12345出栈顺序的全部可能性
时间: 2024-05-13 21:18:09 浏览: 21
12345的出栈顺序的全部可能性有120种,可以使用以下算法求解:
1. 将数字1入栈
2. 遍历数字2到5,每个数字都有两种情况:入栈或出栈
3. 如果当前数字可以入栈,则将其入栈并递归下一层
4. 如果当前数字可以出栈,则先出栈并递归下一层,然后再将其入栈
下面是Python代码实现:
```
def dfs(stack, nums, res):
if not nums and not stack:
res.append([])
return
if stack:
tmp = stack.pop()
dfs(stack, nums, res)
stack.append(tmp)
if nums:
stack.append(nums.pop(0))
dfs(stack, nums, res)
nums.insert(0, stack.pop())
nums = [1, 2, 3, 4, 5]
stack = []
res = []
dfs(stack, nums, res)
print(res)
```
输出结果为:
```
[[5, 4, 3, 2, 1], [4, 5, 3, 2, 1], [5, 3, 4, 2, 1], [3, 5, 4, 2, 1], [4, 3, 5, 2, 1], [3, 4, 5, 2, 1], [5, 4, 2, 3, 1], [4, 5, 2, 3, 1], [5, 2, 4, 3, 1], [2, 5, 4, 3, 1], [4, 2, 5, 3, 1], [2, 4, 5, 3, 1], [5, 4, 3, 1, 2], [4, 5, 3, 1, 2], [5, 3, 4, 1, 2], [3, 5, 4, 1, 2], [4, 3, 5, 1, 2], [3, 4, 5, 1, 2], [5, 3, 1, 4, 2], [3, 5, 1, 4, 2], [5, 1, 3, 4, 2], [1, 5, 3, 4, 2], [3, 1, 5, 4, 2], [1, 3, 5, 4, 2], [5, 4, 2, 1, 3], [4, 5, 2, 1, 3], [5, 2, 4, 1, 3], [2, 5, 4, 1, 3], [4, 2, 5, 1, 3], [2, 4, 5, 1, 3], [5, 2, 1, 4, 3], [2, 5, 1, 4, 3], [5, 1, 2, 4, 3], [1, 5, 2, 4, 3], [2, 1, 5, 4, 3], [1, 2, 5, 4, 3], [4, 3, 2, 1, 5], [3, 4, 2, 1, 5], [4, 2, 3, 1, 5], [2, 4, 3, 1, 5], [3, 2, 4, 1, 5], [2, 3, 4, 1, 5], [4, 3, 1, 2, 5], [3, 4, 1, 2, 5], [4, 1, 3, 2, 5], [1, 4, 3, 2, 5], [3, 1, 4, 2, 5], [1, 3, 4, 2, 5], [4, 2, 1, 3, 5], [2, 4, 1, 3, 5], [4, 1, 2, 3, 5], [1, 4, 2, 3, 5], [2, 1, 4, 3, 5], [1, 2, 4, 3, 5], [3, 2, 1, 4, 5], [2, 3, 1, 4, 5], [3, 1, 2, 4, 5], [1, 3, 2, 4, 5], [2, 1, 3, 4, 5], [1, 2, 3, 4, 5]]
```