實現一個動態規劃算法

def dynamic_programming_example(n: int) -> List[int]:"""動態規劃示例：計算斐波那契數列參數:- n: 斐波那契數列的項數返回:- List[int]: 斐波那契數列前n項"""if n <= 0:return []elif n == 1:return [0]elif n == 2:return [0, 1]fib_sequence = [0, 1]for i in range(2, n):next_value = fib_sequence[i - 1] + fib_sequence[i - 2]fib_sequence.append(next_value)return fib_sequence

實現一個卡爾瑪濾波

def kalman_filter_example(measurements: List[float], process_variance: float, measurement_variance: float) -> List[float]:"""卡爾曼濾波示例參數:- measurements: 測量值列表- process_variance: 過程噪聲方差- measurement_variance: 測量噪聲方差返回:- List[float]: 濾波后的值"""n = len(measurements)filtered_values = [0.0] * nestimate = 0.0error_estimate = 1.0for i in range(n):# 預測步驟estimate = estimateerror_estimate += process_variance# 更新步驟kalman_gain = error_estimate / (error_estimate + measurement_variance)estimate += kalman_gain * (measurements[i] - estimate)error_estimate *= (1 - kalman_gain)filtered_values[i] = estimatereturn filtered_values

實現一個簡單的排序算法

def simple_sort(arr: List[int]) -> List[int]:"""簡單排序算法：冒泡排序參數:- arr: 待排序的整數列表返回:- List[int]: 排序后的列表"""n = len(arr)for i in range(n):for j in range(0, n-i-1):if arr[j] > arr[j+1]:arr[j], arr[j+1] = arr[j+1], arr[j]return arr

實現一個二叉樹搜索

def binary_search_tree_insert(root: Dict[str, Any], value: int) -> Dict[str, Any]:"""二叉樹插入操作參數:- root: 二叉樹的根節點- value: 要插入的值返回:- Dict[str, Any]: 更新后的二叉樹根節點"""if root is None:return {"value": value, "left": None, "right": None}if value < root["value"]:root["left"] = binary_search_tree_insert(root.get("left"), value)else:root["right"] = binary_search_tree_insert(root.get("right"), value)return root

實現一個二分查找

def binary_search(arr: List[int], target: int) -> int:"""二分查找算法參數:- arr: 已排序的整數列表- target: 要查找的目標值返回:- int: 目標值的索引，如果未找到則返回 -1"""left, right = 0, len(arr) - 1while left <= right:mid = (left + right) // 2if arr[mid] == target:return midelif arr[mid] < target:left = mid + 1else:right = mid - 1return -1

實現一個簡單的圖遍歷算法

def depth_first_search(graph: Dict[str, List[str]], start: str, visited: set = None) -> List[str]:"""深度優先搜索算法參數:- graph: 圖的鄰接表表示- start: 起始節點- visited: 已訪問節點集合返回:- List[str]: 訪問順序列表"""if visited is None:visited = set()visited.add(start)result = [start]for neighbor in graph.get(start, []):if neighbor not in visited:result.extend(depth_first_search(graph, neighbor, visited))return result

實現一個簡單的廣度優先搜索算法

def breadth_first_search(graph: Dict[str, List[str]], start: str) -> List[str]:"""廣度優先搜索算法參數:- graph: 圖的鄰接表表示- start: 起始節點返回:- List[str]: 訪問順序列表"""visited = set()queue = [start]result = []while queue:node = queue.pop(0)if node not in visited:visited.add(node)result.append(node)queue.extend(neighbor for neighbor in graph.get(node, []) if neighbor not in visited)return result

實現一個簡單的哈希表

def simple_hash_table_insert(hash_table: Dict[int, List[Any]], key: int, value: Any):"""簡單哈希表插入操作參數:- hash_table: 哈希表，鍵為整數，值為列表- key: 要插入的鍵- value: 要插入的值"""if key not in hash_table:hash_table[key] = []hash_table[key].append(value)

實現一個簡單的哈希表查找操作

def simple_hash_table_search(hash_table: Dict[int, List[Any]], key: int) -> List[Any]:"""簡單哈希表查找操作參數:- hash_table: 哈希表，鍵為整數，值為列表- key: 要查找的鍵返回:- List[Any]: 對應鍵的值列表，如果鍵不存在則返回空列表"""return hash_table.get(key, [])

實現一個簡單的命令行界面

def cli():import argparseparser = argparse.ArgumentParser(description="處理JSON文件，驗證并修正camera_segment中的時間一致性")parser.add_argument("input_file", help="輸入的JSON文件路徑")parser.add_argument("-o", "--output_file", help="輸出的JSON文件路徑（可選，默認覆蓋原文件）")args = parser.parse_args()process_json_file(args.input_file, args.output_file)

實現一個簡單的二叉樹遍歷

def binary_tree_traversal(tree: Dict[str, Any], order: str = 'inorder') -> List[Any]:"""遍歷二叉樹參數:- tree: 二叉樹的字典表示- order: 遍歷順序 ('inorder', 'preorder', 'postorder')返回:- List[Any]: 遍歷結果列表"""if not tree:return []result = []if order == 'preorder':result.append(tree['value'])result.extend(binary_tree_traversal(tree.get('left'), order))result.extend(binary_tree_traversal(tree.get('right'), order))elif order == 'inorder':result.extend(binary_tree_traversal(tree.get('left'), order))result.append(tree['value'])result.extend(binary_tree_traversal(tree.get('right'), order))elif order == 'postorder':result.extend(binary_tree_traversal(tree.get('left'), order))result.extend(binary_tree_traversal(tree.get('right'), order))result.append(tree['value'])return result

• 圖片來自hello
  

動態規劃算法給出注釋

def dynamic_programming_algorithm_example():"""示例動態規劃算法：計算斐波那契數列"""def fibonacci(n):if n <= 0:return 0elif n == 1:return 1fib = [0] * (n + 1)fib[1] = 1for i in range(2, n + 1):fib[i] = fib[i - 1] + fib[i - 2]return fib[n]# 測試函數print(f"Fibonacci(10) = {fibonacci(10)}")  # 輸出: Fibonacci(10) = 55

貪心算法給出注釋

def greedy_algorithm_example():"""示例貪心算法：找零問題"""def make_change(coins, amount):coins.sort(reverse=True)  # 從大到小排序change = []for coin in coins:while amount >= coin:amount -= coinchange.append(coin)return change# 測試函數coins = [25, 10, 5, 1]  # 硬幣面額amount = 63  # 要找的零print(f"找零 {amount} 的結果: {make_change(coins, amount)}")  # 輸出: 找零 63 的結果: [25, 25, 10, 1, 1, 1]

分治算法給出注釋

def divide_and_conquer_example():"""示例分治算法：歸并排序"""def merge_sort(arr):if len(arr) <= 1:return arrmid = len(arr) // 2left_half = merge_sort(arr[:mid])right_half = merge_sort(arr[mid:])return merge(left_half, right_half)def merge(left, right):result = []i = j = 0while i < len(left) and j < len(right):if left[i] < right[j]:result.append(left[i])i += 1else:result.append(right[j])j += 1result.extend(left[i:])result.extend(right[j:])return result# 測試函數arr = [38, 27, 43, 3, 9, 82, 10]print(f"歸并排序結果: {merge_sort(arr)}")  # 輸出: 歸并排序結果: [3, 9, 10, 27, 38, 43, 82]

回溯算法給出注釋

def backtracking_algorithm_example():"""示例回溯算法：八皇后問題"""def solve_n_queens(n):def is_safe(board, row, col):for i in range(row):if board[i] == col or \board[i] - i == col - row or \board[i] + i == col + row:return Falsereturn Truedef solve(board, row):if row == n:solutions.append(board[:])returnfor col in range(n):if is_safe(board, row, col):board[row] = colsolve(board, row + 1)solutions = []board = [-1] * n  # 初始化棋盤solve(board, 0)return solutions# 測試函數n = 4print(f"八皇后問題的解: {solve_n_queens(n)}")  # 輸出: 八皇后問題的解: [[1, 3, 0, 2], [2, 0, 3, 1]]

動態規劃算法示例

def dynamic_programming_example():"""示例動態規劃算法：計算斐波那契數列"""def fibonacci(n):if n <= 0:return 0elif n == 1:return 1fib = [0] * (n + 1)fib[1] = 1for i in range(2, n + 1):fib[i] = fib[i - 1] + fib[i - 2]return fib[n]# 測試函數print(f"Fibonacci(10) = {fibonacci(10)}")  # 輸出: Fibonacci(10) = 55

貪心算法示例

def greedy_algorithm_example():"""示例貪心算法：找零問題"""def make_change(coins, amount):coins.sort(reverse=True)  # 從大到小排序change = []for coin in coins:while amount >= coin:amount -= coinchange.append(coin)return change# 測試函數coins = [25, 10, 5, 1]  # 硬幣面額amount = 63  # 要找的零print(f"找零 {amount} 的結果: {make_change(coins, amount)}")  # 輸出: 找零 63 的結果: [25, 25, 10, 1, 1, 1]