Matrix (Magic Algorithm)

Last night, the seniors taught us such a magic algorithm---matrix fast power, matrix fast power in recursive optimization is quite magical, and high efficiency.

　First, give such an example. We all know about the Fibonacci sequence. F[N]=F[N-1]+F[N+2] (n=108), seeking f[n];

This kind of topic, if use recursion to do go down certainly time-out. But it's easy to solve with matrices.

F[N] * 0 1 = f[n+1]

F[n+1] ... A 1 1 ... C f[n+2] ... b a matrix *c matrix gets B matrix. The C matrix is introduced, and the main core is the introduction of a matrix with a to get the B matrix. (That is, I know the current state and the next state, I will ask the intermediary medium, so that can be infinitely aware of the next state, down the state ....)  The value of ~ ~) we know f[1]=1,f[2]=1; A*cn=b, and then to the Cn quick power to take the mold is OK!

After a little bit of understanding, change it.

　Two, there are a,b,c,d four cities, as shown . from the a->d in the condition of just n steps to go. N is very big and big.　How many ways to ask.

The initial of this is to walk 0 steps to the next position of the Matrix a=e (the unit matrix), and then the obvious mediation matrix is a B c D

A 0 1 1 0

b 0 0 1 1

C 1 1 0 1

D 0 1 1 0....C then a*c can get the number of two steps to a place. Where "1" indicates that A->b has a method.

Third, there are still a,b,c,d four cities,. I'm going to go from a to D in exactly n steps, plus one requirement is the shortest distance. To find the shortest distance. Similar to the previous, this is not a detailed explanation 0.0

Seniors also talked about the regional game several topics, 1:30 will say not clear, from the morning summary to now, should go to eat = = Summarize it

Matrix Fast Power Main is to write the three matrix to solve the problem, although now is only a thought, which is doped with some dynamic programming problems, but very practical, can be very fast to solve the N value is particularly large, or similar combinatorial problems.

Matrix (Magic Algorithm)