【python】算法实现1

实现一个动态规划算法

def dynamic_programming_example(n: int) -> List[int]:
    """
    动态规划示例：计算斐波那契数列

    参数:
    - n: 斐波那契数列的项数

    返回:
    - List[int]: 斐波那契数列前n项
    """
    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

实现一个卡尔玛滤波

def kalman_filter_example(measurements: List[float], process_variance: float, measurement_variance: float) -> List[float]:
    """
    卡尔曼滤波示例

    参数:
    - measurements: 测量值列表
    - process_variance: 过程噪声方差
    - measurement_variance: 测量噪声方差

    返回:
    - List[float]: 滤波后的值
    """
    n = len(measurements)
    filtered_values = [0.0] * n
    estimate = 0.0
    error_estimate = 1.0

    for i in range(n):
        # 预测步骤
        estimate = estimate
        error_estimate += process_variance

        # 更新步骤
        kalman_gain = error_estimate / (error_estimate + measurement_variance)
        estimate += kalman_gain * (measurements[i] - estimate)
        error_estimate *= (1 - kalman_gain)

        filtered_values[i] = estimate

    return filtered_values

实现一个简单的排序算法

def simple_sort(arr: List[int]) -> List[int]:
    """
    简单排序算法：冒泡排序

    参数:
    - arr: 待排序的整数列表

    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

实现一个二叉树搜索

def binary_search_tree_insert(root: Dict[str, Any], value: int) -> Dict[str, Any]:
    """
    二叉树插入操作

    参数:
    - root: 二叉树的根节点
    - value: 要插入的值

    返回:
    - Dict[str, Any]: 更新后的二叉树根节点
    """
    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

实现一个二分查找

def binary_search(arr: List[int], target: int) -> int:
    """
    二分查找算法

    参数:
    - arr: 已排序的整数列表
    - target: 要查找的目标值

    返回:
    - int: 目标值的索引，如果未找到则返回 -1
    """
    left, right = 0, len(arr) - 1

    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1

    return -1

实现一个简单的图遍历算法

def depth_first_search(graph: Dict[str, List[str]], start: str, visited: set = None) -> List[str]:
    """
    深度优先搜索算法

    参数:
    - graph: 图的邻接表表示
    - start: 起始节点
    - visited: 已访问节点集合

    返回:
    - List[str]: 访问顺序列表
    """
    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

实现一个简单的广度优先搜索算法

def breadth_first_search(graph: Dict[str, List[str]], start: str) -> List[str]:
    """
    广度优先搜索算法

    参数:
    - graph: 图的邻接表表示
    - start: 起始节点

    返回:
    - List[str]: 访问顺序列表
    """
    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

实现一个简单的哈希表

def simple_hash_table_insert(hash_table: Dict[int, List[Any]], key: int, value: Any):
    """
    简单哈希表插入操作

    参数:
    - hash_table: 哈希表，键为整数，值为列表
    - key: 要插入的键
    - value: 要插入的值
    """
    if key not in hash_table:
        hash_table[key] = []
    hash_table[key].append(value)
    

实现一个简单的哈希表查找操作

def simple_hash_table_search(hash_table: Dict[int, List[Any]], key: int) -> List[Any]:
    """
    简单哈希表查找操作

    参数:
    - hash_table: 哈希表，键为整数，值为列表
    - key: 要查找的键

    返回:
    - List[Any]: 对应键的值列表，如果键不存在则返回空列表
    """
    return hash_table.get(key, [])

实现一个简单的命令行界面

def cli():
    import argparse

    parser = argparse.ArgumentParser(description="处理JSON文件，验证并修正camera_segment中的时间一致性")
    parser.add_argument("input_file", help="输入的JSON文件路径")
    parser.add_argument("-o", "--output_file", help="输出的JSON文件路径（可选，默认覆盖原文件）")

    args = parser.parse_args()

    process_json_file(args.input_file, args.output_file)

实现一个简单的二叉树遍历

def binary_tree_traversal(tree: Dict[str, Any], order: str = 'inorder') -> List[Any]:
    """
    遍历二叉树

    参数:
    - tree: 二叉树的字典表示
    - order: 遍历顺序 ('inorder', 'preorder', 'postorder')

    返回:
    - List[Any]: 遍历结果列表
    """
    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

• 图片来自hello
  

动态规划算法给出注释

def dynamic_programming_algorithm_example():
    """
    示例动态规划算法：计算斐波那契数列
    """
    def fibonacci(n):
        if n <= 0:
            return 0
        elif n == 1:
            return 1

        fib = [0] * (n + 1)
        fib[1] = 1

        for i in range(2, n + 1):
            fib[i] = fib[i - 1] + fib[i - 2]

        return fib[n]

    # 测试函数
    print(f"Fibonacci(10) = {fibonacci(10)}")  # 输出: Fibonacci(10) = 55
    

贪心算法给出注释

def greedy_algorithm_example():
    """
    示例贪心算法：找零问题
    """
    def make_change(coins, amount):
        coins.sort(reverse=True)  # 从大到小排序
        change = []
        for coin in coins:
            while amount >= coin:
                amount -= coin
                change.append(coin)
        return change

    # 测试函数
    coins = [25, 10, 5, 1]  # 硬币面额
    amount = 63  # 要找的零
    print(f"找零 {amount} 的结果: {make_change(coins, amount)}")  # 输出: 找零 63 的结果: [25, 25, 10, 1, 1, 1]

分治算法给出注释

def divide_and_conquer_example():
    """
    示例分治算法：归并排序
    """
    def merge_sort(arr):
        if len(arr) <= 1:
            return arr

        mid = len(arr) // 2
        left_half = merge_sort(arr[:mid])
        right_half = merge_sort(arr[mid:])

        return merge(left_half, right_half)

    def merge(left, right):
        result = []
        i = j = 0
        while i < len(left) and j < len(right):
            if left[i] < right[j]:
                result.append(left[i])
                i += 1
            else:
                result.append(right[j])
                j += 1
        result.extend(left[i:])
        result.extend(right[j:])
        return result

    # 测试函数
    arr = [38, 27, 43, 3, 9, 82, 10]
    print(f"归并排序结果: {merge_sort(arr)}")  # 输出: 归并排序结果: [3, 9, 10, 27, 38, 43, 82]

回溯算法给出注释

def backtracking_algorithm_example():
    """
    示例回溯算法：八皇后问题
    """
    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 False
            return True

        def solve(board, row):
            if row == n:
                solutions.append(board[:])
                return
            for col in range(n):
                if is_safe(board, row, col):
                    board[row] = col
                    solve(board, row + 1)

        solutions = []
        board = [-1] * n  # 初始化棋盘
        solve(board, 0)
        return solutions

    # 测试函数
    n = 4
    print(f"八皇后问题的解: {solve_n_queens(n)}")  # 输出: 八皇后问题的解: [[1, 3, 0, 2], [2, 0, 3, 1]]

动态规划算法示例

def dynamic_programming_example():
    """
    示例动态规划算法：计算斐波那契数列
    """
    def fibonacci(n):
        if n <= 0:
            return 0
        elif n == 1:
            return 1

        fib = [0] * (n + 1)
        fib[1] = 1

        for i in range(2, n + 1):
            fib[i] = fib[i - 1] + fib[i - 2]

        return fib[n]

    # 测试函数
    print(f"Fibonacci(10) = {fibonacci(10)}")  # 输出: Fibonacci(10) = 55
    

贪心算法示例

def greedy_algorithm_example():
    """
    示例贪心算法：找零问题
    """
    def make_change(coins, amount):
        coins.sort(reverse=True)  # 从大到小排序
        change = []
        for coin in coins:
            while amount >= coin:
                amount -= coin
                change.append(coin)
        return change

    # 测试函数
    coins = [25, 10, 5, 1]  # 硬币面额
    amount = 63  # 要找的零
    print(f"找零 {amount} 的结果: {make_change(coins, amount)}")  # 输出: 找零 63 的结果: [25, 25, 10, 1, 1, 1]