标签：ref job 因子 style contain include div produced not
| Time Limit: 2000MS | Memory Limit: 65536K | |
| Total Submissions: 11654 | Accepted: 3756 |
Description
Input
Output
Sample Input
5 1 30000 2 30000 3 30000 4 30000 5 30000
Sample Output
1 3 11 70 629
Source
Polya定理：
假设$G$是$p$个对象的一个置换群，用$m$种颜色涂染$p$个对象，则不同颜色的方案数为
$L = \frac{1}{|G|}\sum_{g_i \in G}m^{c(g_i)}$
$G = \{g_1, g_2, \dots g_s \}$，$c(g_i)$为置换$g_i$的循环节数
本题而言第$i$种置换的循环节数为$gcd(n, i)$
因此答案为$L = \frac{1}{n}\sum_{i = 1}^n n^{gcd(i, n}$
枚举约数，用欧拉函数计算，时间复杂度$O(T\sqrt(N) f(n))$，$f(n)$表示小于$\sqrt(n)$的质因子的个数
#include<cstdio> #include<algorithm> #include<cmath> #include<map> #define LL long long const int MAXN = 1e5 + 10; inline int read() { char c = getchar(); int x = 0, f = 1; while(c < ‘0‘ || c > ‘9‘) {if(c == ‘-‘) f = -1; c = getchar();} while(c >= ‘0‘ && c <= ‘9‘) x = x * 10 + c - ‘0‘, c = getchar(); return x * f; } int T, N, mod; int fastpow(int a, int p, int mod) { int base = 1; a %= mod; while(p) { if(p & 1) base = (base * a) % mod; a = (a * a) % mod; p >>= 1; } return base % mod; } int prime[MAXN], tot, vis[MAXN]; void Prime() { for(int i = 2; i <= MAXN - 10; i++) { if(!vis[i]) prime[++tot] = i; for(int j = 1; j <= tot && prime[j] * i <= MAXN - 10; j++) { vis[i * prime[j]] = 1; if(!i % prime[j]) break; } } } int phi(int x, int mod) { int limit , ans = x; for(int i = 1; i <= tot && prime[i] * prime[i] <= x; i++) { if(!(x % prime[i])) { ans = ans - ans / prime[i]; while((x % prime[i]) == 0) x /= prime[i]; } } if(x > 1) ans = ans - ans / x; // printf("%d", ans % mod); return ans % mod; } main() { T = read(); Prime(); while(T--) { N = read(); mod = read(); int ans = 0, now = N; for(int d = 1; d * d<= N; d++) { if(d * d == N) ans = (ans + fastpow(N, d - 1, mod) % mod * phi(N / d, mod) % mod) % mod; else if( (N % d) == 0) { ans = (ans + fastpow(N, d - 1, mod) * phi(N / d, mod) + fastpow(N, N / d - 1, mod) * phi(d, mod)) % mod; } //printf("%d\n", ans); } //if(now > 0) ans += fastpow(N, now - 1, mod) * phi(N / now, mod); printf("%d\n", ans % mod); } }
标签：ref job 因子 style contain include div produced not
原文地址：https://www.cnblogs.com/zwfymqz/p/9293465.html
