[alphaorderly] WEEK 06 Solutions

container-with-most-water/alphaorderly.py

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+"""
+Time Complexity: O(n)
+    - n = number of elements in height
+    - Each index is visited at most once by either the left or right pointer.
+
+Space Complexity: O(1)
+    - Only a small constant number of variables are used (left, right, ans).
+
+Approach:
+    - Initialize two pointers at the beginning (left) and end (right) of the array.
+    - At each step, compute the area formed by the lines at left and right.
+    - Update the maximum area found so far.
+    - Move the pointer pointing to the shorter line inward (increase left or decrease right).
+      - Ensure to move shorter line inward to potentially find a taller line that could increase the area.
+      - Because amount of water is determined by the shorter line.
+    - Continue until the two pointers meet.
+    - Return the maximum area found.
+"""
+class Solution:
+    def maxArea(self, height: List[int]) -> int:
+        N = len(height)
+        left, right = 0, N - 1
+        ans = 0
+
+        while left < right:
+            ans = max(ans, min(height[left], height[right]) * (right - left))
+
+            if height[left] < height[right]:
+                left += 1
+            else:
+                right -= 1
+
+        return ans

design-add-and-search-words-data-structure/alphaorderly.py

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+"""
+Trie-based add and search with wildcard support.
+
+### BFS approach ###
+
+Time Complexity:
+    - addWord: O(L), where L is the length of the inserted word.
+    - search: O(N), where N is the length of the search word; search with '.' wildcard may lead to O(B^N) in the worst case,
+      where B is average branching factor. For ordinary searches (no wildcards), still O(N).
+
+Space Complexity: O(T)
+    - T = total number of characters in all inserted words, due to nodes in the trie.
+"""
+
+class WordDictionary:
+
+    def __init__(self):
+        self.children = dict()
+        self.end = False
+
+    def addWord(self, word: str) -> None:
+        node = self
+        for ch in word:
+            if ch not in node.children:
+                node.children[ch] = WordDictionary()
+            node = node.children[ch]
+        node.end = True
+
+    def search(self, word: str) -> bool:
+        search = deque([self])
+        for ch in word:
+            S = len(search)
+            for _ in range(S):
+                node = search.popleft()
+                if ch == '.':
+                    for child in node.children.values():
+                        search.append(child)
+                elif ch not in node.children:
+                    continue
+                else:
+                    search.append(node.children[ch])
+        return any(node.end for node in search)
+
+"""
+Trie-based add and recursive search with wildcard support.
+
+### DFS approach ###
+
+Time Complexity:
+    - addWord: O(L), where L is the length of the inserted word.
+    - search: Worst case O(B^N), where N is the length of the search word and B is average branching factor if all
+      positions are wildcards. Otherwise O(N) for ordinary search.
+
+Space Complexity: O(T)
+    - T = total number of characters in all inserted words (trie size), plus call stack space O(N) during search.
+"""
+
+class WordDictionary:
+
+    def __init__(self):
+        self.children = dict()
+        self.end = False
+
+    def addWord(self, word: str) -> None:
+        node = self
+        for ch in word:
+            if ch not in node.children:
+                node.children[ch] = WordDictionary()
+            node = node.children[ch]
+        node.end = True
+
+    def search(self, word: str) -> bool:
+        def dfs(node: WordDictionary, index: int) -> bool:
+            if index == len(word):
+                return node.end
+            ch = word[index]
+            if ch == ".":
+                for child in node.children.values():
+                    if dfs(child, index + 1):
+                        return True
+            elif ch in node.children:
+                return dfs(node.children[ch], index + 1)
+            return False
+
+        return dfs(self, 0)

longest-increasing-subsequence/alphaorderly.py

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+"""
+Time Complexity: O(n log n)
+Space Complexity: O(n)
+
+### Binary search approach ###
+
+For each number in nums:
+    - Find the insertion position for num in arr to maintain sorted order (binary search).
+    - If num is greater than all elements in arr, append it (extend the LIS).
+    - Otherwise, replace the element at position with num to keep tails as small as possible.
+"""
+class Solution:
+    def lengthOfLIS(self, nums: List[int]) -> int:
+        arr = []
+
+        for num in nums:
+            position = bisect_left(arr, num)
+            if position == len(arr):
+                arr.append(num)
+            else:
+                arr[position] = num
+
+        return len(arr)

spiral-matrix/alphaorderly.py

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+"""
+Spiral traversal of a matrix: visit all elements in "spiral order" (clockwise from top-left).
+
+Time Complexity: O(N), where N is the total number of elements in matrix.
+    - Each element is visited once.
+
+Space Complexity: O(N)
+    - The output array includes all N elements.
+    - The input matrix is modified in-place to mark visited cells.
+"""
+class Solution:
+    def spiralOrder(self, matrix: List[List[int]]) -> List[int]:
+        ROW = len(matrix)
+        COL = len(matrix[0])
+        TARGET = ROW * COL
+        DIR = [[0, 1], [1, 0], [0, -1], [-1, 0]]
+        CHECK = -1000
+
+        ans = []
+
+        def bound(r: int, c: int) -> bool:
+            return 0 <= r < ROW and 0 <= c < COL
+
+        r = c = d = 0
+
+        for _ in range(TARGET):
+            ans.append(matrix[r][c])
+            matrix[r][c] = CHECK
+
+            tr = r + DIR[d][0]
+            tc = c + DIR[d][1]
+            if not bound(tr, tc) or matrix[tr][tc] == CHECK:
+                d = (d + 1) % 4
+            r += DIR[d][0]
+            c += DIR[d][1]
+
+
+        return ans

valid-parentheses/alphaorderly.py

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+"""
+Time Complexity: O(n)
+    - Each character in the input string s is visited exactly once in a single left-to-right scan.
+    - Each push or pop operation on the stack corresponds to a character, for at most O(n) stack operations.
+
+Space Complexity: O(n)
+    - In the worst case (e.g., all opening brackets), the stack may contain up to n elements.
+    - The auxiliary data structure (`pairs`) uses constant space, as there are only three types of parentheses.
+
+Approach:
+    The algorithm uses a stack to simulate balancing of brackets.
+    - For every opening bracket encountered, push it onto the stack.
+    - For every closing bracket, check if the top of the stack holds its matching opening bracket.
+      - If not, or if the stack is empty, the string is invalid.
+    - At the end, if the stack is empty, all open brackets were matched and closed properly.
+"""
+class Solution:
+    def isValid(self, s: str) -> bool:
+        pairs = {"(": ")", "{": "}", "[": "]"}
+        stack = []
+
+        for ch in s:
+            if ch in pairs:
+                stack.append(ch)
+            elif not stack or pairs[stack[-1]] != ch:
+                return False
+            else:
+                stack.pop()
+
+        return len(stack) == 0