HDU 5015 233 Matrix 【矩阵快速幂】

最新推荐文章于 2022-04-14 22:34:08 发布

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最新推荐文章于 2022-04-14 22:34:08 发布

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分类专栏：数学思维文章标签： matrix 矩阵快速幂

本文链接：https://blog.youkuaiyun.com/qq_33184171/article/details/52067386

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该博客介绍了如何利用矩阵快速幂解决HDU 5015题目的过程，详细阐述了如何构造矩阵并进行运算以求得an,m的值。博主分别计算了a[i][0]为0和a[0][i]为0时的情况，并将两者相加得出最终结果。文章包含解题思路、矩阵构造和代码实现。" 123506466,8567465,Django接口中序列化器参数传递技巧,"['Django', '后端', 'Python']

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题目连接:http://acm.hdu.edu.cn/showproblem.php?pid=5015

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233 Matrix

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1817 Accepted Submission(s): 1075

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 a0,1 = 233,a0,2 = 2333,a0,3 = 23333…) Besides, in 233 matrix, we got ai,j = ai-1,j +ai,j-1( i,j ≠ 0). Now you have known a1,0,a2,0,…,an,0, could you tell me an,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 ≤ 109). The second line contains n integers, a1,0,a2,0,…,an,0(0 ≤ ai,0 < 231).

Output
For each case, output an,m mod 10000007.

Sample Input
1 1
1
2 2
0 0
3 7
23 47 16

Sample Output
234
2799
72937

Hint
这里写图片描述