[Swift]LeetCode300. 最長上升子序列 | Longest Increasing Subsequence

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Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: Output: 4 
Explanation: The longest increasing subsequence is , therefore the length is . [10,9,2,5,3,7,101,18][2,3,7,101]4

Note:

• There may be more than one LIS combination, it is only necessary for you to return the length.
• Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

---

給定一個無序的整數數組，找到其中最長上升子序列的長度。

示例:

輸入: 輸出: 4 
解釋: 最長的上升子序列是 它的長度是 。[10,9,2,5,3,7,101,18][2,3,7,101]，4

說明:

• 可能會有多種最長上升子序列的組合，你只須要輸出對應的長度便可。
• 你算法的時間複雜度應該爲 O(n2) 。

進階: 你能將算法的時間複雜度下降到 O(n log n) 嗎?

---

16ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3         if nums.count < 2 {
 4             return nums.count
 5         }
 6         var res = Array(repeating: 0, count: nums.count)
 7         res[0] = nums[0]
 8         var count = 1
 9         var j = 0
10         for i in 0..<nums.count {
11             let tmp = nums[i]
12             if tmp > res[count - 1] {
13                 j = count
14                 count += 1
15             }else {
16                 var left = 0
17                 var right = count - 1
18                 while left < right {
19                     let mid = (left + right) / 2
20                     if res[mid] >= nums[i] {
21                         right = mid
22                     }else {
23                         left = mid + 1
24                     }
25                 }
26                 j = left
27             }
28             res[j] = nums[i]
29         }
30         return count
31     }
32 }

---

56ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3         var results = [Int]()
 4         for num in nums {
 5             var needAdd = true
 6             if results.count > 0 {
 7                 for index in 0..<results.count {
 8                     if num <= results[index] {
 9                         results[index] = num
10                         needAdd = false
11                         break
12                     }
13                 }
14             }
15             if needAdd {
16                 results.append(num)
17             }
18         }
19         return results.count
20     }
21 }

---

300ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3         guard !nums.isEmpty else {
 4             return 0
 5         }
 6         
 7         var dps = Array(repeating: 1, count: nums.count)
 8         var result = 1
 9         for index in 1..<nums.count {
10             let num = nums[index]
11             for j in 0..<index {
12                 if num > nums[j] {
13                     let length = dps[j] + 1
14                     if length > dps[index] {
15                         dps[index] = length
16                         result = max(result, dps[index])
17                     }
18                 }
19             }
20         }
21 
22         return result
23     }
24 }

---

312ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3          var length_global = 0
 4     var length_current = [Int].init(repeating:1 , count: nums.count)
 5     
 6     for i in 0..<nums.count {
 7         for j in 0..<i {
 8             if nums[i] > nums[j] {
 9                 length_current[i] = max(length_current[i], length_current[j] + 1)
10             }
11         }
12         length_global = max(length_global, length_current[i])
13     }
14     
15     return length_global
16     }
17 }

---

376ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3         guard !nums.isEmpty else {
 4             return 0
 5         }
 6         
 7         var dps = Array(repeating: 1, count: nums.count)
 8         var result = 1
 9         for index in 1..<nums.count {
10             let num = nums[index]
11             for j in 0..<index where num > nums[j] {
12                 let length = dps[j] + 1
13                 dps[index] = max(length, dps[index])
14                 result = max(result, dps[index])
15             }
16         }
17 
18         return result
19     }
20 }

---

388ms

 1 class Solution {
 2     func lengthOfLIS(_ nums: [Int]) -> Int {
 3         
 4         if nums.count == 0 {
 5             return 0
 6         }
 7         
 8         var result = 1
 9         var dArr = [Int](repeating: 1, count: nums.count)
10         
11         for i in 0..<nums.count {
12 
13             for j in 0..<i {
14                 
15                 if(nums[j] < nums[i] && (dArr[j] + 1 >= dArr[i])) {
16                     dArr[i] = dArr[j] + 1
17                 }
18             }
19             result = dArr[i] > result ? dArr[i] : result
20         }
21         return result
22     }
23 }