【模板】逆元

標籤：double   const   main   typedef   mem   def   printf   馬虎   不能   

很基礎的東西，但是不能馬虎，有3種方法，下面一一列舉。

一.線性求逆元

#include<iostream>#include<cstdio>#include<cmath>#include<ctime>#include<queue>#include<algorithm>#include<cstring>using namespace std;#define duke(i,a,n) for(int i = a;i <= n;i++)#define lv(i,a,n) for(int i = a;i >= n;i--)#define clean(a) memset(a,0,sizeof(a))const int INF = 1 << 30;typedef long long ll;typedef double db;template <class T>void read(T &x){    char c;    bool op = 0;    while(c = getchar(), c < ‘0‘ || c > ‘9‘)        if(c == ‘-‘) op = 1;    x = c - ‘0‘;    while(c = getchar(), c >= ‘0‘ && c <= ‘9‘)        x = x * 10 + c - ‘0‘;    if(op) x = -x;}template <class T>void write(T x){    if(x < 0) putchar(‘-‘), x = -x;    if(x >= 10) write(x / 10);    putchar(‘0‘ + x % 10);}int n;ll p,inv[3000005];void work(){    inv[1] = 1;    duke(i,2,n)    {        inv[i] = (p - p / i) * inv[p % i] % p;    }    duke(i,1,n)    {        printf("%lld\n",inv[i]);    }}int main(){    read(n);read(p);    work();    return 0;}

二.費馬小定理求逆元

#include<iostream>#include<cstdio>#include<cmath>#include<ctime>#include<queue>#include<algorithm>#include<cstring>using namespace std;#define duke(i,a,n) for(int i = a;i <= n;i++)#define lv(i,a,n) for(int i = a;i >= n;i--)#define clean(a) memset(a,0,sizeof(a))const int INF = 1 << 30;typedef long long ll;typedef double db;template <class T>void read(T &x){    char c;    bool op = 0;    while(c = getchar(), c < ‘0‘ || c > ‘9‘)        if(c == ‘-‘) op = 1;    x = c - ‘0‘;    while(c = getchar(), c >= ‘0‘ && c <= ‘9‘)        x = x * 10 + c - ‘0‘;    if(op) x = -x;}template <class T>void write(T x){    if(x < 0) putchar(‘-‘), x = -x;    if(x >= 10) write(x / 10);    putchar(‘0‘ + x % 10);}ll n,p;ll qpow(ll x,ll y){    ll tot = 1;    while(y)    {        if((y & 1) != 0)        {            tot *= x;        }        x *= x;        x %= p;        tot %= p;        y >>= 1;    }    return tot;}int main(){    read(n);read(p);    printf("%lld\n",qpow(n,p - 2));    return 0;}

三.exgcd求逆元

#include<iostream>#include<cstdio>#include<cmath>#include<ctime>#include<queue>#include<algorithm>#include<cstring>using namespace std;#define duke(i,a,n) for(int i = a;i <= n;i++)#define lv(i,a,n) for(int i = a;i >= n;i--)#define clean(a) memset(a,0,sizeof(a))const int INF = 1 << 30;typedef long long ll;typedef double db;template <class T>void read(T &x){    char c;    bool op = 0;    while(c = getchar(), c < ‘0‘ || c > ‘9‘)        if(c == ‘-‘) op = 1;    x = c - ‘0‘;    while(c = getchar(), c >= ‘0‘ && c <= ‘9‘)        x = x * 10 + c - ‘0‘;    if(op) x = -x;}template <class T>void write(T x){    if(x < 0) putchar(‘-‘), x = -x;    if(x >= 10) write(x / 10);    putchar(‘0‘ + x % 10);}ll exgcd(ll a,ll b,ll &x,ll &y){    if(a == 1 && b == 0)    {        x = 1;        y = 0;        return 1;    }    ll t = exgcd(b,a % b,y,x);    y -= a / b * x;    return t;}int main(){    ll n,p,x,y;    read(n);read(p);    ll t = exgcd(n,p,x,y);    printf("%lld\n",(x % p + p) % p);    return 0;}

 

【模板】逆元