2017山东省赛 Fireworks

最新推荐文章于 2018-05-03 19:37:06 发布

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本文介绍了一种基于杨辉三角原理的烟花爆炸模拟算法。通过解析题目，我们了解到在特定时间点，烟花的位置分布遵循杨辉三角的规律。文章还讨论了如何处理取模运算中的除法问题，介绍了使用逆元及费马小定理来解决这一难题。

Description

Hmz likes to play fireworks, especially when they are put regularly.
Now he puts some fireworks in a line. This time he put a trigger on each firework. With that trigger, each firework will explode and split into two parts per second, which means if a firework is currently in positionx, then in next second one part will be in position x−1 and one inx+1. They can continue spliting without limits, as Hmz likes.
Now there are n fireworks on the number axis. Hmz wants to know after T seconds, how many fireworks are there in position w?

Input

Input contains multiple test cases.
For each test case:

· The first line contains 3 integers n,T,w(n,T,|w|≤105)

· In next n lines, each line contains two integers xi and ci, indicating there are ci fireworks in position xi at the beginning(ci,|xi|≤105).

Output

For each test case, you should output the answer MOD 1000000007.

一开始题意有点理解歪了，于是去网上搜了一下，再对比了一下，才发现是杨辉三角，在t时刻，每个位置烟花的数量符合杨辉三角的数量规律。然而数学太差，对杨辉三角并不熟。搜索了一下，杨辉三角第n行m列的值可以表示为 (N)!/((M)!*(N-M)!)，因为是同一时间，也就是说N是同一个值，这样就可以写出同一层的递推式。，，，，但是这个时候又有一个问题就是除法取模的问题，要用逆元解决，从来没用过逆元又学习了一下费马小定理。根据网上的资料，（a / b） MOD M = a* b^(M-2) (mod M)。之后的只要讨论一下就可以了。再做几道题用用逆元吧！