2017-10-6 清北刷题冲刺班p.m

1.数组异或

#include<iostream>
#include<cstdio>
#define maxn 100010
#define mod 1000000007
using namespace std;
int n,a[maxn],b[maxn],c[maxn];
int main(){
    freopen("xorarray.in","r",stdin);freopen("xorarray.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",&a[i]);
    for(int i=1;i<=n;i++)scanf("%d",&b[i]);
    c[1]=a[1]^b[1];
    for(int i=2;i<=n;i++){
        c[i]=c[i-1];
        for(int j=1;j<i;j++){
            c[i]+=a[i]^b[j];
            if(c[i]>=mod)c[i]-=mod;
        }
        for(int j=1;j<i;j++){
            c[i]+=a[j]^b[i];
            if(c[i]>=mod)c[i]-=mod;
        }
        c[i]+=a[i]^b[i];
        if(c[i]>=mod)c[i]-=mod;
    }
    for(int i=1;i<=n;i++)printf("%d ",c[i]);
    fclose(stdin);fclose(stdout);
    return 0;
}

/*
    累计所有数二进制下的每一位0或1的个数
    又因为是xor，所以a[j][0]*b[j][1]+a[j][1]*b[j][0]
*/
#include<iostream>
#include<cstdio>
#define maxn 100010
#define mod 1000000007
using namespace std;
int n,A[maxn],B[maxn];
int a[32][2],b[32][2],C[maxn];
int main(){
    //freopen("Cola.txt","r",stdin);
    freopen("xorarray.in","r",stdin);freopen("xorarray.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",&A[i]);
    for(int i=1;i<=n;i++)scanf("%d",&B[i]);
    for(int i=1;i<=n;i++){
        for(int j=0;j<=30;j++){
            a[j][(A[i]>>j)&1]++;
            b[j][(B[i]>>j)&1]++;
            long long c=(1LL*a[j][1]*b[j][0]%mod+1LL*a[j][0]*b[j][1]%mod)%mod;
            c=c*(1<<j)%mod;
            C[i]=(C[i]+c)%mod;
        }
    }
    for(int i=1;i<=n;i++)printf("%d ",C[i]);
    return 0;
}

2.侦探游戏（最小生成树，期望）

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#define maxn 20010
using namespace std;
int n,m,num,head[maxn],dis[maxn],D[maxn];
double ans,w;
bool v[maxn];
struct node{
    int to,pre,v;
}e[100010*2];
void Insert(int from,int to,int v){
    e[++num].to=to;
    e[num].v=v;
    e[num].pre=head[from];
    head[from]=num;
}
void spfa(int s1,int s2){
    queue<int>q;
    memset(v,0,sizeof(v));memset(dis,127/3,sizeof(dis));
    v[s1]=1;v[s2]=1;dis[s1]=0;dis[s2]=0;
    if(!v[1])v[1]=1,dis[1]=0,q.push(1);
    q.push(s1);q.push(s2);
    while(!q.empty()){
        int now=q.front();q.pop();v[now]=0;
        for(int i=head[now];i;i=e[i].pre){
            int to=e[i].to;
            if(dis[to]>dis[now]+e[i].v){
                dis[to]=dis[now]+e[i].v;
                if(!v[to]){
                    v[to]=1;
                    q.push(to);
                }
            }
        }
    }
    for(int i=1;i<=n;i++){
        ans+=(double)dis[i]*w;
    }
    int k=min(D[s1],D[s2]);
    ans+=(double)k*w;
}
void SPFA(int s){
    queue<int>q;
    memset(v,0,sizeof(v));
    memset(D,127/3,sizeof(D));
    v[s]=1;D[s]=0;
    q.push(s);
    while(!q.empty()){
        int now=q.front();q.pop();v[now]=0;
        for(int i=head[now];i;i=e[i].pre){
            int to=e[i].to;
            if(D[to]>D[now]+e[i].v){
                D[to]=D[now]+e[i].v;
                if(!v[to]){
                    v[to]=1;
                    q.push(to);
                }
            }
        }
    }
}
int main(){
    //freopen("Cola.txt","r",stdin);
    freopen("detective.in","r",stdin);freopen("detective.out","w",stdout);
    scanf("%d%d",&n,&m);
    w=(double)(n*(n-1))/2.0;
    w=1.0/w;
    int x,y,z;
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&x,&y,&z);
        Insert(x,y,z);Insert(y,x,z);
    }
    SPFA(1);
    for(int i=1;i<=n;i++){
        for(int j=1;j<i;j++){
            spfa(i,j);
        }
    }
    printf("%.2lf",ans);
    /*int sz=sizeof(head)+sizeof(e);
    cout<<sz/1048576;*/
}

/*
    暴力算法：
    求一遍最小生成树，枚举两个点，想象将两个点连上权值为0的边，然后进行倍增，求两点之间最长的一条边，删除这条边，当前树上所有边权和即为此时的花费，最后除以n*(n-1)
*/

/*
    枚举哪一条边可以删掉，由于克鲁斯卡尔最小生成树边是按从大到小顺序选入的，所以当前讨论的这条边一定是图上最大的边，而且既然他是最小生成树的一条边，他所连接的两个集合一定是两个树，将两棵树大小进行乘法原理，累计答案 （我在胡言乱语什么）
*/
#include<iostream>
#include<cstdio>
#include<algorithm>
#define maxn 20010
#define maxm 100010
using namespace std;
struct node{
    int from,to,v;
    bool operator < (const node a)const{
        return v<a.v;
    }
}e[maxm];
int n,m,fa[maxn],s[maxn];
unsigned long long sum,cnt;
int find(int a){
    if(a==fa[a])return a;
    return fa[a]=find(fa[a]);
}
int main(){
    //freopen("Cola.txt","r",stdin);
    freopen("detective.in","r",stdin);freopen("detective.out","w",stdout);
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)fa[i]=i,s[i]=1;
    for(int i=1;i<=m;i++)scanf("%d%d%d",&e[i].from,&e[i].to,&e[i].v);
    sort(e+1,e+m+1);
    for(int i=1;i<=m;i++){
        int x=find(e[i].from),y=find(e[i].to);
        if(x==y)continue;
        cnt+=1ULL*s[x]*s[y]*e[i].v;
        sum+=e[i].v;
        fa[y]=x;s[x]+=s[y];
    }
    double ans=sum-cnt/((n*(n-1))/2.0);
    //double ans = sum - 2.0 * cnt / n / (n - 1);
    printf("%.2lf",ans);
    return 0;
}

3.棋盘迷宫（分治，搜索）

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
int n,m,x1,x2,y1,y2,e[2][2]={{0,1},{1,0}};
char map[510][510];
bool vis[250010];
int f(int x,int y){
    return (x-1)*m+y;
}
bool BFS(){
    queue<int>q;
    memset(vis,0,sizeof(vis));
    vis[f(x1,y1)]=1;
    q.push(f(x1,y1));
    while(!q.empty()){
        int now=q.front();q.pop();
        int x=(now-1)/m+1,y=now-(x-1)*m;
        for(int i=0;i<2;i++){
            int xx=x+e[i][0],yy=y+e[i][1];
            int w=f(xx,yy);
            if(xx==x2&&yy==y2)return 1;
            if(xx>=1&&xx<=n&&yy>=1&&yy<=n&&xx<=x2&&yy<=y2&&!vis[w]&&map[xx][yy]=='.'){
                vis[w]=1;
                q.push(w);
            }
        }
    }
    return 0;
}
int main(){
    //freopen("Cola.txt","r",stdin);
    freopen("boardgame.in","r",stdin);freopen("boardgame.out","w",stdout);
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)scanf("%s",map[i]+1);
    int q;
    scanf("%d",&q);
    while(q--){
        scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
        if(x2<x1||y2<y1){
            printf("No
");
            continue;
        }
        if(x1==x2){
            bool flag=0;
            for(int i=y1;i<=y2;i++){
                if(map[x1][i]=='#'){
                    flag=1;
                    printf("No
");break;
                }
            }
            if(!flag)printf("Yes
");
            continue;
        }
        if(y1==y2){
            bool flag=0;
            for(int i=x1;i<=x2;i++){
                if(map[i][y1]=='#'){
                    flag=1;
                    printf("No
");break;
                }
            }
            if(!flag)printf("Yes
");
            continue;
        }
        int fl=BFS();
        if(fl)printf("Yes
");
        else printf("No
");
    }
    fclose(stdin);fclose(stdout);
    return 0;
}

/*
    考试的时候忘记判断起点和终点是否合法了
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
int n,m,x1,x2,y1,y2,e[2][2]={{0,1},{1,0}};
char map[510][510];
bool vis[250010];
int f(int x,int y){
    return (x-1)*m+y;
}
bool BFS(){
    queue<int>q;
    memset(vis,0,sizeof(vis));
    vis[f(x1,y1)]=1;
    q.push(f(x1,y1));
    while(!q.empty()){
        int now=q.front();q.pop();
        int x=(now-1)/m+1,y=now-(x-1)*m;
        for(int i=0;i<2;i++){
            int xx=x+e[i][0],yy=y+e[i][1];
            int w=f(xx,yy);
            if(xx>=1&&xx<=n&&yy>=1&&yy<=n&&xx<=x2&&yy<=y2&&!vis[w]&&map[xx][yy]=='.'){
                if(xx==x2&&yy==y2)return 1;
                vis[w]=1;
                q.push(w);
            }
        }
    }
    return 0;
}
int main(){
    //freopen("Cola.txt","r",stdin);
    freopen("boardgame.in","r",stdin);freopen("boardgame.out","w",stdout);
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)scanf("%s",map[i]+1);
    int q;
    scanf("%d",&q);
    while(q--){
        scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
        if(x2<x1||y2<y1){
            printf("No
");
            continue;
        }
        if(x1==x2){
            bool flag=0;
            for(int i=y1;i<=y2;i++){
                if(map[x1][i]=='#'){
                    flag=1;
                    printf("No
");break;
                }
            }
            if(!flag)printf("Yes
");
            continue;
        }
        if(y1==y2){
            bool flag=0;
            for(int i=x1;i<=x2;i++){
                if(map[i][y1]=='#'){
                    flag=1;
                    printf("No
");break;
                }
            }
            if(!flag)printf("Yes
");
            continue;
        }
        if(map[x1][y1]=='#'){
            printf("No
");
            continue;
        }
        int fl=BFS();
        if(fl)printf("Yes
");
        else printf("No
");
    }
    fclose(stdin);fclose(stdout);
    return 0;
}