Secret Code

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 670    Accepted Submission(s): 109

Problem Description
The Sarcophagus itself is locked by a secret numerical code. When somebody wants to open it, he must know the code and set it exactly on the top of the Sarcophagus. A very intricate mechanism then opens the cover. If an incorrect code is entered, the tickets inside would catch fire immediately and they would have been lost forever. The code (consisting of up to 100 integers) was hidden in the Alexandrian Library but unfortunately, as you probably know, the library burned down completely. 
But an almost unknown archaeologist has obtained a copy of the code something during the 18th century. He was afraid that the code could get to the ``wrong people'' so he has encoded the numbers in a very special way. He took a random complex number B that was greater (in absolute value) than any of the encoded numbers. Then he counted the numbers as the digits of the system with basis B. That means the sequence of numbers an, an-1, ..., a1, a0 was encoded as the number X = a0 + a1B + a2B2 + ...+ anBn. 
Your goal is to decrypt the secret code, i.e. to express a given number X in the number system to the base B. In other words, given the numbers X and Byou are to determine the ``digit'' a0 through an. 
 
Input
The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case consists of one single line containing four integer numbers Xr, Xi, Br, Bi (|Xr|,|Xi| <= 1000000, |Br|,|Bi| <= 16). These numbers indicate the real and complex components of numbers X and B, i.e. X = Xr + i.Xi, B = Br + i.Bi. B is the basis of the system (|B| > 1), X is the number you have to express. 
 
Output
Your program must output a single line for each test case. The line should contain the ``digits'' an, an-1, ..., a1, a0, separated by commas. The following conditions must be satisfied:  for all i in {0, 1, 2, ...n}: 0 <= ai < |B|  X = a0 + a1B + a2B2 + ...+ anBn  if n > 0 then an <> 0  n <= 100  If there are no numbers meeting these criteria, output the sentence "The code cannot be decrypted.". If there are more possibilities, print any of them. 
 
Sample Input
4
-935 2475 -11 -15
1 0 -3 -2
93 16 3 2
191 -192 11 -12
 
Sample Output
8,11,18
1
The code cannot be decrypted.
16,15

 #include<stdio.h>
#include<string.h>
const int M = ;
typedef __int64 ll ;
ll xr , xi , br , bi ;
int n ;
ll ini ;
ll a[M] ;
ll t ; bool dfs (ll l , ll r , int dep)
{
if (dep > ) return false ;
if (l == && r == ) {
n = dep ;
return true ;
}
ll al , ar ;
for (int i = ; i * i < ini ; i ++) {
al = l - i ; ar = r ;
if ( ( (1ll * al * br + 1ll *ar * bi) % t ) == && ((1ll *ar * br -1ll * al * bi) % t) == ) {
a[dep] = i ;
if ( dfs ( ((1ll * al * br + 1ll * ar * bi) / t) , ((1ll * ar * br - 1ll * al * bi) / t) , dep + ) )
return true ;
}
}
return false ;
} int main ()
{
//freopen ("a.txt" , "r" , stdin ) ;
ll T ;
scanf ("%I64d" , &T ) ;
while (T --) {
scanf ("%I64d%I64d%I64d%I64d" , &xr , &xi , &br , &bi ) ;
t = br * br + bi * bi ;
ini = br * br + bi * bi ;
if (dfs (xr , xi , ) ) {
if (n == ) puts ("") ;
else {
for (int i = n - ; i >= ; i --) printf ("%I64d%c" , a[i] , i == ? '\n' : ',') ;
}
}
else puts ("The code cannot be decrypted.") ;
}
return ;
}

秦九韶算法:

一般地,一元n次多项式的求值需要经过[n(n+1)]/2次乘法和n次加法,而秦九韶算法只需要n次乘法和n次加法。在人工计算时,一次大大简化了运算过程。
把一个n次多项式
改写成如下形式:
多项式的值时,首先计算最内层括号内一次多项式的值,即
然后由内向外逐层计算一次多项式的值,即
这样,求n次多项式f(x)的值就转化为求n个一次多项式的值。
结论:对于一个n次多项式,至多做n次乘法和n次加法。(当最高次项系数不为1时分别为n次乘法和n次加法 ,当最高次项系数为1时,分别为n-1 次乘法 ,n次加法。)
复数除法运算:
设复数 a + bi  ,  c + di ;
t = c * c + d * d ;
则 (a + bi) / (c + di ) = (ac + bd) / t + (bc - ad) / t  * i ;

hdu.1111.Secret Code(dfs + 秦九韶算法)的更多相关文章

  1. HDU 1111 Secret Code (DFS)

    题目链接 题意 : 给你复数X的Xr和Xi,B的Br和Bi,让你求一个数列,使得X = a0 + a1B + a2B2 + ...+ anBn,X=Xr+i*Xi,B=Br+Bi*i : 思路 : 首 ...

  2. HDU 1111 Secret Code(数论的dfs)

    Secret Code Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u Submit ...

  3. hdu 1111 Secret Code

    http://acm.hdu.edu.cn/showproblem.php?pid=1111 复数除法: #include <cstdio> #include <cstring> ...

  4. [swustoj 679] Secret Code

    Secret Code 问题描述 The Sarcophagus itself is locked by a secret numerical code. When somebody wants to ...

  5. 秦九韶算法 & 三分法

    前言 今天考试出了一个题 郭郭模拟退火骗了75分 于是再次把咕咕了好久的模退提上日程 如果进展顺利 明后天应该会开爬山算法和模退的博客笔记 今天先把今天考试的正解学习一下--三分法 引入 老规矩上板子 ...

  6. Android Secret Code

    我们很多人应该都做过这样的操作,打开拨号键盘输入*#*#4636#*#*等字符就会弹出一个界面显示手机相关的一些信息,这个功能在Android中被称为android secret code,除了这些系 ...

  7. bzoj3157国王奇遇记(秦九韶算法+矩乘)&&bzoj233AC达成

    bz第233题,用一种233333333的做法过掉了(为啥我YY出一个算法来就是全网最慢的啊...) 题意:求sigma{(i^m)*(m^i),1<=i<=n},n<=10^9,m ...

  8. Android 编程下的 Secret Code

    我们很多人应该都做过这样的操作,打开拨号键盘输入 *#*#4636#*#* 等字符就会弹出一个界面显示手机相关的一些信息,这个功能在 Android 中被称为 Android Secret Code, ...

  9. The secret code

    The secret code Input file: stdinOutput file: stTime limit: 1 sec Memory limit: 256 MbAfter returnin ...

随机推荐

  1. AngularJs ngCloak、ngController、ngInit、ngModel

    ngCloak ngCloak指令是为了防止Angular应用在启动加载的时候html模板将会被短暂性的展示.这个指令可以用来避免由HTML模板显示造成不良的闪烁效果. 格式: ng-cloak   ...

  2. 第六次作业——利用MFC实现计算器图形界面以及简单四则运算表达式批处理

    参考资料:      1.MFC响应键盘      2.计算器实例      3.MFC文件对话框      4.MFCUpdateData()函数的使用      5.MFC教程      6.wi ...

  3. Appium for IOS testing on Mac

    一:环境 1.Mac OS X 10.9.1 2.Xcod 5.0.2 3.Appium 1.3.6 下载地址:https://bitbucket.org/appium/appium.app/down ...

  4. [POJ2773]:Happy 2006

    传送门 同样是欧拉函数的基本应用. $\phi (N)$表示$[1,N]$中,$gcd(i,N)==1$的数的个数,同理,其也能表示$[K \times N+1,(K+1) \times N]$中$g ...

  5. JavaScript中捕获/阻止捕获、冒泡/阻止冒泡

    JavaScript中捕获/阻止捕获.冒泡/阻止冒泡 事件流描述的是从页面中接收事件的顺序.提出事件流概念的正是IE和Netscape,但是前者提出的是我们常用的事件冒泡流,而后者提出的是事件捕获流. ...

  6. spring--aop总结

    AOP(Aspect Oriented Programming的缩写)所用的思想其实和设计模式是一样的,即在不修改原代码的情况下统一增加或者修改功能.还有,AOP大多用在spring里面. AOP是面 ...

  7. JS-Array数组对象

    <!DOCTYPE html><html> <head> <meta charset="UTF-8"> <title>A ...

  8. dedecms笔记

    截取字符串 方法一: [field:title function="cn_substr(@me,10)"/] 方法二: {dede:arclist typeid=’9′ title ...

  9. imageserver

    https://bitbucket.org/tamtam-nl/tamtam-nuget-imageserver/overview https://www.nuget.org/packages/Tam ...

  10. ServiceBase 备份

    using CanDoo.Contracts; using CanDoo.Core.Data; using System; using System.Collections.Generic; usin ...