poj2663 Tri Tiling

Tri TilingTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 5843Accepted: 3128

Description

In how many ways can you tile a 3xn rectangle with 2x1 dominoes? 
Here is a sample tiling of a 3x12 rectangle. 

Input

Input
consists of several test cases followed by a line containing -1. Each
test case is a line containing an integer 0 <= n <= 30.

Output

For each test case, output one integer number giving the number of possible tilings.

Sample Input

2

8

12

-1

Sample Output

3

153

2131

Source

Waterloo local 2005.09.24

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(参考Matrix67,图片源自Matrix67）；

共8个状态，建图如上，进行n+1次矩阵乘法，然后 000—>111为答案。

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 1 Program Stone;
 2
 3 const a:array[1..8,1..8]of longint=((0,0,0,0,0,1,0,0),
 4
 5                                     (0,0,0,0,1,0,0,0),
 6
 7                                     (0,0,0,0,0,1,0,1),
 8
 9                                     (0,0,0,0,0,0,1,0),
10
11                                     (0,1,0,0,0,1,0,0),
12
13                                     (1,0,1,0,1,0,0,0),
14
15                                     (0,0,0,1,0,0,0,0),
16
17                                     (0,0,1,0,0,0,0,0));
18
19 type ar=array[1..8,1..8]of longint;
20
21 var i,j,k,l,n:longint;
22
23     qu,ti:ar;
24
25
26
27  Procedure time(a,b:ar);
28
29  var i,j,k:longint;
30
31   begin
32
33     fillchar(ti,sizeof(ti),0);
34
35     for i:=1 to 8 do
36
37      for j:=1 to 8 do
38
39       for k:=1 to 8 do
40
41        inc(ti[i,j],a[i,k]*b[k,j]);
42
43   end;
44
45
46
47  Procedure quick(k:longint);
48
49   begin
50
51    if k=1 then begin qu:=a;exit;end;
52
53    quick(k div 2);
54
55    time(qu,qu);
56
57    if k mod 2<>0 then time(ti,a);
58
59    qu:=ti;
60
61   end;
62
63
64
65 Begin
66
67  assign(input,‘input.in‘);reset(input);
68
69   readln(n);
70
71   while n<>-1 do
72
73    begin
74
75     quick(n+1);
76
77     writeln(qu[1,6]);
78
79     readln(n);
80
81    end;
82
83  close(input);
84
85 end.