Polya 定理练习题

来源：互联网发布：移动广告网络平台编辑：程序博客网时间：2024/06/06 18:54

《算法竞赛入门经典：训练指南》上的例题。

顺便做了 UVa11762:
P143 , 期望Dp

Uva10294,11077,LA3641:
P146~149 , Polya定理

Uva11762

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>const int maxn = 1e6+4;int prime[maxn], tot;bool check[maxn];double f[maxn];bool vis[maxn];void PreWork(){    for(int i = 2; i < maxn; i++)    {        if(!check[i]) prime[++tot] = i;        for(int j = 1; j <= tot && i*prime[j] < maxn; j++)        {            check[i*prime[j]] = true;            if(!(i%prime[j])) break;            }    }}double dp(int x){    if(x == 1) return 0;    if(vis[x]) return f[x];    vis[x] = true;    double &ans = f[x];    int g = 0, p = 0;    ans = 0;    for(p = 1; p <= tot && prime[p] <= x; p++)        if(!(x%prime[p])) ans += dp(x/prime[p]), g++;       ans = (ans + (--p))/g;    return ans;}int main(){    int T;#ifndef ONLINE_JUDGE        freopen("uva11762.in","r",stdin);    freopen("uva11762.out","w",stdout);#endif    PreWork(), std::cin >> T;    for(int i = 1, q; i <= T; i++)        scanf("%d",&q), printf("Case %d: %.10lf\n", i, dp(q));#ifndef ONLINE_JUDGE    fclose(stdin);    fclose(stdout);#endif    return 0;       }

LA3641

#include<cstdio>#include<cstdlib>#include<iostream>#include<algorithm>void Solve(){    char str[30] = {'\0'};    bool hash[30] = {false};     int cnt[30] = {0};    bool flag = true;    std::cin >> str;    for(int i = 0; i < 26; i++)        if(!hash[i])        {            int len = 0;            for(int j = i; !hash[j]; len++)                hash[j] = true, j = str[j]-'A';            cnt[len]++;        }    for(int i = 2; i <= 26; i += 2)        if(cnt[i]&1) {flag = false; break;}    if(flag) std::cout << "Yes" << std::endl;    else std::cout << "No" << std::endl;        }int main(){    int T;#ifndef ONLINE_JUDGE    freopen("LA3641.in","r",stdin);    freopen("LA3641.out","w",stdout);   #endif    std::cin >> T;    while(T--) Solve();#ifndef ONLINE_JUDGE    fclose(stdin);    fclose(stdout);#endif    return 0;       }

UVa10294

#include<cstdio>#include<cstdlib>#include<iostream>#include<algorithm>int n, t;long long power(int x,int y){    long long ret = 1;    while(y--) ret *= x;    return ret;}int gcd(int x,int y){    if(!y) return x;    return gcd(y,x%y); }int main(){#ifndef ONLINE_JUDGE    freopen("uva10294.in","r",stdin);    freopen("uva10294.out","w",stdout); #endif    while(~scanf("%d",&n))    {        long long a = 0, b = 0;        std::cin >> t;        for(int i = 0; i < n; i++) a += power(t,gcd(i,n));        if(n&1) b = n *power(t,(n+1)>>1);        else  b = (n>>1)*(power(t, (n>>1)+1) + power(t, n>>1));        std::cout << a/n << ' ' << (((a+b)/n)>>1) << std::endl;         }#ifndef ONLINE_JUDGE    fclose(stdin);    fclose(stdout);#endif    return 0;       }

UVa11077

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>const int maxn = 30;int n, k;unsigned long long f[maxn][maxn];int main(){#ifndef ONLINE_JUDGE    freopen("uva11077.in","r",stdin);    freopen("uva11077.out","w",stdout); #endif    f[1][0] = 1;    for(int i = 2; i <= 21; i++)        for(int j = 0; j < i; j++)            f[i][j] = f[i-1][j] + ((j)?f[i-1][j-1]*(i-1):0);    while(true)    {        std::cin >> n >> k;        if(!(n+k))break;        std::cout << f[n][k] << std::endl;    }#ifndef ONLINE_JUDGE    fclose(stdin);    fclose(stdout);#endif}

0 0