feature: longest increasing subsequence bs revisit

dynamic_programming/LongestIncreasingSubsequence.py

@@ -14,6 +14,25 @@ def length_of_lis_bottom_up(self, nums: List[int]) -> int:
     return max(dp)
 
 
+# O(n * log(n)) time || O(n) space
+def length_of_lis_bs(self, nums: List[int]) -> int:
+    tails = [0] * len(nums)
+    res = 0
+    for num in nums:
+        low, high = 0, res
+        while low != high:
+            mid = low + (high - low) // 2
+            if tails[mid] < num:
+                low = mid + 1
+            else:
+                high = mid
+
+        tails[low] = num
+        res = max(res, low + 1)
+
+    return res
+
+
 # O(n * log(n)) time || O(n) space
 def length_of_lis(self, nums: List[int]) -> int:
     sub = []

dynamic_programming/test/test_length_of_lis.py

@@ -1,19 +1,22 @@
 import unittest
 
-from dynamic_programming.LongestIncreasingSubsequence import length_of_lis, length_of_lis_bottom_up
+from dynamic_programming.LongestIncreasingSubsequence import length_of_lis, length_of_lis_bottom_up, length_of_lis_bs
 
 
 class MyTestCase(unittest.TestCase):
     def test_length_of_lis(self):
         self.assertEqual(4, length_of_lis_bottom_up(self, [10, 9, 2, 5, 3, 7, 101, 18]))
+        self.assertEqual(4, length_of_lis_bs(self, [10, 9, 2, 5, 3, 7, 101, 18]))
         self.assertEqual(4, length_of_lis(self, [10, 9, 2, 5, 3, 7, 101, 18]))
 
     def test_length_of_lis_1(self):
         self.assertEqual(4, length_of_lis_bottom_up(self, [0, 1, 0, 3, 2, 3]))
+        self.assertEqual(4, length_of_lis_bs(self, [0, 1, 0, 3, 2, 3]))
         self.assertEqual(4, length_of_lis(self, [0, 1, 0, 3, 2, 3]))
 
     def test_length_of_lis_2(self):
         self.assertEqual(1, length_of_lis_bottom_up(self, [7, 7, 7, 7, 7, 7, 7]))
+        self.assertEqual(1, length_of_lis_bs(self, [7, 7, 7, 7, 7, 7, 7]))
         self.assertEqual(1, length_of_lis(self, [7, 7, 7, 7, 7, 7, 7]))