HDOJ 1014 Uniform Generator

Uniform Generator

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 11395    Accepted Submission(s): 4506

Problem Description

Computer simulations often require random numbers. One way to generate pseudo-random numbers is via a function of the form

seed(x+1) = [seed(x) + STEP] % MOD

where '%' is the modulus operator. 

Such a function will generate pseudo-random numbers (seed) between 0 and MOD-1. One problem with functions of this form is that they will always generate the same pattern over and over. In order to minimize this effect, selecting the STEP and MOD values carefully can result in a uniform distribution of all values between (and including) 0 and MOD-1. 

For example, if STEP = 3 and MOD = 5, the function will generate the series of pseudo-random numbers 0, 3, 1, 4, 2 in a repeating cycle. In this example, all of the numbers between and including 0 and MOD-1 will be generated every MOD iterations of the function. Note that by the nature of the function to generate the same seed(x+1) every time seed(x) occurs means that if a function will generate all the numbers between 0 and MOD-1, it will generate pseudo-random numbers uniformly with every MOD iterations. 

If STEP = 15 and MOD = 20, the function generates the series 0, 15, 10, 5 (or any other repeating series if the initial seed is other than 0). This is a poor selection of STEP and MOD because no initial seed will generate all of the numbers from 0 and MOD-1. 

Your program will determine if choices of STEP and MOD will generate a uniform distribution of pseudo-random numbers. 

 

Input

Each line of input will contain a pair of integers for STEP and MOD in that order (1 <= STEP, MOD <= 100000).

 

Output

For each line of input, your program should print the STEP value right- justified in columns 1 through 10, the MOD value right-justified in columns 11 through 20 and either "Good Choice" or "Bad Choice" left-justified starting in column 25. The "Good Choice" message should be printed when the selection of STEP and MOD will generate all the numbers between and including 0 and MOD-1 when MOD numbers are generated. Otherwise, your program should print the message "Bad Choice". After each output test set, your program should print exactly one blank line.

 

Sample Input

3 515 2063923 99999

 

Sample Output

         3         5    Good Choice        15        20    Bad Choice     63923     99999    Good Choice

 

Source

South Central USA 1996

 

Recommend

JGShining

 

题目大意：输入两个数STEP和MOD，借公式生成伪随机数。根据公式：seed(x+1)=[seed(x)+STEP]%MOD，且 seed(x) 从0开始  。如果所有的seed(x)满足从0到mod-1的话，就是  
 good choice否则，就是bad  choice   

eg：
STEP=3，MOD=5  
则seed(x):0  3  1  4  2

一开始觉得应该用数学方法，怕朴素TLE，找不到数学方法只得硬着头皮写。还好数据很弱

//朴素算法 #include <iostream>#include <iomanip>using namespace std;int main(int argc, char *argv[]){bool a[100001];int step,mod,i,s,flag;while (cin>>step>>mod){memset(a,0,sizeof(a));a[0]=1; s=0; flag=1;for(i=1;i<mod;++i){if (a[(s+step)%mod]){flag=0; continue;}s=(s+step)%mod;a[s]=0;}if (flag) cout<<setw(10)<<step<<setw(10)<<mod<<"    Good Choice"<<"\n\n";     else cout<<setw(10)<<step<<setw(10)<<mod<<"    Bad Choice"<<"\n\n"; }return 0;}

后来百度了别人的解法。在ACM2272902662的CSDN博客上发现了数学方法的解释。还有，他的gcd函数很简洁，果断抄走了  3Q

//数学方法 #include <iostream>#include <iomanip>using namespace std;int gcd(int a,int b); int main(int argc, char *argv[]){int step,mod;while (cin>>step>>mod)if (gcd(step,mod)==1) cout<<setw(10)<<step<<setw(10)<<mod<<"    Good Choice"<<"\n\n"; else cout<<setw(10)<<step<<setw(10)<<mod<<"    Bad Choice"<<"\n\n";return 0;}int gcd(int a,int b){return b? gcd(b,a%b):a;}

kdwycz的网站：  http://kdwycz.com/

kdwyz的刷题空间：http://blog.csdn.net/kdwycz