【补题】第十七届同济大学友谊赛

先放代码，题解日后再更。

A.张老师和菜哭武的游戏

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;

#define RG register int
#define LL long long

LL GCD(LL a,LL b){return b==0?a:GCD(b,a%b);}
int T;
LL N,A,B;

int main(){
    cin>>T;
    while(T--){
        cin>>N>>A>>B;
        if((N/GCD(A,B))%2==1) cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }
    return 0;
}

B.伤害计算

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;

#define RG register int
#define LL long long

string S;

double ndx(int n,int x){
    return (double)n*(double)((1+x)*x)/2.0/(double)x;
}

int main(){
    cin>>S;
    double Ans=0;
    int a=0,b=0;bool d=false;
    for(RG i=0;i<S.size();++i){
        if(S[i]=='+'){
            if(!d) Ans+=a;
            else Ans+=ndx(a,b);
            d=false;a=b=0;
        }
        else if(S[i]=='d') d=true;
        else{
            if(!d) a=a*10+S[i]-'0';
            else b=b*10+S[i]-'0';
        }
    }
    if(!d) Ans+=a;
    else Ans+=ndx(a,b);
    int temp=Ans;
    if(Ans!=temp) printf("%.1f\n",Ans);
    else cout<<temp<<endl;
    return 0;
}

C.张老师的旅行

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;

#define RG register int
#define LL long long

template<typename elemType>
inline void Read(elemType &T){
    elemType X=0,w=0; char ch=0;
    while(!isdigit(ch)) {w|=ch=='-';ch=getchar();}
    while(isdigit(ch)) X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
    T=(w?-X:X);
}

LL dp[1005][1005][2];
LL p[1005],t[1005];
int N,st;

int main(){
    Read(N);
    for(RG i=1;i<=N;++i)
        Read(p[i]);
    for(RG i=1;i<=N;++i){
        Read(t[i]);
        if(t[i]==0) st=i;
    }
    memset(dp,0x3f,sizeof(dp));
    dp[st][st][0]=dp[st][st][1]=0;
    for(RG Len=2;Len<=N;++Len){
        for(RG L=1;L+Len-1<=N;++L){
            int R=L+Len-1;
            if(dp[L+1][R][0]+p[L+1]-p[L]<=t[L])
                dp[L][R][0]=min(dp[L][R][0],dp[L+1][R][0]+p[L+1]-p[L]);
            if(dp[L+1][R][1]+p[R]-p[L]<=t[L])
                dp[L][R][0]=min(dp[L][R][0],dp[L+1][R][1]+p[R]-p[L]);
            if(dp[L][R-1][1]+p[R]-p[R-1]<=t[R])
                dp[L][R][1]=min(dp[L][R][1],dp[L][R-1][1]+p[R]-p[R-1]);
            if(dp[L][R-1][0]+p[R]-p[L]<=t[R])
                dp[L][R][1]=min(dp[L][R][1],dp[L][R-1][0]+p[R]-p[L]);
        }
    }
    LL Ans=min(dp[1][N][0],dp[1][N][1]);
    if(Ans>1000000000000LL) printf("-1\n");
    else printf("%lld\n",Ans);
    return 0;
}

D.车辆调度

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;

#define RG register int
#define LL long long

int Car[5][2];
char G[15][15],G2[15][15];
int N,M,K,num=0;
int dx[4]={-1,1,0,0},dy[4]={0,0,-1,1};
bool Ans=false;

int Maintain(int x,int y,int d){
    int limit=max(N,M);
    int i=1;
    for(i=1;i<limit;++i){
        int nx=x+dx[d]*i;
        int ny=y+dy[d]*i;
        if(nx<1||nx>N||ny<1||ny>M) break;
        if(G[nx][ny]=='R'||G[nx][ny]=='X') break;
    }
    return i-1;
}

void DFS(int Step){
    if(Ans) return;
    if(Step==K){
        for(RG i=1;i<=num;++i)
            if(G2[Car[i][0]][Car[i][1]]=='D'){Ans=true;break;}
        return;
    }
    for(int i=1;i<=num;++i){
        if(Ans) return;
        for(int dir=0;dir<4;++dir){
            int dis=Maintain(Car[i][0],Car[i][1],dir);
            int nx=Car[i][0]+dis*dx[dir];
            int ny=Car[i][1]+dis*dy[dir];
            int x=Car[i][0],y=Car[i][1];
            if(dis==0) continue;
            if(G[nx][ny]=='D'){Ans=true;return;}
            char temp=G[nx][ny];
            G[x][y]=G2[x][y];
            G[nx][ny]='R';
            Car[i][0]=nx;Car[i][1]=ny;
            DFS(Step+1);
            G[nx][ny]=temp;
            G[x][y]='R';
            Car[i][0]=x;Car[i][1]=y;
        }
    }
    return;
}

int main(){
    ios::sync_with_stdio(false);
    cin>>M>>N>>K;
    for(RG i=1;i<=N;++i)
        for(RG j=1;j<=M;++j){
            cin>>G[i][j];
            G2[i][j]=G[i][j];
            if(G[i][j]=='R'){G2[i][j]='.';++num;Car[num][0]=i;Car[num][1]=j;}
        }
    DFS(0);
    if(Ans) cout<<"YES"<<endl;
    else cout<<"NO"<<endl;
    return 0;
}

E.弦

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;

#define RG register int
#define LL long long

LL Inv[20000010];
const LL MOD=1000000007LL;

void Init(){
    Inv[1]=1;
    for(register int i=2;i<=20000005;++i)
        Inv[i]=((-(MOD/i)*Inv[MOD%i])%MOD+MOD)%MOD;
    return;
}

LL F(LL n){
    LL now=1,last=0;
    for(RG i=2;i<=n;i++){
        last=now;
        now=last*(LL)(4*i-2)%MOD*Inv[i+1]%MOD;
    }
    return last;
}

LL C2(LL n){
    return (2LL*Inv[n]%MOD)*Inv[n-1]%MOD;
}

int main(){
    Init();
    int n;LL c=1;cin>>n;
    LL fact=1LL;
    for(RG i=0;i<n;++i){
        c=(c*C2(2*n-i*2))%MOD;
        fact=(fact*(LL)(i+1))%MOD;
    }
    LL Ans=(F(n+1)*fact)%MOD*c%MOD;
    printf("%lld\n",Ans);
	return 0;
}

F.排列计算

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
using namespace std;

#define RG register int
#define LL long long

template<typename elemType>
inline void Read(elemType &T){
    elemType X=0,w=0; char ch=0;
    while(!isdigit(ch)) {w|=ch=='-';ch=getchar();}
    while(isdigit(ch)) X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
    T=(w?-X:X);
}

struct SegTreeNode{LL Value,Lazytag;};
SegTreeNode SegTree[800010];
int N,M;

inline void Push_Down(int Root,int L,int R){
    if(!SegTree[Root].Lazytag) return;
    LL Add=SegTree[Root].Lazytag;
    SegTree[Root].Lazytag=0;
    int mid=(L+R)>>1;
    SegTree[Root<<1].Value+=(LL)(mid-L+1)*Add;
    SegTree[Root<<1|1].Value+=(LL)(R-mid)*Add;
    SegTree[Root<<1].Lazytag+=Add;
    SegTree[Root<<1|1].Lazytag+=Add;
    return;
}

void Update(int Root,int L,int R,int QL,int QR,LL Add){
    if(R<QL||QR<L) return;
    if(QL<=L && R<=QR){
        SegTree[Root].Value+=(LL)(R-L+1)*Add;
        SegTree[Root].Lazytag+=Add;
        return;
    }
    int mid=(L+R)>>1;
    Push_Down(Root,L,R);
    Update(Root<<1,L,mid,QL,QR,Add);
    Update(Root<<1|1,mid+1,R,QL,QR,Add);
    SegTree[Root].Value=SegTree[Root<<1].Value+SegTree[Root<<1|1].Value;
    return;
}

LL Query(int Root,int L,int R,int QL,int QR){
    if(R<QL||QR<L) return 0;
    if(QL<=L && R<=QR) return SegTree[Root].Value;
    int mid=(L+R)>>1;
    Push_Down(Root,L,R);
    return Query(Root<<1,L,mid,QL,QR)+Query(Root<<1|1,mid+1,R,QL,QR);
}

vector<int> Ans;

int main(){
    Read(N);Read(M);
    while(M--){
        int L,R;LL Add;
        Read(L);Read(R);
        Update(1,1,N,L,R,1);
    }
    for(RG i=1;i<=N;++i)
        Ans.push_back(Query(1,1,N,i,i));
    sort(Ans.begin(),Ans.end());
    LL Res=0;
    for(RG i=1;i<=N;++i)
        Res+=(LL)Ans[i-1]*(LL)i;
    cout<<Res<<endl;

    return 0;
}

H.时空栈

Code

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
using namespace std;

#define RG register int
#define LL long long
const int INF=2147483647;

template<typename elemType>
inline void Read(elemType &T){
    elemType X=0,w=0; char ch=0;
    while(!isdigit(ch)) {w|=ch=='-';ch=getchar();}
    while(isdigit(ch)) X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
    T=(w?-X:X);
}

int SegTree[800010],val[200010];
int N,Index;

void Insert_Node(int Root,int L,int R,int Pos,int Add){
    if(L==R){SegTree[Root]+=Add;return;}
    int mid=(L+R)>>1;
    if(Pos<=mid) Insert_Node(Root<<1,L,mid,Pos,Add);
    else Insert_Node(Root<<1|1,mid+1,R,Pos,Add);
    SegTree[Root]=SegTree[Root<<1]+SegTree[Root<<1|1];
    return;
}

int Query(int Root,int L,int R,int QL,int QR){
    if(R<QL||QR<L) return 0;
    if(QL<=L && R<=QR) return SegTree[Root];
    int mid=(L+R)>>1;
    return Query(Root<<1,L,mid,QL,QR)+Query(Root<<1|1,mid+1,R,QL,QR);
}

int Ask(int Root,int L,int R,int Ed,int Sum){
    if(L==R){
        if(Sum==1) return L;
        return -1;
    }
    int mid=(L+R)>>1;
    if(mid<Ed){
        int temp=Ask(Root<<1|1,mid+1,R,Ed,Sum-SegTree[Root<<1]);
        if(temp!=-1) return temp;
    }
    return Ask(Root<<1,L,mid,Ed,Sum);
}

int main(){
    Read(N);
    for(RG i=1;i<=N;++i){
        int opt,Time,Value;
        Read(opt);Read(Time);
        if(opt==0){Read(Value);val[Time]=Value;Insert_Node(1,1,N,Time,1);}
        else if(opt==1) Insert_Node(1,1,N,Time,-1);
        else printf("%d\n",val[Ask(1,1,N,Time,Query(1,1,N,1,Time))]);
    }
    return 0;
}