Polya 定理练习题 分类： uva 2015-06-17 22:13 28人阅读 评论(0) 收藏

《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
[k] << std::endl;
}

#ifndef ONLINE_JUDGE
fclose(stdin);
fclose(stdout);
#endif
}