LA 4119 Always an integer （数论+模拟）

ACM-ICPC Live Archive

　　一道模拟题，题意是问一个给出的多项式代入正整数得到的值是否总是整数。

　　这题是一道数论题，其实对于这个式子，我们只要计算1~最高次项是否都满足即可。

　　做的时候，模拟出了点小错误，一直wa。幸亏最后还是能找到错误的位置。

代码如下：

 #include <iostream>
 #include <algorithm>
 #include <cstdio>
 #include <cstring>
 #include <cctype>

 using namespace std;

 const int N = ;
 typedef long long LL;
 char str[N];

 LL powmod(LL a, LL p, LL m) {
     LL ret = ;
     while (p > ) {
         if (p & ) ret *= a, ret %= m;
         a *= a, a %= m;
         p >>= ;
     }
     return ret;
 }

 char *fuckbrace(char *s) {
     char *p = s;
     if (*p == '(') {
         while (*s && *s != ')') s++;
         *s = ;
         p++;
     }
     return p;
 }

 void scan(char *s, LL &n) {
     while (*s && !isdigit(*s)) s++;
     n = ;
     while (*s && isdigit(*s)) n = n *  + *s - '', s++;
 }

 LL gettop(char *p) {
     char *i = strstr(p, "^");
     LL ret = ;
     if (i) scan(i, ret);
     return ret;
 }

 LL cal(char *s, LL x, LL m) {
     LL ret = , tmp = , t, p;
     while (*s) {
         if (isdigit(*s)) {
             scan(s, t);
             tmp *= t;
             tmp %= m;
             while (isdigit(*s)) s++;
             //cout << *s << endl;
             if (*s == 'n') {
                 LL temp = tmp;
                 tmp *= x;
                 tmp %= m;
                 if (*(s + ) == '^') {
                     scan(s + , p);
                     if (p == ) tmp = temp;
                     tmp *= powmod(x, p - , m);
                     tmp %= m;
                     s += ;
                     while (isdigit(*s)) s++;
                 } else s++;
             }
             ret += tmp;
             ret %= m;
             tmp = ;
         } else if (*s == '-') {
             tmp *= -;
             s++;
         } else if (*s == '+') s++;
         else if (*s == 'n') {
             //cout << "is n??" << endl;
             LL temp = tmp;
             tmp *= x;
             tmp %= m;
             if (*(s + ) == '^') {
                 scan(s + , p);
                 if (p == ) tmp = temp;
                 //cout << x << ' ' << p << ' ' << m << ' ' << powmod(x, p - 1, m) << endl;
                 tmp *= powmod(x, p - , m);
                 tmp %= m;
                 s += ;
                 while (isdigit(*s)) s++;
             } else s++;
             //cout << ret << ' ' << tmp << endl;
             ret += tmp;
             ret %= m;
             tmp = ;
         } else {
             puts("WTF?...");
             cout << s << endl;
             while () ;
         }
     }
     return ret;
 }

 bool check(char *s, LL a, LL b, LL m) {
     for (LL i = a; i <= b; i++) {
         if (cal(s, i, m)) return false;
         //cout << s << ' ' << i << ' ' << m << ' ' << cal(s, (LL) i, m) << endl;
     }
     return true;
 }

 int main() {
     int cas = ;
     //freopen("in", "r", stdin);
     while (cin >> str && strcmp(str, ".")) {
         LL D;
         char *p = str;
         while (*p && *p != '/') p++;
         if (*p) {
             *(p++) = ;
             sscanf(p, "%lld", &D);
         } else {
             puts("are u kidding?= =");
             while () ;
         }
         if (D > 0x7fffffff) {
             puts("fuck you");
             while () ;
         }
         p = fuckbrace(str);
         //cout << p << ' ' << D << endl;
         LL top = gettop(p);
         //cout << top << endl;
         if (check(p, , top << , D)) printf("Case %d: Always an integer\n", cas++);
         else printf("Case %d: Not always an integer\n", cas++);
     }
     return ;
 }

——written by Lyon