uva1069 Always an integer【解法一】

Combinatorics is a branch of mathematics chie y concerned with
counting discrete objects. For instance, how many ways can you pick
two people out of a crowd of n people? Into how many regions can you
divide a circular disk by connecting n points on its boundary with one
an- other? How many cubes are in a pyramid with square layers ranging
from 1  1 to n  n cubes? Many questions like these have answers that
can be reduced to simple polynomials in n . The answer to the rst
question above is n ( n

随机若干个n代入验证。
正解见【这里】。

#include<cstdio>#include<cstring>#include<cstdlib>#define LL long longconst int T=10000;LL a[110],t[110],d,r[10010];char s[100010];int n;bool init(){    int x,f,p=0;    char c;    scanf("%s",s);    c=s[p++];    if (c=='.') return 0;    n=0;    c=s[p++];    while (c!=')')    {        n++;        if (c=='-')        {            f=-1;            c=s[p++];        }        else f=1;        if (c=='+') c=s[p++];        x=0;        while (c>='0'&&c<='9')        {            x=x*10+c-'0';            c=s[p++];        }        if (!x) x=1;        x*=f;        a[n]=x;        if (c!='n')        {            t[n]=0;            continue;        }        c=s[p++];        x=0;        if (c=='^')        {            c=s[p++];            while (c>='0'&&c<='9')            {                x=x*10+c-'0';                c=s[p++];            }        }        else x=1;        t[n]=x;    }    c=s[p++];    c=s[p++];    x=0;    while (c>='0'&&c<='9')    {        x=x*10+c-'0';        c=s[p++];    }    d=x;    return 1;}LL pow(LL base,LL p){    LL ret=1;    while (p)    {        if (p&1) ret=ret*base%d;        base=base*base%d;        p>>=1;    }    return ret;}bool solve(){    int i,j;    LL x;    for (i=1;i<=T;i++)    {        x=0;        for (j=1;j<=n;j++)          x=((x+pow(r[i],t[j])*a[j]%d)%d+d)%d;        if (x) return 0;    }    return 1;}void make(){    int i;    srand(123);    for (i=1;i<=T;i++)      r[i]=rand();}int main(){    int K=0;    make();    while (init())    {        printf("Case %d: ",++K);        if (solve()) printf("Always an integer\n");        else printf("Not always an integer\n");    }}