LA 4119 Always an integer （数论+模拟）

　　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\n", cas++);
133         else printf("Case %d: Not always an integer\n", cas++);
134     }
135     return 0;
136 }

View Code

——written by Lyon

posted @ 2013-07-29 00:50 LyonLys 阅读(316) 评论(0) 编辑收藏举报

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