[Swift]LeetCode494. 目標和 | Target Sum

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You are given a list of non-negative integers, a1, a2, ..., an, and a target, S. Now you have 2 symbols +and -. For each integer, you should choose one from + and - as its new symbol.

Find out how many ways to assign symbols to make sum of integers equal to target S.

Example 1:

Input: nums is [1, 1, 1, 1, 1], S is 3. 
Output: 5
Explanation: 

-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3

There are 5 ways to assign symbols to make the sum of nums be target 3. 

Note:

1. The length of the given array is positive and will not exceed 20.
2. The sum of elements in the given array will not exceed 1000.
3. Your output answer is guaranteed to be fitted in a 32-bit integer.

---

給定一個非負整數數組，a1, a2, ..., an, 和一個目標數，S。如今你有兩個符號 + 和 -。對於數組中的任意一個整數，你均可以從 + 或 -中選擇一個符號添加在前面。

返回能夠使最終數組和爲目標數 S 的全部添加符號的方法數。

示例 1:

輸入: nums: [1, 1, 1, 1, 1], S: 3
輸出: 5
解釋: 

-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3

一共有5種方法讓最終目標和爲3。

注意:

1. 數組的長度不會超過20，而且數組中的值全爲正數。
2. 初始的數組的和不會超過1000。
3. 保證返回的最終結果爲32位整數。

---

Runtime: 160 ms

Memory Usage: 3.9 MB

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         var sum:Int = 0
 4         for n in nums
 5         {
 6             sum += n
 7         }
 8         return sum < S || (S + sum) % 2 > 0 ? 0 : subsetSum(nums, (S + sum) >> 1)
 9     }
10     
11     func subsetSum(_ nums: [Int], _ S: Int) -> Int
12     {
13         var dp:[Int] = [Int](repeating:0,count:S + 1)
14         dp[0] = 1
15         for n in nums
16         {
17             if n <= S
18             {
19                 for i in (n...S).reversed()
20                 {
21                     dp[i] += dp[i - n]
22 
23                 }
24             }
25             
26         }
27         return dp[S]
28     }
29 }

---

216ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         var cache: [[Int: Int]] = Array(repeating: [:], count: nums.count)
 4         return helper(nums, 0, S, &cache)
 5     }
 6     
 7     private func helper(_ nums: [Int], _ index: Int, _ S: Int, _ cache: inout [[Int: Int]]) -> Int {
 8         if index >= nums.count {
 9             return S == 0 ? 1 : 0
10         }
11         if let res = cache[index][S] {
12             return res
13         }
14         
15         let a = -nums[index] + helper(nums, index + 1, S + nums[index], &cache)
16         let b = nums[index] + helper(nums, index + 1, S - nums[index], &cache)
17         cache[index][S] = a + b
18         return a + b
19     }
20 }

---

280ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         var dp = [Int: Int]()
 4         var f = 0
 5         
 6         // init
 7         dp[nums[0]] = 1
 8         dp[-nums[0]] = 1
 9         
10         for i in 1..<nums.count {
11             let n = nums[i]
12             var tmp = dp
13             dp.removeAll(keepingCapacity: true)
14             
15             for k in tmp.keys {
16                 dp[k + n, default: 0] += tmp[k]!
17                 dp[k - n, default: 0] += tmp[k]!
18             }
19         }
20         var ans = dp[S] ?? 0
21         if nums[0] == 0 {
22             ans *= 2
23         }
24         return ans
25     }
26 }

---

528ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         var dic = [0:1]
 4         for num in nums {
 5             var curDic = [Int : Int]()
 6             
 7             for (key, value) in dic {
 8                 if let curNumAdd = curDic[key + num] {
 9                     curDic[key + num] = curNumAdd + value
10                 } else {
11                     curDic[key + num] = value
12                 }
13                 
14                 if let curNumMinus = curDic[key - num] {
15                     curDic[key - num] = curNumMinus + value
16                 } else {
17                     curDic[key - num] = value
18                 }
19             }
20             dic = curDic
21         }
22         return dic[S] ?? 0
23     }
24 }

---

1312ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         return numsOfPaths(nums, S, currentIndex: 0, sumSoFar: 0)
 4     }
 5     
 6     func numsOfPaths(_ nums: [Int], _ S: Int, currentIndex: Int, sumSoFar: Int) -> Int {
 7         let elem = nums[currentIndex]
 8         if currentIndex == nums.count - 1 {
 9             var result = 0
10             if S == sumSoFar + elem {
11                 result += 1
12             }
13             if S == sumSoFar - elem {
14                 result +=  1
15             } 
16             return result
17         }
18 
19         return numsOfPaths(nums, S, currentIndex: currentIndex + 1, sumSoFar: sumSoFar + elem) +
20             numsOfPaths(nums, S, currentIndex: currentIndex + 1, sumSoFar: sumSoFar - elem)
21     }
22 }

---

2240ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         var dps: [String: Int] = [:]
 4         return findTargetSumWays(nums, S, 0, &dps)
 5     }
 6 
 7     func findTargetSumWays(_ nums: [Int], _ S: Int, _ index: Int, _ dps: inout [String: Int]) -> Int {
 8         let key = "\(index)-\(S)"
 9         if let count = dps[key] {
10             return count
11         }
12 
13         guard index < nums.count else {
14             if S == 0 {
15                 return 1
16             } else {
17                 return 0
18             }
19         }
20 
21         let count = findTargetSumWays(nums, S - nums[index], index + 1, &dps)
22         let count2 = findTargetSumWays(nums, S - (-nums[index]), index + 1, &dps)
23         dps[key] = count + count2
24         return count + count2
25     }
26 }

---

2868ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         func findTargetSumWays(_ nums: [Int], index: Int, S: Int, sum: Int) -> Int {
 4             var res = 0
 5 
 6             if index == nums.count {
 7                 return sum == S ? res + 1 : res
 8             }
 9 
10             res += findTargetSumWays(nums, index: index + 1, S: S, sum: sum + nums[index])
11             res += findTargetSumWays(nums, index: index + 1, S: S, sum: sum - nums[index])
12 
13             return res
14         }
15 
16         return findTargetSumWays(nums, index: 0, S: S, sum: 0)
17     }
18 }

---

3156ms

 1 class Solution {
 2     func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
 3         return helper(nums, 0, S)
 4     }
 5     
 6     private func helper(_ nums: [Int], _ index: Int, _ S: Int) -> Int {
 7         if index >= nums.count {
 8             return S == 0 ? 1 : 0
 9         }
10         
11         let a = -nums[index] + helper(nums, index + 1, S + nums[index])
12         let b = nums[index] + helper(nums, index + 1, S - nums[index])
13         return a + b
14     }
15 }