2016-05-23

Posted 2020-07-11

微机原理：8086算术指令，跳转指令

操作系统：进程调度算法，银行家算法

python：列表，字典，类与对象

算法：数论（扩展欧几里得，一元线性同余方程组）

在hihocoder上学习这两个，一元线性那题最大公约数变量用着用着就写乱了，查代码能力还有待加强。。。

数论学起来压力好大

扩展欧几里得：

#include<stdio.h>
#include<utility>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> xy;
xy ans,cst(0,1);
ll gcd(ll x,ll y)
{
    if (x%y==0) return y;
        else return gcd(y,x%y);
}
xy extend_gcd(ll a,ll b)
{
    if (a%b==0) return cst;
    xy tempxy=extend_gcd(b,a%b);
    xy x_y;
    x_y.first=tempxy.second;
    x_y.second=tempxy.first-a/b*tempxy.second;
    return x_y;
}
int main()
{
    ll s1,s2,v1,v2,m,a,b,c,judge;
    scanf("%lld%lld%lld%lld%lld",&s1,&s2,&v1,&v2,&m);
    a=v1-v2;b=m;c=s2-s1;
    if (a<0) a=(a+m)%m;
    judge=gcd(a,b);
    if (c%judge!=0) {printf("-1\n");return 0;}
    a/=judge;
    b/=judge;
    c/=judge;
    ans=extend_gcd(a,b);
    ans.first=(ans.first*c)%b;
    while (ans.first<0) ans.first+=b;
    printf("%lld\n",ans.first);
    return 0;
}

一元线性同余方程组：

#include<stdio.h>
using namespace std;
typedef long long ll;
struct pair
{
    ll x,y;
    pair(){}
    pair(ll xx,ll yy)
    {
        x=xx;y=yy;
    }
};
ll m[1010],r[1010];
pair ans,cst(0,1);
ll gcd(ll x,ll y)
{
    if (x%y==0) return y;
        else return gcd(y,x%y);
}
pair extend_gcd(ll a,ll b)
{
    if (a%b==0) return cst;
    pair temp=extend_gcd(b,a%b);
    pair xy;
    xy.x=temp.y;
    xy.y=temp.x-a/b*temp.y;
    return xy;
}
int main()
{
    ll n,i,R,M,a,b,c,judge;
    scanf("%lld",&n);
    for (i=1;i<=n;i++)
        scanf("%lld%lld",&m[i],&r[i]);
    R=r[1];M=m[1];
    pair ans;
    for (i=2;i<=n;i++)
    {
        a=M;b=m[i];c=r[i]-R;
        judge=gcd(a,b);
        if (c%judge!=0) {printf("-1\n");return 0;}
        a/=judge;b/=judge;c/=judge;
        ans=extend_gcd(a,b);
        ans.x=(c*ans.x)%b;
        R=R+M*ans.x;
        M=M/judge*m[i];
        R=R%M;
    }
    while (R<0) R+=M;
    printf("%lld\n",R);
    return 0;
}