Interview: Waiting Time

It is known that there are two buses at the bus station at the door of my house.

One of them passes through my house every m minutes.

Another car goes through my house every n minutes.

I can wait for a car to take a bus to work ....

SoAverageHow long can I wait for a car ??

 

The application scenario is for map pathfinding.Algorithm... Calculate the waiting time (used to estimate how long it will take you to reach your destination ).

 

A very simple tip: if there is only one car m, the average time is m/2. If there is one more car n... the time used must be less than M/2.

PS: There are many friends who will think the answer is (m + n)/2, which is obviously incorrect, because I just need to wait for a car to go to work.

PS: M * n/(m + n) is also incorrect.

PS: I don't know when to get out and wait for the bus, and I don't know when M and N start. It's random.

 

Some simple verification logic is attached for checking:

Assume that the result is S.

So there must be

S <n/2

S <m/2

Suppose M is very large, so s must be approximately equal to n/2.

 

PS: so far, the fastest friend has spent 40 minutes to figure out...---# amount... in fact, this question is very simple.

PS: DoProgramI 've been doing this for too long. Don't get stuck.... try to figure it out and see if my mind can be turned over.

 

PS:... release some answers first

 

1. When M = N, the interval between the two vehicles is equal, so the interval between the two buses is very important.

Assuming that the time interval is K, the average time is from 0 to N (2 k * k + N * n-2kn) DK/2n * n

The average waiting time is N/3.

The credit picture cannot be obtained.

2. When 2n> m> N

Assuming that the time interval is K, the average time is from 0 to m for K credits.

(2 k * k + 2n * n + M * m-2mk-2mn-2nk) DK/2 M * m

Result: (3N * m * m-9m * n + 11N * n * N)/18 m * m

If this is an error, please correct it.