uva1563

https://vjudge.net/problem/UVA-1563

高斯消元解同余方程组 就是把原来的除法换成逆元，其他的都一样

#include<bits/stdc++.h>
using namespace std;
const int N = ;
int n, p;
int a[N][N];
char s[N];
int power(int x, int t)
{
    int ret = ;
    for(; t; t >>= , x = x * x % p) if(t & ) ret = ret * x % p;
//    printf("ret=%d\n", ret);
    return ret;
}
void build()
{
    for(int i = ; i < n; ++i)
    {
        if(s[i + ] == '*') a[i][n] = ;
        else a[i][n] = s[i + ] - 'a' + ;
    }
    for(int k = ; k < n; ++k)
        for(int i = ; i < n; ++i)
            a[k][i] = power(k + , i);
}
void gauss_jordan()
{
    for(int now = ; now < n; ++now)
    {
        int x = now;
        for(int i = now; i < n; ++i) if(abs(a[i][now]) > abs(a[x][now])) x = i;
        for(int i = ; i <= n; ++i) swap(a[now][i], a[x][i]);
        int inv = power(a[now][now], p - );
        for(int i = now; i <= n; ++i) a[now][i] = a[now][i] * inv % p; // /a[now][now]
        for(int i = ; i < n; ++i) if(i != now && a[i][now])
        {
            int t = a[i][now]; // a[i][j] = a[i][j] - t * a[now][j]
            for(int j = ; j <= n; ++j) a[i][j] = ((a[i][j] % p - t * a[now][j] % p) % p + p)% p;
        }
    }
}
int main()
{
    int T; scanf("%d", &T);
    while(T--)
    {
        memset(a, , sizeof(a));
        scanf("%d%s", &p, s + ); n = strlen(s + );
        build();
        gauss_jordan();
        for(int i = ; i < n - ; ++i) printf("%d ", a[i][n]);
        printf("%d\n", a[n - ][n]);
    }
    return ;
}