Han Xin and His Troops
中国剩余定理
JAVA板子
/*中国剩余定理,根据公式需要求取大数的逆元*/ import java.math.BigInteger; import java.util.ArrayList; import java.util.Scanner; public class Main { static BigInteger m[]=new BigInteger[105]; static BigInteger c[]=new BigInteger[105]; static int n; static BigInteger _m; static BigInteger x,y; public static BigInteger[] ex_gcd(BigInteger a,BigInteger b){ BigInteger ans; BigInteger[] result=new BigInteger[3]; if(b.equals(BigInteger.ZERO)) { result[0]=a; result[1]=BigInteger.ONE; result[2]=BigInteger.ZERO; return result; } BigInteger [] temp=ex_gcd(b,a.mod(b)); ans = temp[0]; result[0]=ans; result[1]=temp[2]; result[2]=temp[1].subtract((a.divide(b)).multiply(temp[2])); //System.out.println(result[0]+" "+result[1]+" "+result[2]); return result; } static BigInteger getInv(BigInteger a,BigInteger md) { //x=BigInteger.ZERO;y=BigInteger.ZERO; BigInteger d[]=ex_gcd(a,md); //System.out.println(a+" "+md); //System.out.println(x+" "+y); //System.out.println(d[1]); return (d[0].equals(BigInteger.ONE))?(d[1].add(md)).mod(md):BigInteger.valueOf(-1); } static BigInteger exCRT(int n) { BigInteger m1,m2,c1,c2,d; for(int i=2;i<=n;i++) { m1=m[i-1];m2=m[i];c1=c[i-1];c2=c[i]; d=m1.gcd(m2); if(!(c2.subtract(c1)).mod(d).equals(BigInteger.ZERO))return BigInteger.valueOf(-1);//此时无法合并 m[i] = m[i-1] .multiply(m[i]).divide(d) ; BigInteger t=(c2.subtract(c1)).divide(d); //System.out.println(t); c[i] = t.multiply( getInv(m1.divide(d),m2.divide(d))) .mod ( m2.divide(d) ).multiply(m1) .add(c1) ; //System.out.println(c[i]); // System.out.println(getInv(m1.divide(d),m2.divide(d))); c[i] = ( (c[i] .mod(m[i])) .add(m[i]) ) .mod( m[i]); // System.out.println(m[i]); } return c[n]; } public static void main(String[] args) { Scanner sc=new Scanner(System.in); n=sc.nextInt(); _m=sc.nextBigInteger(); // int k=0; for(int i=1;i<=n;i++){ m[i]=sc.nextBigInteger(); c[i]=sc.nextBigInteger(); } BigInteger ans=exCRT(n); //System.out.println(ans); if(ans.compareTo(_m)>0){ System.out.println("he was probably lying"); }else if(ans.equals(BigInteger.valueOf(-1))){ System.out.println("he was definitely lying"); }else System.out.println(ans); } }