Intermixed sequence of Push and pop operations why is this sequence not possible
algorithm, c++, data-structures, stack
Solution
Ok, So the program always pushes 0-9 in that order, so looking at each line, we work out which order the pushes and pops happen
**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 ?
The next pop MUST be 7, because it was pushed before 8, it cannot be 1.
Problem
I'm studying for a final and I can't figure this question out: Suppose that a client performs an intermixed sequence of stack push and pop operations. The push operations push the integers 0 through 9 in order on to the stack; the pop operations print out the return value. Which of the following sequences could not occur? (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 1 0 (e) All of these sequences are possible The answer is C but im not sure how to come to that conclusion