2016 Multi-University Training Contest 3 题解(待续)

原创 于 2016-07-28 00:05:05 发布 · 344 阅读 · 0 ·
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本文解析了五道算法题目，包括求平方根的迭代方法、概率计算、状态搜索、数学公式推导及教师问题，提供了完整的C++代码实现。

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Sqrt Bo

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip> 
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %I64d\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
ull f(ull x){return sqrt((ll)x);}
int main()
{
//  freopen("A.in","r",stdin);
//  freopen(".out","w",stdout);
    string s;
    while(cin>>s) {

        if (s.length()>16) {puts("TAT");continue;}
        stringstream ss;
        ss<<s;
        ull p;
        ss>>p;
        int t=0;
        Rep(i,5) {
            if (p==1) break;
            p=f(p); ++t;
        }
        if (p==1) cout<<t<<endl;
        else puts("TAT"); 
    }


    return 0;
}

Permutation Bo

找规律

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip> 
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %I64d\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
int main()
{
//  freopen("B.in","r",stdin);
//  freopen(".out","w",stdout);
    int n;
    while(cin>>n) {
        double p=0;
        if (n==1) {
            int c=read();
            cout<<c<<endl;
            continue;
        }
        For(i,n) {
            int c=read();
            if (i==1||i==n) p+=(double)c/2;
            else p+=(double)c/3;
        }
        printf("%.6lf\n",p);
    }


    return 0;
}

Life Winner Bo

状态图暴力搜

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip> 
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %I64d\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
#define MAXN (1000+10)
int f[MAXN][MAXN],dir[3][2]={{1,1},{0,1},{1,0}};
int n=1000,m=1000;
bool inside(int i,int j){
    if (i&&j&&i<=n&&j<=m) return 1;return 0;
}
void prwork(){
    memset(f,-1,sizeof(f));
    f[n][m]=0; //0 last 1 win -1 unknown
    ForD(i,n) ForD(j,m) {
        if (f[i][j]!=-1) continue;
        int p=0,c=0,q=0;
        Rep(di,3) {
            int x=i+dir[di][0],y=j+dir[di][1];
            if (inside(x,y)) {
                c++;
                if (0==f[x][y]) ++p;
                if (1==f[x][y]) ++q;

            }
        }
        if (p) f[i][j]=1;
        else if (c==q) f[i][j]=0;
    }
}
int g[MAXN][MAXN],gir[2][2]={{1,2},{2,1}};
void pr2work(){
    memset(g,-1,sizeof(g));
    g[n][m]=0; //0 last 1 win -1 unknown
    ForD(i,n) ForD(j,m) {
        if (g[i][j]!=-1) continue;
        int p=0,c=0,q=0;
        Rep(di,2) {
            int x=i+gir[di][0],y=j+gir[di][1];
            if (inside(x,y)) {
                c++;
                if (0==g[x][y]) ++p;
                if (1==g[x][y]) ++q;
            }
        }
        if (p) g[i][j]=1;
        else if (c==0) continue;
        else if (c==q) g[i][j]=0;
    }
}

int t[MAXN][MAXN],tir[2][2]={{1,2},{2,1}};
void pr3work(){
    memset(t,0,sizeof(t));
    t[n][m]=0; //0 last 1 win -1 unknown
    ForD(i,n) ForD(j,m) {
        if (t[i][j]==1) continue;
        Fork(k,1,j-1) t[i][k]=1;
        Fork(k,1,i-1) t[k][j]=1;
        for(int k=1;;k++) {
            if (!inside(i-k,j-1)) break;
            t[i-k][j-k]=1;
        }               
    }
}
void h(int x){
    if (x==0) puts("G");
    else if (x==1) puts("B");
    else puts("D");
}
int main()
{
//  freopen("C.in","r",stdin);
//  freopen(".out","w",stdout);
    int T=read();
    prwork();
    pr2work();
    pr3work();
    while(T--) {
        int ty=read(),x=read(),y=read();
        if (ty==1) {
            h(f[n-x+1][m-y+1]);
        }else if (ty==2) {
            if (x==y) h(0);
            else h(1);
        }else if (ty==3) {
            h(g[n-x+1][m-y+1]);
        }else {
            h(t[n-x+1][m-y+1]);
        }
    }


    return 0;
}

Rower Bo

数学公式题，不会推公式。。
官方题解http://bestcoder.hdu.edu.cn/blog/2016-multi-university-training-contest-3-solutions-by-%E7%BB%8D%E5%85%B4%E4%B8%80%E4%B8%AD/

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip> 
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %I64d\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
int main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    int a,v1,v2; 
    while(cin>>a>>v1>>v2) {
        if (a==0) puts("0");
        else if (v1<=v2) puts("Infinity");
        else printf("%.10lf\n",(double)a*v1/(v1*v1-v2*v2));
    }


    return 0;
}

Teacher Bo

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<iomanip> 
#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<sstream>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %I64d\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
int Abs(int x){if (x<0)return -x;return x;}
int ha[200000+10]={0};
#define MAXN (200000+10)
int x[MAXN],y[MAXN];
int main()
{
//  freopen("k.in","r",stdin);
//  freopen(".out","w",stdout);
    int T=read();
    For(kcase,T) {
        int n=read(),m=read();
        Rep(i,n) cin>>x[i]>>y[i];
        bool fl=0;
        Rep(i,n) {
            Fork(j,i+1,n-1) {
                int t=Abs(x[i]-x[j])+Abs(y[i]-y[j]);
                if (ha[t]!=kcase) ha[t]=kcase;
                else {
                    fl=1;break;
                }
            }
            if (fl) break;
        }
        if (fl) puts("YES"); else puts("NO");
    }


    return 0;
}
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