[Swift]LeetCode494.目标和|TargetSum

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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:

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

给定一个非负整数数组，a1, a2, ..., an, 和一个目标数，S。现在你有两个符号 + 和 -。对于数组中的任意一个整数，你都可以从 + 或 -中选择一个符号添加在前面。

返回可以使最终数组和为目标数 S 的所有添加符号的方法数。

示例 1:

输入: nums: [1, 1, 1, 1, 1], S: 3
输出: 5
解释: 

-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种方法让最终目标和为3。

注意:

数组的长度不会超过20，并且数组中的值全为正数。
初始的数组的和不会超过1000。
保证返回的最终结果为32位整数。

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 }