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：
1 #include <iostream> 2 #include <algorithm> 3 #include <cstdio> 4 #include <cstring> 5 #include <cctype> 6 7 using namespace std; 8 9 const int N = 11111; 10 typedef long long LL; 11 char str[N]; 12 13 LL powmod(LL a, LL p, LL m) { 14 LL ret = 1; 15 while (p > 0) { 16 if (p & 1) ret *= a, ret %= m; 17 a *= a, a %= m; 18 p >>= 1; 19 } 20 return ret; 21 } 22 23 char *fuckbrace(char *s) { 24 char *p = s; 25 if (*p == '(') { 26 while (*s && *s != ')') s++; 27 *s = 0; 28 p++; 29 } 30 return p; 31 } 32 33 void scan(char *s, LL &n) { 34 while (*s && !isdigit(*s)) s++; 35 n = 0; 36 while (*s && isdigit(*s)) n = n * 10 + *s - '0', s++; 37 } 38 39 LL gettop(char *p) { 40 char *i = strstr(p, "^"); 41 LL ret = 1; 42 if (i) scan(i, ret); 43 return ret; 44 } 45 46 LL cal(char *s, LL x, LL m) { 47 LL ret = 0, tmp = 1, t, p; 48 while (*s) { 49 if (isdigit(*s)) { 50 scan(s, t); 51 tmp *= t; 52 tmp %= m; 53 while (isdigit(*s)) s++; 54 //cout << *s << endl; 55 if (*s == 'n') { 56 LL temp = tmp; 57 tmp *= x; 58 tmp %= m; 59 if (*(s + 1) == '^') { 60 scan(s + 2, p); 61 if (p == 0) tmp = temp; 62 tmp *= powmod(x, p - 1, m); 63 tmp %= m; 64 s += 2; 65 while (isdigit(*s)) s++; 66 } else s++; 67 } 68 ret += tmp; 69 ret %= m; 70 tmp = 1; 71 } else if (*s == '-') { 72 tmp *= -1; 73 s++; 74 } else if (*s == '+') s++; 75 else if (*s == 'n') { 76 //cout << "is n??" << endl; 77 LL temp = tmp; 78 tmp *= x; 79 tmp %= m; 80 if (*(s + 1) == '^') { 81 scan(s + 2, p); 82 if (p == 0) tmp = temp; 83 //cout << x << ' ' << p << ' ' << m << ' ' << powmod(x, p - 1, m) << endl; 84 tmp *= powmod(x, p - 1, m); 85 tmp %= m; 86 s += 2; 87 while (isdigit(*s)) s++; 88 } else s++; 89 //cout << ret << ' ' << tmp << endl; 90 ret += tmp; 91 ret %= m; 92 tmp = 1; 93 } else { 94 puts("WTF?..."); 95 cout << s << endl; 96 while (1) ; 97 } 98 } 99 return ret; 100 } 101 102 bool check(char *s, LL a, LL b, LL m) { 103 for (LL i = a; i <= b; i++) { 104 if (cal(s, i, m)) return false; 105 //cout << s << ' ' << i << ' ' << m << ' ' << cal(s, (LL) i, m) << endl; 106 } 107 return true; 108 } 109 110 int main() { 111 int cas = 1; 112 //freopen("in", "r", stdin); 113 while (cin >> str && strcmp(str, ".")) { 114 LL D; 115 char *p = str; 116 while (*p && *p != '/') p++; 117 if (*p) { 118 *(p++) = 0; 119 sscanf(p, "%lld", &D); 120 } else { 121 puts("are u kidding?= ="); 122 while (1) ; 123 } 124 if (D > 0x7fffffff) { 125 puts("fuck you"); 126 while (1) ; 127 } 128 p = fuckbrace(str); 129 //cout << p << ' ' << D << endl; 130 LL top = gettop(p); 131 //cout << top << endl; 132 if (check(p, 1, top << 1, D)) printf("Case %d: Always an integer ", cas++); 133 else printf("Case %d: Not always an integer ", cas++); 134 } 135 return 0; 136 }
——written by Lyon