[bhyun-kim, 김병현] Week 12 Solutions

Author: sbk1014

jump-game/bhyun-kim.py

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+"""
+55. Jump Game
+https://leetcode.com/problems/jump-game/
+
+Solution:
+    To solve this problem, we can use the greedy approach.
+    We iterate through the array and keep track of the maximum index we can reach.
+    If the current index is greater than the maximum index we can reach, we return False.
+    Otherwise, we update the maximum index we can reach.
+    If we reach the end of the array, we return True.
+
+Time complexity: O(n)
+    - We iterate through each element in the array once.
+
+Space complexity: O(1)
+    - We use a constant amount of extra space.
+"""
+
+from typing import List
+
+
+class Solution:
+    def canJump(self, nums: List[int]) -> bool:
+        max_reach = 0
+        for i, jump in enumerate(nums):
+            if i > max_reach:
+                return False
+            max_reach = max(max_reach, i + jump)
+        return max_reach >= len(nums) - 1

longest-common-subsequence/bhyun-kim.py

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+"""
+1143. Longest Common Subsequence
+https://leetcode.com/problems/longest-common-subsequence
+
+Solution:
+    To solve this problem, we can use the dynamic programming approach.
+    We create a 2D list to store the length of the longest common subsequence of the two strings.
+    We iterate through the two strings and update the length of the longest common subsequence.
+    We return the length of the longest common subsequence.
+
+Time complexity: O(n1 * n2)
+    - We iterate through each character in the two strings once.
+    - The time complexity is O(n1 * n2) for updating the length of the longest common subsequence.
+
+Space complexity: O(n1 * n2)
+    - We use a 2D list to store the length of the longest common subsequence of the two strings.
+"""
+
+
+class Solution:
+    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
+        n1 = len(text1)
+        n2 = len(text2)
+        dp = [[0 for i in range(n2 + 1)] for j in range(n1 + 1)]
+        maximum = 0
+        for i in range(1, n1 + 1):
+            for j in range(1, n2 + 1):
+                if text1[i - 1] == text2[j - 1]:
+                    dp[i][j] = dp[i - 1][j - 1] + 1
+                else:
+                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+            maximum = max(dp[i][j], maximum)
+
+        return maximum

longest-increasing-subsequence/bhyun-kim.py

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+"""
+300. Longest Increasing Subsequence
+https://leetcode.com/problems/longest-increasing-subsequence/
+
+Solution:
+    To solve this problem, we can use the dynamic programming approach.
+    We create a list to store the longest increasing subsequence ending at each index.
+    We iterate through the array and update the longest increasing subsequence ending at each index.
+    We return the maximum length of the longest increasing subsequence.
+
+Time complexity: O(n log n)
+    - We iterate through each element in the array once.
+    - We use the bisect_left function to find the position to insert the element in the sub list.
+    - The time complexity is O(n log n) for inserting elements in the sub list.
+
+Space complexity: O(n)
+    - We use a list to store the longest increasing subsequence ending at each index.
+"""
+
+from typing import List
+from bisect import bisect_left
+
+
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        sub = []
+        for num in nums:
+            pos = bisect_left(sub, num)
+            if pos < len(sub):
+                sub[pos] = num
+            else:
+                sub.append(num)
+        return len(sub)

maximum-subarray/bhyun-kim.py

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+"""
+53. Maximum Subarray
+https://leetcode.com/problems/maximum-subarray
+
+Solution:
+    To solve this problem, we can use the Kadane's algorithm.
+    We keep track of the current sum and the maximum sum.
+    We iterate through the array and update the current sum and maximum sum.
+    If the current sum is greater than the maximum sum, we update the maximum sum.
+    We return the maximum sum at the end.
+
+Time complexity: O(n)
+    - We iterate through each element in the array once.
+
+Space complexity: O(1)
+    - We use a constant amount of extra space.
+"""
+
+
+from typing import List
+
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        current_sum = max_sum = nums[0]
+
+        for num in nums[1:]:
+            current_sum = max(num, current_sum + num)
+            max_sum = max(max_sum, current_sum)
+
+        return max_sum

unique-paths/bhyun-kim.py

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+"""
+62. Unique Paths
+https://leetcode.com/problems/unique-paths/
+
+Solution:
+    To solve this problem, we can use the combinatorics approach.
+    We can calculate the number of unique paths using the formula C(m+n-2, m-1).
+    We can create a helper function to calculate the factorial of a number.
+    We calculate the numerator and denominator separately and return the result.
+
+Time complexity: O(m+n)
+    - We calculate the factorial of m+n-2, m-1, and n-1.
+    - The time complexity is O(m+n) for calculating the factorials.
+
+Space complexity: O(1)
+    - We use a constant amount of extra space.
+"""
+
+
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        def factorial(num):
+            previous = 1
+            current = 1
+            for i in range(2, num + 1):
+                current = previous * i
+                previous = current
+            return current
+
+        max_num = m + n - 2
+        numerator = factorial(max_num)
+        factorial_m_minus_1 = factorial(m - 1)
+        factorial_n_minus_1 = factorial(n - 1)
+        result = numerator // (factorial_m_minus_1 * factorial_n_minus_1)
+        return result