[DP] Refactor the solution to Longest Increasing Subsequence

DP/LongestIncreasingSubsequence.swift

@@ -1,23 +1,39 @@
 /**
  * Question Link: https://leetcode.com/problems/longest-increasing-subsequence/
- * Primary idea: Dynamic Programming, transition function is len[i] = max(len[i], len[j] + 1)
- * Time Complexity: O(n^2), Space Complexity: O(n)
+ * Primary idea: Dynamic Programming, update the array which ends at current index using binary search
+ * Time Complexity: O(nlogn), Space Complexity: O(n)
  */
 
 class LongestIncreasingSubsequence {
-    func lengthOfLIS(nums: [Int]) -> Int {
-        var length_global = 0
-        var length_current = [Int](count: nums.count, repeatedValue: 1)
+    func lengthOfLIS(_ nums: [Int]) -> Int {
+        guard let first = nums.first else {
+            return 0
+        }
+
+        var ends = [first]
 
-        for i in 0..<nums.count {
-            for j in 0..<i {
-                if nums[i] > nums[j] {
-                    length_current[i] = max(length_current[i], length_current[j] + 1)
+        for i in 1..<nums.count {
+
+            // find first greater ends number
+            var left = 0, right = ends.count 
+
+            while left < right {
+                let mid = (right - left) / 2 + left
+
+                if ends[mid] < nums[i] {
+                    left = mid + 1
+                } else {
+                    right = mid
                 }
             }
-            length_global = max(length_global, length_current[i])
+
+            if right >= ends.count {
+                ends.append(nums[i])
+            } else {
+                ends[right] = nums[i]
+            }
         }
 
-        return length_global
+        return ends.count
     }
 }

README.md

@@ -224,7 +224,7 @@
 [Maximum Sum of 3 Non-Overlapping Subarrays](https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/)| [Swift](./DP/MaximumSumThreeNonOverlappingSubarrays.swift)| Hard| O(n)| O(n)|
 [Coin Change](https://leetcode.com/problems/coin-change/)| [Swift](./DP/CoinChange.swift)| Medium| O(n^2)| O(n)|
 [Coin Change II](https://leetcode.com/problems/coin-change-ii/)| [Swift](./DP/CoinChangeII.swift)| Medium| O(n^2)| O(n)|
-[Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)| [Swift](./DP/LongestIncreasingSubsequence.swift)| Medium| O(n^2)| O(n)|
+[Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)| [Swift](./DP/LongestIncreasingSubsequence.swift)| Medium| O(nlogn)| O(n)|
 [Palindromic Substrings](https://leetcode.com/problems/palindromic-substrings/)| [Swift](./DP/PalindromicSubstrings.swift)| Medium| O(n^2)| O(n^2)|
 [Longest Palindromic Substring](https://leetcode.com/problems/longest-palindromic-substring/)| [Swift](./DP/LongestPalindromicSubstring.swift)| Medium| O(n^2)| O(n^2)|
 [Perfect Squares](https://leetcode.com/problems/perfect-squares/)| [Swift](./DP/PerfectSquares.swift)| Medium| O(n^2)| O(n)|