1．Fibonacci数列递归算法的实现，集合全排列问题递归算法的实现，整数划分问题递归算法的实现； 2．循环赛日程表问题和棋盘覆盖分治算法的实现

1. Fibonacci数列递归算法的实现： ```python def fibonacci(n): if n <= 1: return n else: return fibonacci(n-1) + fibonacci(n-2) ``` 2. 集合全排列问题递归算法的实现： ```python def permute(nums): result = [] backtrack(nums, [], result) return result def backtrack(nums, path, result): if not nums: result.append(path) else: for i in range(len(nums)): backtrack(nums[:i] + nums[i+1:], path + [nums[i]], result) ``` 3. 整数划分问题递归算法的实现： ```python def integer_partition(n, m): if n == 0 or m == 1: return 1 elif n < m: return integer_partition(n, n) else: return integer_partition(n, m-1) + integer_partition(n-m, m) ``` 4. 循环赛日程表问题的分治算法实现： ```python def schedule(n): if n == 1: return [[0]] else: prev = schedule(n // 2) curr = [] for i in range(n): curr.extend([row + [row[-1] + n//2] for row in prev]) prev = prev[-1:] + prev[:-1] return curr ``` 5. 棋盘覆盖分治算法的实现（采用分治算法的思想，具体实现有多种方式）： ```python def chessboard_cover(board, tr, tc, dr, dc, size, special_row, special_col): if size == 1: return current_tile = tile++ sub_tile = tile tile += 1 half_size = size // 2 # 特殊方格在左上角象限 if special_row < tr + half_size and special_col < tc + half_size: chessboard_cover(board, tr, tc, dr, dc, half_size, special_row, special_col) else: board[tr + half_size - 1][tc + half_size - 1] = sub_tile chessboard_cover(board, tr, tc, tr + half_size - 1, tc + half_size - 1, half_size, special_row, special_col) # 特殊方格在右上角象限 if special_row < tr + half_size and special_col >= tc + half_size: chessboard_cover(board, tr, tc + half_size, dr, dc, half_size, special_row, special_col) else: board[tr + half_size - 1][tc + half_size] = sub_tile chessboard_cover(board, tr, tc + half_size, tr + half_size - 1, tc + half_size, half_size, special_row, special_col) # 特殊方格在左下角象限 if special_row >= tr + half_size and special_col < tc + half_size: chessboard_cover(board, tr + half_size, tc, dr, dc, half_size, special_row, special_col) else: board[tr + half_size][tc + half_size - 1] = sub_tile chessboard_cover(board, tr + half_size, tc, tr + half_size, tc + half_size - 1, half_size, special_row, special_col) # 特殊方格在右下角象限 if special_row >= tr + half_size and special_col >= tc + half_size: chessboard_cover(board, tr + half_size, tc + half_size, dr, dc, half_size, special_row, special_col) else: board[tr + half_size][tc + half_size] = sub_tile chessboard_cover(board, tr + half_size, tc + half_size, tr + half_size, tc + half_size, half_size, special_row, special_col) ``` 请注意，这些算法的实现仅供参考，并未进行详尽的错误处理和优化。在实际应用中，需要根据具体情况进行适当的修改和改进。