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question:# Matrix Multiplication Coding Challenge **Context**: Matrix multiplication is a fundamental operation in various fields including graphics processing, data transformations, and machine learning. Understanding and implementing matrix multiplication can help solidify concepts related to nested loops and multidimensional data structures. **Objective**: Write a function `multiply(multiplicand, multiplier)` that multiplies two given two-dimensional matrices (lists of lists) and returns their product. Ensure to handle incompatible matrix dimensions gracefully and consider efficiency for larger matrices. **Input**: - Two matrixes as two-dimensional lists: - `multiplicand`: List[List[int]] — a matrix with dimensions m x n. - `multiplier`: List[List[int]] — a matrix with dimensions n x p. **Output**: - The resultant matrix as a two-dimensional list: List[List[int]] — a matrix with dimensions m x p. **Constraints**: - Each inner list in the input matrices represents a row. - Elements of the matrices will be integers. - Handling the case when the number of columns in the multiplicand is not equal to the number of rows in the multiplier by raising an exception. **Example**: ```python # Example 1: multiplicand = [ [1, 2], [3, 4] ] multiplier = [ [2, 0], [1, 2] ] # Resultant Matrix should be: # [ # [4, 4], # [10, 8] # ] result = multiply(multiplicand, multiplier) print(result) # Expected Output: [[4, 4], [10, 8]] ``` **Performance Requirements**: Ensure the implementation runs efficiently within acceptable limits for matrix dimensions up to 100x100. **Implementation**: Consider edge cases and ensure your implementation is robust against invalid inputs.
answer:def multiply(multiplicand, multiplier): Multiplies two given two-dimensional matrices and returns their product. :param multiplicand: List[List[int]] — matrix with dimensions m x n :param multiplier: List[List[int]] — matrix with dimensions n x p :return: List[List[int]] — resulting matrix with dimensions m x p :raises ValueError: if the number of columns in the multiplicand is not equal to the number of rows in the multiplier # Check dimensions m = len(multiplicand) n = len(multiplicand[0]) n2 = len(multiplier) p = len(multiplier[0]) if n != n2: raise ValueError("Incompatible dimensions for matrix multiplication.") # Initialize the result matrix with zeros result = [[0 for _ in range(p)] for _ in range(m)] # Perform matrix multiplication for i in range(m): for j in range(p): for k in range(n): result[i][j] += multiplicand[i][k] * multiplier[k][j] return result
question:You are required to implement a class `DynamicSeparateChainingHashTable` that extends the functionality of a standard Separate Chaining Hash Table by dynamically resizing the table when the load factor exceeds a certain threshold. # Requirements: 1. **Class Definition**: * Implement the class `DynamicSeparateChainingHashTable` which should inherit from `SeparateChainingHashTable`. 2. **Dynamic Resizing**: * When the number of elements (load factor) exceeds 0.75 times the current table size, double the table size. * Rehash all elements when resizing. 3. **Input and Output**: * Implement the same `put`, `get`, and `del_` methods to insert, retrieve, and delete key-value pairs. * Ensure that other utility functions like `__len__`, `__getitem__`, and `__setitem__` work seamlessly. # Function Signatures: ```python class DynamicSeparateChainingHashTable(SeparateChainingHashTable): def __init__(self, size=11): super().__init__(size) def put(self, key, value): # New code for resizing if necessary super().put(key, value) def get(self, key): return super().get(key) def del_(self, key): super().del_(key) def _resize_and_rehash(self): # Implement the logic to resize and rehash all elements pass ``` # Details: 1. **Dynamic Resizing**: - When resizing, double the current size of the table and rehash all existing elements. - `_resize_and_rehash` function should create a new table with doubled size and rehash all elements from the old table to the new table. 2. **Edge Cases**: - Resizing should happen transparently without disrupting ongoing operations. - Handle scenarios where keys are frequently inserted and deleted, maintaining a balanced load factor. 3. **Performance**: - Ensure resizing and rehashing maintains average case O(1) insertion and lookup time, but understand that resizing will have O(n). - Optimize the `put` method to check load factor and trigger resizing. # Example: ```python >>> table = DynamicSeparateChainingHashTable(size=4) >>> table.put('key1', 'value1') >>> table.put('key2', 'value2') >>> table.put('key3', 'value3') >>> table.put('key4', 'value4') # This should trigger resizing >>> table.get('key1') 'value1' >>> table.del_('key2') >>> table.get('key2') is None True ``` # Constraints: * Assume keys are strings and values are any data type. * Keys will contain only printable ASCII characters. Implement the `DynamicSeparateChainingHashTable` class enhancing the provided code with a detailed focus on dynamic resizing and element rehashing.
answer:class SeparateChainingHashTable: def __init__(self, size=11): self.size = size self.table = [[] for _ in range(size)] self.num_elements = 0 def hash_function(self, key): return hash(key) % self.size def put(self, key, value): index = self.hash_function(key) for entry in self.table[index]: if entry[0] == key: entry[1] = value return self.table[index].append([key, value]) self.num_elements += 1 def get(self, key): index = self.hash_function(key) for entry in self.table[index]: if entry[0] == key: return entry[1] return None def del_(self, key): index = self.hash_function(key) for i, entry in enumerate(self.table[index]): if entry[0] == key: del self.table[index][i] self.num_elements -= 1 return return None def __len__(self): return self.num_elements def __getitem__(self, key): return self.get(key) def __setitem__(self, key, value): self.put(key, value) class DynamicSeparateChainingHashTable(SeparateChainingHashTable): def __init__(self, size=11): super().__init__(size) self.load_factor_threshold = 0.75 def put(self, key, value): super().put(key, value) if self.num_elements / self.size > self.load_factor_threshold: self._resize_and_rehash() def _resize_and_rehash(self): old_table = self.table new_size = self.size * 2 self.size = new_size self.table = [[] for _ in range(new_size)] self.num_elements = 0 for bucket in old_table: for key, value in bucket: super().put(key, value)
question:Implement a function `reverse_stutter` that takes a stack as a parameter and reverses the order of the elements in the stack and then duplicates each reversed element twice. This should be achieved using a single queue as auxiliary storage. Function Signature: ```python def reverse_stutter(stack: list) -> list: pass ``` Input: A list of integers representing the stack with the top of the stack being the last element of the list. Example: ``` stack = [3, 7, 1, 14, 9] ``` Output: A list of integers representing the modified stack, where the elements are reversed and each element is duplicated twice. Example: ``` reverse_stutter([3, 7, 1, 14, 9]) -> [9, 9, 14, 14, 1, 1, 7, 7, 3, 3] ``` Constraints: 1. The function should use only O(n) auxiliary space. 2. The solution should run in O(n) time complexity. 3. You may assume the stack will not hold more than 1000 elements. Notes: - An empty stack should return an empty list. - Consider edge cases such as a stack with one element. Example: ```python assert reverse_stutter([3, 7, 1, 14, 9]) == [9, 9, 14, 14, 1, 1, 7, 7, 3, 3] assert reverse_stutter([]) == [] assert reverse_stutter([8]) == [8, 8] ```
answer:from collections import deque def reverse_stutter(stack: list) -> list: Takes a stack (represented as a list with the top being the last element) and returns a new stack where the elements are in reverse order and each is duplicated twice. if not stack: return [] queue = deque() # Move elements from stack to queue while stack: queue.append(stack.pop()) # Move elements back to stack, now in reverse order and duplicate each while queue: elem = queue.popleft() stack.append(elem) stack.append(elem) return stack
question:# Rotate Matrix 90 Degrees (Clockwise) Consider an `n x n` 2D matrix representing an image. You need to rotate the image 90 degrees clockwise in-place, without using any extra space. # Function Signature ```python def rotate(mat: List[List[int]]) -> None: pass ``` # Input * A 2D list `mat` with dimensions `n x n` where `n` is an integer (1 ≤ n ≤ 20). # Output * The function should modify the 2D list `mat` in place such that it represents the image rotated 90 degrees clockwise. # Examples ```python # Example 1 mat = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] rotate(mat) print(mat) # Output: # [ # [7, 4, 1], # [8, 5, 2], # [9, 6, 3] # ] # Example 2 mat = [ [1, 2], [3, 4] ] rotate(mat) print(mat) # Output: # [ # [3, 1], # [4, 2] # ] ``` # Constraints * The function must modify the matrix in-place. * You cannot use any additional data structures for storage. # Detailed Requirements 1. Ensure your function handles all edge cases like an empty matrix and matrices with single element. 2. The input matrix will always be a square matrix (n x n). # Performance Requirements * The time complexity of your solution should be O(n^2), and the space complexity should be O(1). # Implementation Steps 1. Reverse the rows of the matrix. 2. Swap the symmetry elements by traversing only half of the matrix diagonally.
answer:def rotate(mat): Rotates the given n x n 2D matrix by 90 degrees clockwise in place. n = len(mat) # Step 1: Reverse the matrix rows mat.reverse() # Step 2: Transpose the matrix for i in range(n): for j in range(i, n): mat[i][j], mat[j][i] = mat[j][i], mat[i][j]