Analysis of N-tower problems.

First, let's talk about the Three Towers.

The recursive formula is f (n) = 2f (n-1) + 1.

First, let's talk about how this formula was introduced.

 

We need to move all the plates on the first tower to the last one.

Suppose there are n plates.

Then, we need to first move n-1 dishes to the second tower,

Then, move the largest plate to the 3rd towers.

Finally, move n-1 plates to the third tower.

 

Therefore, F (n) = f (n-1) + 1 + f (n-1) is obtained)

That is, the formula F (n) = 2f (n-1) + 1.

 

 

Four-tower problem: (this method has a problem. It will be wrong at 10. Please give me some advice !)

According to some derivation, the following conclusions are drawn:

 

/F (n) = 1 n = 1

| F (n) = 3 N = 2

| F (n) = 2f (n-2) + 3 n = 3

/F (n) = 2f (n-3) + 7 N> = 4

 

Why is n> = 4?

To get the minimum number of moves, we just need to move the previous n-3 plate to the auxiliary Tower first.

Then move the last three plates to the last tower based on the three towers. (Because one of the towers has been occupied by n-3 plates)

Finally move the n-3 plate to the last tower.

So F (n) = f (n-3) + 7 + f (n-3)

7 is the number of times the three towers need to be moved.

 

Five, six, and seven ...... And so on...

The N-tower problem has also been solved perfectly.