【矩阵快速幂】 hdu5015 233Matrix
233 Matrix
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 2178 Accepted Submission(s): 1273
Problem Description
In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333... (it means a
0,1 = 233,a
0,2 = 2333,a
0,3 = 23333...) Besides, in 233 matrix, we got a
i,j = a
i-1,j +a
i,j-1( i,j ≠ 0). Now you have known a
1,0,a
2,0,...,a
n,0, could you tell me a
n,m in the 233 matrix?
Input
There are multiple test cases. Please process till EOF.
For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 10 9). The second line contains n integers, a 1,0,a 2,0,...,a n,0(0 ≤ a i,0 < 2 31).
For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 10 9). The second line contains n integers, a 1,0,a 2,0,...,a n,0(0 ≤ a i,0 < 2 31).
Output
For each case, output a
n,m mod 10000007.
Sample Input
1 1 1 2 2 0 0 3 7 23 47 16
Sample Output
234 2799 72937
Hint
Source
2014 ACM/ICPC Asia Regional Xi'an Online
转载：
很显然矩阵的第一列为：
0
a[1]
a[2]
a[3]
a[4]
我们转化一下，转化为
23
a[1]
a[2]
a[3]
a[4]
3
那么由第一列转移到第二列则为
23*10+3
a[1]+23*10+3
a[2]+a[1]+23*10+3
a[3]+a[2]+a[1]+23*10+3
a[4]+a[3]+a[2]+a[1]+23*10+3
3
很显然转移矩阵A就出来了：
10 0 0 0 0 1
10 1 0 0 0 1
10 1 1 0 0 1
10 1 1 1 0 1
10 1 1 1 1 1
0 0 0 0 0 1
那么最后一列就是A的m次方*第一列。
我不会构造这题矩阵，要多练多想啊！！
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手残，mod打错了，耽误了一小时 ；
手残，mod少打了一个零，耽误一小时；