POJ1006（中国剩余定理+大衍求一术）

标签：剩余定理+大衍求一术

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.

解题思路：

	题目大意就是身体、情感、智力的周期分别为23、28和33。给你三者峰值出现的时间，问下一次三个高峰同时出现的所需天数。

	强大的数学····Orz····给出剩余定理的例子：

n%3=2,n%5=3,n%7=2且3，5，7互质

使5×7被3除余1，用35×2=70；

使3×7被5除余1，用21×1=21；

使3×5被7除余1，用15×1=15。

（70×2+21×3+15×2）%（3×5×7）=23   

同样，这道题也应该是：

使33×28被23除余1，用33×28×6=5544；

使23×33被28除余1，用23×33×19=14421；

使23×28被33除余1，用23×28×2=1288。

（5544×p+14421×e+1288×i）%（23×28×33）=n+d

n=（5544×p+14421×e+1288×i-d）%（23×28×33）

完整代码：

#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
using namespace std;

#pragma comment(linker, "/STACK:102400000,102400000")

typedef long long LL;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;

/** Constant List .. **/ //{

const int MOD = int(1e9)+7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
int p , e , i , d;
int main()
{
    #ifdef DoubleQ
    freopen("in.txt","r",stdin);
    #endif
    int cas = 1;
    while(~scanf("%d%d%d%d",&p,&e,&i,&d))
    {
        if(p == -1 && e == -1 && i == -1 && d == -1)
            break;
        LL res = (5544 * p + 14421 * e + 1288 * i - d + 23 * 28 * 33 ) % (23 * 28 * 33);
        if(res <= 0)
            res = 23 * 28 * 33 - d;
        printf("Case %d: the next triple peak occurs in %lld days.\n" , cas ++ , res);
    }
}

POJ1006（中国剩余定理+大衍求一术）

标签：剩余定理+大衍求一术

原文地址：http://blog.csdn.net/u013447865/article/details/40925967