推送和弹出操作的混合序列为什么这个序列不可能

Question

大家好,我正在学习决赛,我不能解决这个问题:

假设客户端执行堆栈推送和弹出操作的混合序列.推送操作按顺序将整数0到9推送到堆栈; 弹出操作打印出返回值.以下哪个序列不会发生？

(a)4 3 2 1 0 9 8 7 6 5
(b)2 1 4 3 6 5 8 7 9 0
(c)0 4 6 5 3 8 1 7 2 9
(d)4 6 8 7 5 3 2 9 10
(e)所有这些序列都是可能的

答案是C,但我不确定如何得出这个结论

Answer 1

好的,所以程序总是以这个顺序按0-9,所以看看每一行,我们找出推动和弹出的顺序

**The first line.**   - Stack is
Pushes 0, 1, 2, 3, 4  - [0, 1, 2, 3, 4]
Pops   4, 3, 2, 1, 0  - []
Pushes 5, 6, 7, 8, 9  - [5, 6, 7, 8, 9]
Pops   9, 8, 7, 6, 5  - []

**Second line**  - Stack is  
Pushes 0, 1, 2   - [0, 1, 2]  
Pops   2, 1      - [0]  
Pushes 3, 4      - [0, 3, 4]  
Pops   4, 3      - [0]  
Pushes 5, 6      - [0, 5, 6]  
Pops   6, 5      - [0]  
Pushes 7, 8      - [0, 7, 8]  
Pops   8, 7      - [0]  
Pushes 9         - [0, 9]  
Pops   9, 0      - []  

**Third line**    - Stack is   
Pushes 0          - [0]  
Pops   0          - []  
Pushes 1, 2, 3, 4 - [1, 2, 3, 4]  
Pops   4,         - [1, 2, 3]  
Pushes 5, 6       - [1, 2, 3, 5, 6]  
Pops   6, 5, 3    - [1, 2]  
Pushes 7, 8       - [1, 2, 7, 8]  
Pops   8          - [1, 2, 7]   
Pops   ?            

下一个pop必须是7,因为它在8之前被推,它不能是1.