We can just simulate the process mentioned in the description by maintaining a variable for the direction.

Code

Python3

def passThePillow(self, n: int, time: int) -> int:
    if n > time:
        return time + 1
    if n == time: return n - 1
 
    direction = True
    nn = 1
    for i in range(time):
        if nn == 1:
            direction = True
        elif nn == n:
            direction = False
        if direction: nn += 1
        else:         nn -= 1
    
    return nn

Big O Analysis

Runtime

The runtime complexity here is $O (T)$ since we are simulating the process for each second till (T-1).
Memory

The memory usage is $O (1)$ since no explicit data-structure is used in place.

— A

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