HANOI tower (Application of divide and conquer Law)

1. Divide and conquer Law

The design idea of the division and control law is to break down a big problem that is hard to solve directly into the same problems of small scale, so as to break through and conquer each other separately.

Generally, the splitting algorithm has three steps on each layer of recursion:

(1) decomposition: the problem is broken down into a series of subproblems.

(2) solving: recursively solving each subproblem. If the sub-problem is small enough, solve it directly.

(3) Merge: Merge the subproblem into the original problem.

2. Hanoi Tower

Typical application of divide and conquer law:

When there is only one plate, you can directly move from A to C;

If we know the n-1 Plate moving scheme, the N Plate moving scheme is as follows:

First, move n-1-1 plates from A to B with the help of C, and then directly move the n-th plate from A to C, then, the n-1 plates at B are moved from B to C with. Now, all the dishes are moved.

Void Hanoi (int n, char a, char B, char c) // move n plates from A to C through B

{

If (n> 1 ){

Hanoi (n-1, A, C, B); // first move the first n-1 plates from A to B

Move (n, a, c); // move the nth plate from A to C.

Hanoi (n-1, B, A, C); // move the n-1-1 plate from B to C through

} Else {

Move (n, a, c); // when there is only one plate, move directly from A to C. Recursive exit

}

}