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
时间: 2024-04-09 14:33:05 浏览: 5
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。