[bhyun-kim, 김병현] Week 10 solutions

Author: sbk1014

graph-valid-tree/bhyun-kim.py

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+"""
+261. Graph Valid Tree
+https://leetcode.com/problems/graph-valid-tree/
+
+Solution:
+    To solve this problem, we can use the depth-first search (DFS) algorithm.
+    We can create an adjacency list to represent the graph.
+    Then, we can perform a DFS starting from node 0 to check if all nodes are visited.
+    If all nodes are visited, we return True; otherwise, we return False.
+
+Time complexity: O(n)
+    - We visit each node once.
+    - The DFS has a time complexity of O(n).
+
+Space complexity: O(n)
+    - We use an adjacency list to store the graph.
+    - The space complexity is O(n) for the adjacency list.
+"""
+
+
+from typing import List
+
+
+class Solution:
+    def validTree(self, n: int, edges: List[List[int]]) -> bool:
+        if len(edges) != n - 1:
+            return False
+
+        # Initialize adjacency list
+        graph = {i: [] for i in range(n)}
+        for a, b in edges:
+            graph[a].append(b)
+            graph[b].append(a)
+
+        # Function to perform DFS
+        def dfs(node, parent):
+            visited.add(node)
+            for neighbor in graph[node]:
+                if neighbor == parent:
+                    continue
+                if neighbor in visited or not dfs(neighbor, node):
+                    return False
+            return True
+
+        visited = set()
+
+        # Start DFS from node 0
+        if not dfs(0, -1):
+            return False
+
+        # Check if all nodes are visited
+        return len(visited) == n

house-robber-ii/bhyun-kim.py

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+"""
+213. House Robber II
+https://leetcode.com/problems/house-robber-ii/
+
+Solution:
+    To solve this problem, we can use the dynamic programming approach.
+    We can create a helper function to solve the house robber problem for a given range of houses.
+    We consider two cases:
+        - Rob houses from 0 to n-2.
+        - Rob houses from 1 to n-1.
+    We return the maximum amount of money that can be robbed from these two cases.
+
+Time complexity: O(n)
+    - We iterate through each house once.
+    - The helper function has a time complexity of O(n).
+
+Space complexity: O(n)
+    - We use a dynamic programming array to store the maximum amount of money that can be robbed.
+    - The space complexity is O(n) for the dynamic programming array.
+
+"""
+
+from typing import List
+
+
+class Solution:
+    def rob(self, nums: List[int]) -> int:
+        def rob_linear(houses):
+            if not houses:
+                return 0
+            if len(houses) == 1:
+                return houses[0]
+            dp = [0] * len(houses)
+            dp[0] = houses[0]
+            dp[1] = max(houses[0], houses[1])
+            for i in range(2, len(houses)):
+                dp[i] = max(dp[i - 1], houses[i] + dp[i - 2])
+            return dp[-1]
+
+        n = len(nums)
+        if n == 1:
+            return nums[0]
+        if n == 2:
+            return max(nums[0], nums[1])
+
+        # Case 1: Rob houses from 0 to n-2
+        case1 = rob_linear(nums[:-1])
+        # Case 2: Rob houses from 1 to n-1
+        case2 = rob_linear(nums[1:])
+
+        return max(case1, case2)

house-robber/bhyun-kim.py

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+"""
+198. House Robber
+https://leetcode.com/problems/house-robber/
+
+Solution:
+    To solve this problem, we can use the dynamic programming approach.
+    We can create a dynamic programming array to store the maximum amount of money that can be robbed.
+    We consider two cases:
+        - Rob the current house and the house two steps back.
+        - Skip the current house and rob the house one step back.
+    We return the maximum amount of money that can be robbed from these two cases.
+
+Time complexity: O(n)
+    - We iterate through each house once.
+    - The dynamic programming array has a time complexity of O(n).
+
+Space complexity: O(n)
+    - We use a dynamic programming array to store the maximum amount of money that can be robbed.
+    - The space complexity is O(n) for the dynamic programming array.
+"""
+
+from typing import List
+
+
+class Solution:
+    def rob(self, nums: List[int]) -> int:
+        if not nums:
+            return 0
+        if len(nums) == 1:
+            return nums[0]
+
+        n = len(nums)
+        dp = [0] * n
+        dp[0] = nums[0]
+        dp[1] = max(nums[0], nums[1])
+
+        for i in range(2, n):
+            dp[i] = max(dp[i - 1], nums[i] + dp[i - 2])
+
+        return dp[-1]

longest-palindromic-substring/bhyun-kim.py

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+"""
+5. Longest Palindromic Substring
+https://leetcode.com/problems/longest-palindromic-substring/
+
+Solution:
+    To solve this problem, we can use the expand from center approach.
+    We can iterate through each character in the string and expand around it to find palindromes.
+    We handle both odd-length and even-length palindromes by checking two cases.
+    We return the longest palindrome found.
+
+Time complexity: O(n^2)
+    - We iterate through each character in the string.
+    - For each character, we expand around it to find palindromes.
+
+Space complexity: O(1)
+    - We use constant space to store the maximum palindrome found.
+
+"""
+
+
+class Solution:
+    def longestPalindrome(self, s: str) -> str:
+        if len(s) <= 1:
+            return s
+
+        def expand_from_center(left, right):
+            while left >= 0 and right < len(s) and s[left] == s[right]:
+                left -= 1
+                right += 1
+            return s[left + 1 : right]
+
+        max_str = s[0]
+
+        for i in range(len(s) - 1):
+            odd = expand_from_center(i, i)
+            even = expand_from_center(i, i + 1)
+
+            if len(odd) > len(max_str):
+                max_str = odd
+            if len(even) > len(max_str):
+                max_str = even
+
+        return max_str

number-of-connected-components-in-an-undirected-graph/bhyun-kim.py

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+"""
+323. Number of Connected Components in an Undirected Graph
+https://leetcode.com/problems/number-of-connected-components-in-an-undirected-graph/
+
+Solution:
+    To solve this problem, we can use the depth-first search (DFS) algorithm.
+    We can create an adjacency list to represent the graph.
+    Then, we can perform a DFS starting from each node to count the number of connected components.
+    We keep track of visited nodes to avoid revisiting nodes.
+    The number of connected components is the number of times we perform DFS.
+
+Time complexity: O(n+m)
+    - We visit each node and edge once.
+    - The DFS has a time complexity of O(n+m).
+
+Space complexity: O(n+m)
+    - We use an adjacency list to store the graph.
+    - The space complexity is O(n+m) for the adjacency list and visited set.
+
+"""
+
+from typing import List
+
+
+class Solution:
+    def countComponents(self, n: int, edges: List[List[int]]) -> int:
+        # Initialize the graph as an adjacency list
+        graph = {i: [] for i in range(n)}
+        for a, b in edges:
+            graph[a].append(b)
+            graph[b].append(a)
+
+        # Set to keep track of visited nodes
+        visited = set()
+
+        # Function to perform DFS
+        def dfs(node):
+            stack = [node]
+            while stack:
+                current = stack.pop()
+                for neighbor in graph[current]:
+                    if neighbor not in visited:
+                        visited.add(neighbor)
+                        stack.append(neighbor)
+
+        # Count connected components
+        count = 0
+        for i in range(n):
+            if i not in visited:
+                count += 1
+                visited.add(i)
+                dfs(i)
+
+        return count