the girl has, represented with their stick length. Your output will either be true or false, to represent whether you could make one square using all the matchsticks the little match girl has.

Example 1:

Input: [1,1,2,2,2]
Output: true

Explanation: You can form a square with length 2, one side of the square came two sticks with length 1. 

Example 2:

Input: [3,3,3,3,4]
Output: false

Explanation: You cannot find a way to form a square with all the matchsticks. 

Note:

1. The length sum of the given matchsticks is in the range of 0
   to 10^9.
2. The length of the given matchstick array will not exceed 15.

還記得童話《賣火柴的小女孩》嗎？現在，你知道小女孩有多少根火柴，請找出一種能使用所有火柴拼成一個正方形的方法。不能折斷火柴，可以把火柴連接起來，並且每根火柴都要用到。

輸入為小女孩擁有火柴的數目，每根火柴用其長度表示。輸出即為是否能用所有的火柴拼成正方形。

示例 1:

輸入: [1,1,2,2,2]
輸出: true

解釋: 能拼成一個邊長為2的正方形，每邊兩根火柴。

示例 2:

輸入: [3,3,3,3,4]
輸出: false

解釋: 不能用所有火柴拼成一個正方形。

註意:

1. 給定的火柴長度和在 0 到 10^9之間。
2. 火柴數組的長度不超過15。

 1 class Solution {
 2     func makesquare(_ nums: [Int]) -> Bool {
 3         if nums.isEmpty || nums.count < 4 {return false}
 4         var sum:Int = nums.reduce(0, +)
 5         if sum % 4 != 0 {return false}
 6         var n:Int = nums.count
 7         var all:Int = (1 << n) - 1
 8         var target:Int = sum / 4
 9         var masks:[Int] = [Int]()
10         var validHalf:[Bool] = [Bool](repeating:false,count:1 << n)
11         for i in 0...all
12         {
13             var curSum:Int = 0
14             for j in 0...15
15             {
16                 if ((i >> j) & 1) == 1
17                 {
18                     curSum += nums[j]
19                 }
20             }
21             if curSum == target
22             {
23                 for mask in masks
24                 {
25                     if (mask & i) != 0 {continue}
26                     var half:Int = mask | i
27                     validHalf[half] = true
28                     if validHalf[all ^ half] {return true}
29                 }
30                 masks.append(i)
31             }
32         }
33         return false
34     }
35 }

3911 kb

 1 class Solution {
 2     func makesquare(_ nums: [Int]) -> Bool {
 3         guard  nums.count >= 4 else { return false }
 4         let sum = nums.reduce(0, { $0 + $1 })
 5         if sum % 4 != 0 {
 6             return false
 7         }
 8         var sides: [Int] = Array(repeating: 0, count: 4)
 9         return dfs(nums.sorted(by: >), 0, &sides, sum / 4)
10     }
11     
12     func dfs(_ nums: [Int], _ index: Int, _ sides: inout [Int], _ target: Int) -> Bool {
13         if index == nums.count {
14             return sides[0] == sides[1] && sides[0] == sides[2] && sides[0] == sides[3] && sides[0] == target
15         }
16         
17         for i in 0 ..< sides.count {
18             if sides[i] + nums[index] > target {
19                 continue
20             }
21             sides[i] += nums[index]
22             if dfs(nums, index + 1, &sides, target) {
23                 return true
24             }
25             sides[i] -= nums[index]
26         }
27         return false
28     }
29 }

[Swift]LeetCode473. 火柴拼正方形 | Matchsticks to Square