Longest increasing subsequence

arai60/longest_increasing_subsequence/phase1.py

@@ -0,0 +1,8 @@
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        lis_so_far = [1] * len(nums) # lis: longest increasing subsequence 
+        for i in range(len(nums)-1):
+            for j in range(i+1, len(nums)):
+                if nums[i] < nums[j] and lis_so_far[j] < lis_so_far[i] + 1:
+                    lis_so_far[j] = lis_so_far[i] + 1
+        return max(lis_so_far)

arai60/longest_increasing_subsequence/phase2.py

@@ -0,0 +1,29 @@
+"""
+Reference
+hayashi-ayさん: https://github.com/hayashi-ay/leetcode/pull/27/files
+rossy0213さん: https://github.com/rossy0213/leetcode/pull/15/files
+sakupan102さん: https://github.com/sakupan102/arai60-practice/pull/32/files 二分探索のところの議論がためになりました
+Exzrgsさん: https://github.com/Exzrgs/LeetCode/pull/18/files
+
+phase1の方法の動的計画法ではなくすることで最後のmax(lis_so_far)の作業をなくすことにした。
+"""
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        lis_so_far = [1] * len(nums) # lis: longest increasing subsequence 
+        max_lis = 1
+        for i in range(len(nums)):
+            for j in range(i):
+                if nums[j] < nums[i]:
+                    lis_so_far[i] = max(lis_so_far[i], lis_so_far[j] + 1)
+            max_lis = max(max_lis, lis_so_far[i])
+        return max_lis
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        MAX_NUM = 10 ** 4
+        increasing_subsequence = [MAX_NUM + 1] * len(nums)
+        for num in nums:
+            index = bisect_left(increasing_subsequence, num)
+            increasing_subsequence[index] = num
+        return bisect_left(increasing_subsequence, MAX_NUM + 1)

arai60/longest_increasing_subsequence/phase3.py

@@ -0,0 +1,10 @@
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        lis_so_far = [1] * len(nums) # lis means longest increasing subsequence
+        max_lis = 1
+        for i in range(1, len(nums)):
+            for j in range(i):
+                if nums[j] < nums[i]:
+                    lis_so_far[i] = max(lis_so_far[i], lis_so_far[j] + 1)
+            max_lis = max(lis_so_far[i], max_lis)
+        return max_lis

arai60/longest_increasing_subsequence/phase4.py

@@ -0,0 +1,9 @@
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        lis_so_far = [1] * len(nums) # lis means longest increasing subsequence
+        max_lis = 1
+        for i in range(1, len(nums)):
+            for j in range(i):
+                if nums[j] < nums[i]:
+                    lis_so_far[i] = max(lis_so_far[i], lis_so_far[j] + 1)
+        return max(lis_so_far)

arai60/longest_increasing_subsequence/phase5.py

@@ -0,0 +1,10 @@
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        lis_so_far = []
+        for num in nums:
+            index = bisect.bisect_left(lis_so_far, num)
+            if index == len(lis_so_far):
+                lis_so_far.append(num)
+            elif index < len(lis_so_far):
+                lis_so_far[index] = num
+        return len(lis_so_far)