POJ 1006 生理周期(中国剩余定理)

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Description

Input

Output

Sample Input

0 0 0 0
0 0 0 100
5 20 34 325
4 5 6 7
283 102 23 320
203 301 203 40
-1 -1 -1 -1

Sample Output

Case 1: the next triple peak occurs in 21252 days.
Case 2: the next triple peak occurs in 21152 days.
Case 3: the next triple peak occurs in 19575 days.
Case 4: the next triple peak occurs in 16994 days.
Case 5: the next triple peak occurs in 8910 days.
Case 6: the next triple peak occurs in 10789 days.

思路：

易列出同余方程组：

X ≡ p(mod 23)

X ≡ e(mod 28)

X ≡  i (mod 33)

因为23，28，33互素，所以用中国剩余定理结论：解为sigma（ri*Mi*Mi^-1）

//148K	47MS	C++	716B
#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
int r[4];
int m[4]={0,23,28,33};
int M=m[1]*m[2]*m[3];
int x,y;
int e_gcd(int a,int b,int&x,int &y)
{
    int ans;
    if(b==0) ans=a,x=1,y=0;
    else ans=e_gcd(b,a%b,y,x),y-=(a/b)*x;
    return ans;
}
int main()
{

    int d;
    int cas=0;
    while(scanf("%d%d%d%d",&r[1],&r[2],&r[3],&d),~d)
    {
        cas++;
        int ans=0;
        for(int i=1;i<=3;i++)
        {
            int a=M/m[i];
            e_gcd(a,m[i],x,y);
            ans+=a*x*r[i];
        }
        printf("Case %d: the next triple peak occurs in %d days.\n",cas,((ans-d)%M+M-1)%M+1);
    }
    return 0;
}

POJ 1006 生理周期(中国剩余定理)

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原文地址：http://blog.csdn.net/kalilili/article/details/44938069