ZOJ month contest D.Determinant and Matrix

ACM

Time Limit: 2 Seconds Memory Limit: 65536 KB

##Description
Recently, LBH is learning the curse linear algebra. Thus he is very interested in matrix and determinant now. In order to practice his ability of solving the problem of linear algebra, he just invent some problems by himself. Once the problems was create, he would solve it immediately. However, he meet a problem that was so hard that he couldn’t work out even though racked his brains. The problem was described as follow:

To a integer martix Mnn(aij), we define two function add(Mnn(aij))=Mnn(aij + 1) and sub(Mnn(aij))=Mnn(aij - 1) which were exactly like this:

FFT求快速卷积的思考

ACM

离散型卷积的定义是:$$y(n)=\sum_{m=0}^{n} x(m)h(n-m)$$

注意,h函数是反转的。

在Chipher Messages一题中,b串需要反转再与a串匹配。

比如说:

a串: 110110110,则:

b`串:1011<——这里才是原来b串的头。但是向上对应到a串时,已经是m-1这个位置了。所以说,小于m-1的卷积是没有意义的。

于是,base=m。整体匹配。

Timus 1996 Cipher Message 3 KMP+FFT求卷积

ACM

题目链接:click here

##description
Emperor Palpatine has been ruling the Empire for 25 years and Darth Vader has been the head of the Empire Armed Forces. However, the Rebel movement is strong like it never used to be. One of the rebel leaders, Princess Leia from Alderaan, managed to get hold of secret blueprints of the Death Star, the imperial war station.

The Princess was going to deliver the station plan to the secret base for further analysis and searching for vulnerable spots. But her ship was attacked by the space destroyer “Devastator” headed by Darth Vader. At the last moment Princess Leia managed to send her findings to one of the closest planet called Tatooine with her droid R2-D2. Quite conveniently, an old friend of her father Obi-Wan Kenobi lives on that planet.

R2-D2 realizes the importance of his mission. He is going to encrypt the information so that the wrong people won’t get it.

(转)关于卷积的一个血腥的讲解,看完给跪了

ACM

比如说你的老板命令你干活,你却到楼下打台球去了,后来被老板发现,他非常气愤,扇了你一巴掌(注意,这就是输入信号,脉冲),于是你的脸上会渐渐地(贱贱地)鼓起来一个包,你的脸就是一个系统,而鼓起来的包就是你的脸对巴掌的响应,好,这样就和信号系统建立起来意义对应的联系。下面还需要一些假设来保证论证的严谨:假定你的脸是线性时不变系统,也就是说,无论什么时候老板打你一巴掌,打在你脸的同一位置(这似乎要求你的脸足够光滑,如果你说你长了很多青春痘,甚至整个脸皮处处连续处处不可导,那难度太大了,我就无话可说了哈哈),你的脸上总是会在相同的时间间隔内鼓起来一个相同高度的包来,并且假定以鼓起来的包的大小作为系统输出。好了,那么,下面可以进入核心内容——卷积了!

HDU 4952 Number Transformation

ACM

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 612 Accepted Submission(s): 310

Problem Description

Teacher Mai has an integer x.

He does the following operations k times. In the i-th operation, x becomes the least integer no less than x, which is the multiple of i.

He wants to know what is the number x now.