[Swift]LeetCode494. 目标和 | 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.

---

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:

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

---

Runtime: 160 ms

Memory Usage: 3.9 MB

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        var sum:Int = 0
        for n in nums
        {
            sum += n
        }
        return sum < S || (S + sum) % 2 > 0 ? 0 : subsetSum(nums, (S + sum) >> 1)
    }
    
    func subsetSum(_ nums: [Int], _ S: Int) -> Int
    {
        var dp:[Int] = [Int](repeating:0,count:S + 1)
        dp[0] = 1
        for n in nums
        {
            if n <= S
            {
                for i in (n...S).reversed()
                {
                    dp[i] += dp[i - n]

                }
            }
            
        }
        return dp[S]
    }
}

---

216ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        var cache: [[Int: Int]] = Array(repeating: [:], count: nums.count)
        return helper(nums, 0, S, &cache)
    }
    
    private func helper(_ nums: [Int], _ index: Int, _ S: Int, _ cache: inout [[Int: Int]]) -> Int {
        if index >= nums.count {
            return S == 0 ? 1 : 0
        }
        if let res = cache[index][S] {
            return res
        }
        
        let a = -nums[index] + helper(nums, index + 1, S + nums[index], &cache)
        let b = nums[index] + helper(nums, index + 1, S - nums[index], &cache)
        cache[index][S] = a + b
        return a + b
    }
}

---

280ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        var dp = [Int: Int]()
        var f = 0
        
        // init
        dp[nums[0]] = 1
        dp[-nums[0]] = 1
        
        for i in 1..<nums.count {
            let n = nums[i]
            var tmp = dp
            dp.removeAll(keepingCapacity: true)
            
            for k in tmp.keys {
                dp[k + n, default: 0] += tmp[k]!
                dp[k - n, default: 0] += tmp[k]!
            }
        }
        var ans = dp[S] ?? 0
        if nums[0] == 0 {
            ans *= 2
        }
        return ans
    }
}

---

528ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        var dic = [0:1]
        for num in nums {
            var curDic = [Int : Int]()
            
            for (key, value) in dic {
                if let curNumAdd = curDic[key + num] {
                    curDic[key + num] = curNumAdd + value
                } else {
                    curDic[key + num] = value
                }
                
                if let curNumMinus = curDic[key - num] {
                    curDic[key - num] = curNumMinus + value
                } else {
                    curDic[key - num] = value
                }
            }
            dic = curDic
        }
        return dic[S] ?? 0
    }
}

---

1312ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        return numsOfPaths(nums, S, currentIndex: 0, sumSoFar: 0)
    }
    
    func numsOfPaths(_ nums: [Int], _ S: Int, currentIndex: Int, sumSoFar: Int) -> Int {
        let elem = nums[currentIndex]
        if currentIndex == nums.count - 1 {
            var result = 0
            if S == sumSoFar + elem {
                result += 1
            }
            if S == sumSoFar - elem {
                result +=  1
            } 
            return result
        }

        return numsOfPaths(nums, S, currentIndex: currentIndex + 1, sumSoFar: sumSoFar + elem) +
            numsOfPaths(nums, S, currentIndex: currentIndex + 1, sumSoFar: sumSoFar - elem)
    }
}

---

2240ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        var dps: [String: Int] = [:]
        return findTargetSumWays(nums, S, 0, &dps)
    }

    func findTargetSumWays(_ nums: [Int], _ S: Int, _ index: Int, _ dps: inout [String: Int]) -> Int {
        let key = "\(index)-\(S)"
        if let count = dps[key] {
            return count
        }

        guard index < nums.count else {
            if S == 0 {
                return 1
            } else {
                return 0
            }
        }

        let count = findTargetSumWays(nums, S - nums[index], index + 1, &dps)
        let count2 = findTargetSumWays(nums, S - (-nums[index]), index + 1, &dps)
        dps[key] = count + count2
        return count + count2
    }
}

---

2868ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        func findTargetSumWays(_ nums: [Int], index: Int, S: Int, sum: Int) -> Int {
            var res = 0

            if index == nums.count {
                return sum == S ? res + 1 : res
            }

            res += findTargetSumWays(nums, index: index + 1, S: S, sum: sum + nums[index])
            res += findTargetSumWays(nums, index: index + 1, S: S, sum: sum - nums[index])

            return res
        }

        return findTargetSumWays(nums, index: 0, S: S, sum: 0)
    }
}

---

3156ms

class Solution {
    func findTargetSumWays(_ nums: [Int], _ S: Int) -> Int {
        return helper(nums, 0, S)
    }
    
    private func helper(_ nums: [Int], _ index: Int, _ S: Int) -> Int {
        if index >= nums.count {
            return S == 0 ? 1 : 0
        }
        
        let a = -nums[index] + helper(nums, index + 1, S + nums[index])
        let b = nums[index] + helper(nums, index + 1, S - nums[index])
        return a + b
    }
}