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 }
原文地址：https://www.cnblogs.com/strengthen/p/10348807.html
时间： 2024-10-15 10:35:22