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 }