中国剩余定理matlab非互质,中国剩余定理模板（互质版和非互质版）

互质版：

#include

#include

#include

using namespace std;

typedef __int64 int64;

int64 a[15],b[15];

int64 Extend_Euclid(int64 a, int64 b, int64&x, int64& y)

{

if(b==0)

{

x=1,y=0;

return a;

}

int64 d = Extend_Euclid(b,a%b,x,y);

int64 t = x;

x = y;

y = t - a/b*y;

return d;

}

//求解模线性方程组x=ai(mod ni)

int64 China_Reminder(int len, int64* a, int64* n)

{

int i;

int64 N = 1;

int64 result = 0;

for(i = 0; i < len; i++)

N = N*n[i];

for(i = 0; i < len; i++)

{

int64 m = N/n[i];

int64 x,y;

Extend_Euclid(m,n[i],x,y);

x = (x%n[i]+n[i])%n[i];

result = (result + m*a[i]*x%N)%N;

}

return result;

}

int main()

{

int n;

while(scanf("%d",&n)!=EOF)

{

for(int i = 0; i < n; i++)

scanf("%I64d %I64d",&a[i],&b[i]);

printf("%I64d\n",China_Reminder(n,b,a));

}

return 0;

}

非互质版：

/**

中国剩余定理(不互质)

*/

#include

#include

#include

using namespace std;

typedef __int64 int64;

int64 Mod;

int64 gcd(int64 a, int64 b)

{

if(b==0)

return a;

return gcd(b,a%b);

}

int64 Extend_Euclid(int64 a, int64 b, int64&x, int64& y)

{

if(b==0)

{

x=1,y=0;

return a;

}

int64 d = Extend_Euclid(b,a%b,x,y);

int64 t = x;

x = y;

y = t - a/b*y;

return d;

}

//a在模n乘法下的逆元，没有则返回-1

int64 inv(int64 a, int64 n)

{

int64 x,y;

int64 t = Extend_Euclid(a,n,x,y);

if(t != 1)

return -1;

return (x%n+n)%n;

}

//将两个方程合并为一个

bool merge(int64 a1, int64 n1, int64 a2, int64 n2, int64& a3, int64& n3)

{

int64 d = gcd(n1,n2);

int64 c = a2-a1;

if(c%d)

return false;

c = (c%n2+n2)%n2;

c /= d;

n1 /= d;

n2 /= d;

c *= inv(n1,n2);

c %= n2;

c *= n1*d;

c += a1;

n3 = n1*n2*d;

a3 = (c%n3+n3)%n3;

return true;

}

//求模线性方程组x=ai(mod ni),ni可以不互质

int64 China_Reminder2(int len, int64* a, int64* n)

{

int64 a1=a[0],n1=n[0];

int64 a2,n2;

for(int i = 1; i < len; i++)

{

int64 aa,nn;

a2 = a[i],n2=n[i];

if(!merge(a1,n1,a2,n2,aa,nn))

return -1;

a1 = aa;

n1 = nn;

}

Mod = n1;

return (a1%n1+n1)%n1;

}

int64 a[1000],b[1000];

int main()

{

int i;

int k;

while(scanf("%d",&k)!=EOF)

{

for(i = 0; i < k; i++)

scanf("%I64d %I64d",&a[i],&b[i]);

printf("%I64d\n",China_Reminder2(k,b,a));

}

return 0;

}

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