Codeforces Beta Round #9 (Div. 2 Only)

Codeforces Beta Round #9 (Div. 2 Only)

http://codeforces.com/contest/9

A

gcd水题

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define maxn 1000010
typedef long long ll;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */
int gcd(int a,int b){
    if(b==0) return a;
    return gcd(b,a%b);
}

int main(){
    #ifndef ONLINE_JUDGE
      //  freopen("1.txt","r",stdin);
    #endif
    int n,m;
    cin>>n>>m;
    n=max(n,m);
    int fz=6-n+1;
    int fm=6;
    int d=gcd(fz,fm);
   // cout<<fz<<" "<<fm<<endl;
    cout<<fz/d<<"/"<<fm/d<<endl;
}

B

模拟题

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define maxn 1000010
typedef long long ll;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */
struct Point{
    ll x,y;
}a[105];

double dist[105][105];

int main(){
    #ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
    #endif
    ll n,vb,vs;
    cin>>n>>vb>>vs;
    for(int i=1;i<=n;i++){
        cin>>a[i].x;
        a[i].y=0;
    }
    ll sx,sy;
    cin>>sx>>sy;
    for(int i=1;i<=n;i++){
        dist[1][i]=sqrt(sqr(a[1].x-a[i].x)+sqr(a[1].y-a[i].y));
    }
    for(int i=1;i<=n;i++){
        dist[i][103]=sqrt(sqr(a[i].x-sx)+sqr(a[i].y-sy));
    }
    double ans=1e18;
    ll pos=0;
    for(int i=1;i<=n;i++){
        if(a[i].x!=0){
            double t1=dist[1][i]/vb;
            double t2=dist[i][103]/vs;
            if(ans>=t1+t2){
                ans=t1+t2;
                pos=i;
            }
        }
    }
    cout<<pos<<endl;
}

C

dfs

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define maxn 1000010
typedef long long ll;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */
map<ll,int>mp;
ll n;
int ans;

void dfs(int pos){
    if(pos>n) return;
    if(!mp[pos]){
        ans++;
        mp[pos]=1;
    }
    else return;
    dfs(pos*10);
    dfs(pos*10+1);
}

int main(){
    #ifndef ONLINE_JUDGE
       // freopen("1.txt","r",stdin);
    #endif
    cin>>n;
    dfs(1);
    cout<<ans<<endl;
}

D

参考博客：http://www.cnblogs.com/qscqesze/p/5414271.html

DP

dp[i][j]表示当前用了i个节点，高度小于等于j的方案数

dp[i][j] = sigma(dp[k][j-1]*dp[i-k-1][j-1])

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define maxn 1000010
typedef long long ll;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

long long dp[45][45];

int main(){
    #ifndef ONLINE_JUDGE
       // freopen("1.txt","r",stdin);
    #endif
    int n,h;
    cin>>n>>h;
    for(int i=1;i<=n;i++){
        dp[0][i-1]=1;
        for(int j=1;j<=n;j++){
            for(int k=0;k<j;k++){
                dp[j][i]+=dp[k][i-1]*dp[j-k-1][i-1];
            }
        }
    }
    cout<<dp[n][n]-dp[n][h-1]<<endl;
}

E

题意：给出n个点，m条边，问是否能通过加一些边，使得n个点构成有且仅有n条边的单个环

直接构造就好

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define maxn 1000010
typedef long long ll;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */
int fa[55];
int d[55];
vector<pair<int,int> > ve,ans;
int Find(int x){
    int r=x,y;
    while(x!=fa[x]){
        x=fa[x];
    }
    while(r!=x){
        y=fa[r];
        fa[r]=x;
        r=y;
    }
    return x;
}
void join(int x,int y)
{
    int xx=Find(x);
    int yy=Find(y);
    if(xx!=yy) fa[xx]=yy;
}
int main(){
    int n,m;
    cin>>n>>m;
    int v,u;
    for(int i=1;i<=n;i++) fa[i]=i;
    for(int i=1;i<=m;i++){
        cin>>u>>v;
        ve.push_back(make_pair(u,v));
        join(u,v);
        d[v]++,d[u]++;
        if(d[u]>2||d[v]>2){
            cout<<"NO"<<endl;
            return 0;
        }
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<i;j++){
            if(d[j]<=1&&d[i]<=1&&Find(i)!=Find(j))
            {
                ans.push_back(make_pair(j,i));
                join(i,j);
                d[i]++,d[j]++;
            }
        }
    }
    for(int i=1;i<=n;i++){
        if(d[i]!=2){
            for(int j=1;j<i;j++){
                if(d[j]==1){
                    ans.push_back(make_pair(j,i));
                    join(i,j);
                    d[i]++,d[j]++;
                }
            }
        }
    }
    for(int i=1;i<=n;i++)
        if(d[i]==0)ans.push_back(make_pair(i,i));
    int p = Find(1);
    for(int i=1;i<=n;i++)
        if(Find(i)!=p){
            cout<<"NO"<<endl;
            return 0;
        }
    cout<<"YES"<<endl;
    cout<<ans.size()<<endl;
    for(int i=0;i<ans.size();i++)
        cout<<ans[i].first<<" "<<ans[i].second<<endl;
}