2019牛客暑期多校训练营（第十场）Han Xin and His Troops(高精度拓展中国剩余定理

题目来源

​​https://ac.nowcoder.com/acm/contest/890/D​​

题意

和

如果不存在则输出：​​​he was definitely lying​​​存在但是则输出：​​​he was probably lying​​​否则输出

思路

二次剩余(高精度

C++

#include<bits/stdc++.h>
using namespace std;

#define
I read(){long long x;scanf("%lld",&x);return x;}
void exgcd(I a,I&x,I b,I&y,I c) { //  assert(__gcd(a,b)==c)
    if (b == 0) x = c / a, y = 0;
    else exgcd(b, y, a % b, x, c), y -= a / b * x;
}

bool merge(I x1,I p1,I x2,I p2,I&x,I&p) {
    I u, v, d = __gcd(p1, p2);
    if ((x2 - x1) % d != 0) return false;
    exgcd(p1, u, p2, v, x2 - x1);
    p = p1 / d * p2;//lcm
    I n = p2 / d;
    u = ((u % n) + n) % n;
    x = u * p1 + x1;
    return true;
}

int main() {
    I n = read(), m = read();
    I x = 0, p = 1, flag = 0;
    for (I i = 0; i < n; i++) {
        I p1 = read(), x1 = read();
        if (flag == 2) continue;
        if (!merge(x, p, x1, p1, x, p)) flag = 2;
        else if (x > m) flag = 1;
    }
    if (flag == 0) printf("%lld", x);
    else if (flag == 1) puts("he was probably lying");
    else puts("he was definitely lying");
    return 0;
}

Python

#!/usr/bin/python
# -*- coding: utf-8 -*-
def gcd(a,b):
    return a if b==0 else gcd(b,a%b)
 
def exgcd(a,b):
    if b==0:
        return 1,0
    y,x=exgcd(b,a%b)
    y-=(a//b)*x
    return x,y
 
def inv(a,b):
    x,y=exgcd(a,b)
    return (x%b+b)%b
    
def main(): 
    n,M=map(lambda x:int(x),input().split(' '))
    m=-1;c=-1
    for i in range(n):
        a,b=map(lambda x:int(x),input().split(' '))
        if c==-1:
            m=a;c=b
        else:
            g=gcd(m,a)
            if (c-b)%g!=0:
                print('he was definitely lying')
                exit()
            c+=(inv(m//g,a//g)*(b-c)//g)%(a//g)*m
            m=m*a//g
    if M>=c:
        print(str(c))
    else:
        print('he was probably lying')
        
if __name__ == '__main__':
    main()

Java

import java.math.BigInteger;
import java.util.Scanner;
 
public class Main{
    public static boolean vis = false;
    public static BigInteger x;
    public static BigInteger y;
    public static BigInteger m[] = new BigInteger[200];
    public static BigInteger r[] = new BigInteger[200];
    public static void main(String[] args){
       Scanner cin = new Scanner(System.in);
       int n = cin.nextInt();
       BigInteger M = cin.nextBigInteger();
       for(int i = 1;i <= n; ++i){
           m[i] = cin.nextBigInteger();
           r[i] = cin.nextBigInteger();
       }
       BigInteger ans = excrt(n);
       if(vis) System.out.println("he was definitely lying");
       else if(ans.compareTo(M)>0) System.out.println("he was probably lying");
       else System.out.println(ans);
     }
     public static BigInteger exgcd(BigInteger a,BigInteger b){
         if(b==BigInteger.ZERO){
             x = BigInteger.ONE;
             y = BigInteger.ZERO;
             return a;
         }
         BigInteger d = exgcd(b,a.mod(b));
         BigInteger t = x;
         x = y;
         y = t.subtract(a.divide(b).multiply(y));
         return d;
     }
     public static BigInteger excrt(int n){
         BigInteger a = m[1],rr=r[1];
         for(int i=2;i<=n;++i){
             BigInteger b = m[i];
             BigInteger c = r[i].subtract(rr);
             BigInteger d = exgcd(a,b);
             if(c.mod(d) != BigInteger.ZERO){
                 vis = true;
                 return BigInteger.ZERO;
             }
             c = c.divide(d); b = b.divide(d);
             x = (x.multiply(c).mod(b).add(b)).mod(b);
             BigInteger lcm = a.multiply(b);
             rr = (x.multiply(a).mod(lcm).add(rr)).mod(lcm);
             a = lcm ;
         }
         return rr;
     }
}