• BZOJ 4456 [Zjoi2016]旅行者


    题解:分治

    div(a,b,c,d,l,r)

    表示处理在(a,b)(c,d)这个矩形内走,队列(l,r)中询问的答案

    枚举较短中线上的点,求最短路

    如果x,y不再同一侧,那么最短路一定经过中线,处理完毕

    如果在同一侧,那么最短路可能经过也可能不经过中线,所以递归两边处理

    犯过的SB错误:

    把询问分组的时候把原数组覆盖了

    横纵坐标不分

    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<queue>
    using namespace std;
    const int maxn=300009;
    const int oo=1000000000;
    
    int n,m,TT;
    int downdist[maxn],rightdist[maxn];
    
    int limx1,limy1,limx2,limy2;
    
    inline int P(int x,int y){
        return (x-1)*m+y;
    }
    inline bool Isinrange(int u){
        int y=(u-1)%m+1;
        int x=(u-y)/m+1;
        return (x>=limx1)&&(x<=limx2)&&(y>=limy1)&&(y<=limy2);
    }
    
    
    int d[maxn];
    int vis[maxn];
    struct HeapNode{
        int v,mindist;
        HeapNode(int x){
            v=x;mindist=d[x];
        }
        bool operator < (const HeapNode &rhs) const{
            return mindist>rhs.mindist;
        }
    };
    priority_queue<HeapNode>q;
    
    void Dijkstra(int s){
        for(int i=limx1;i<=limx2;++i){
            for(int j=limy1;j<=limy2;++j){
                d[P(i,j)]=oo;vis[P(i,j)]=0;
            }
        }
        
        d[s]=0;q.push(HeapNode(s));
        while(!q.empty()){
            HeapNode x=q.top();q.pop();
            int u=x.v;
            if(vis[u])continue;
            vis[u]=1;
            int v;
            v=u+m;
            if(v<=n*m){
                if(d[u]+downdist[u]<d[v]){
                    d[v]=d[u]+downdist[u];
                    q.push(HeapNode(v));
                }
            }
            v=u-m;
            if(v>0){
                if(d[u]+downdist[v]<d[v]){
                    d[v]=d[u]+downdist[v];
                    q.push(HeapNode(v));
                }
            }
            v=u+1;
            if((u%m!=0)){
                if(d[u]+rightdist[u]<d[v]){
                    d[v]=d[u]+rightdist[u];
                    q.push(HeapNode(v));
                }
            }
            v=u-1;
            if(((u-1)%m!=0)){
                if(d[u]+rightdist[v]<d[v]){
                    d[v]=d[u]+rightdist[v];
                    q.push(HeapNode(v));
                }
            }
        }
    }
    
    int qs[maxn];
    int qx1[maxn],qy1[maxn],qx2[maxn],qy2[maxn];
    int ans[maxn];
    int tmpq[maxn];
    
    void DivCon(int upx,int upy,int downx,int downy,int ll,int rr){
        if(ll>rr)return;
        int deltx=downx-upx;
        int delty=downy-upy;
        limx1=upx;limy1=upy;
        limx2=downx;limy2=downy;
    
        int p1=ll,p2=rr;
        if(deltx<=delty){
            int mid=(upy+downy)>>1;
            for(int i=upx;i<=downx;++i){
                Dijkstra(P(i,mid));
                for(int k=ll;k<=rr;++k){
                    int t=qs[k];
                    int a=P(qx1[t],qy1[t]);
                    int b=P(qx2[t],qy2[t]);
                    ans[t]=min(ans[t],d[a]+d[b]);
                }
            }
            for(int k=ll;k<=rr;++k){
                int t=qs[k];
                if(((qy1[t]<=mid)&&(qy2[t]>=mid))||((qy1[t]>=mid)&&(qy2[t]<=mid)))continue;
                if(qy1[t]<=mid){
                    tmpq[p1]=t;++p1;
                }
                if(qy1[t]>=mid){
                    tmpq[p2]=t;--p2;
                }
            }
            for(int i=ll;i<=rr;++i)qs[i]=tmpq[i];
            DivCon(upx,upy,downx,mid-1,ll,p1-1);
            DivCon(upx,mid+1,downx,downy,p2+1,rr);
        }else{
            int mid=(upx+downx)>>1;
            for(int i=upy;i<=downy;++i){
                Dijkstra(P(mid,i));
                for(int k=ll;k<=rr;++k){
                    int t=qs[k];
                    int a=P(qx1[t],qy1[t]);
                    int b=P(qx2[t],qy2[t]);
                    ans[t]=min(ans[t],d[a]+d[b]);
                }
            }
            
            for(int k=ll;k<=rr;++k){
                int t=qs[k];
                if(((qx1[t]<=mid)&&(qx2[t]>=mid))||((qx1[t]>=mid)&&(qx2[t]<=mid)))continue;
                if(qx1[t]<=mid){
                    tmpq[p1]=t;++p1;
                }
                if(qx1[t]>=mid){
                    tmpq[p2]=t;--p2;
                }
            }
            for(int i=ll;i<=rr;++i)qs[i]=tmpq[i];
            DivCon(upx,upy,mid-1,downy,ll,p1-1);
            DivCon(mid+1,upy,downx,downy,p2+1,rr);
        }
    }
    
    
    int main(){
    //    freopen("tourist.in","r",stdin);
    //    freopen("tourist.out","w",stdout);
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;++i){
            for(int j=1;j<m;++j){
                scanf("%d",&rightdist[P(i,j)]);
            }
        }
        for(int i=1;i<=n-1;++i){
            for(int j=1;j<=m;++j){
                scanf("%d",&downdist[P(i,j)]);
            }
        }
        
        scanf("%d",&TT);
        for(int i=1;i<=TT;++i){
            scanf("%d%d%d%d",&qx1[i],&qy1[i],&qx2[i],&qy2[i]);
        }
        for(int i=1;i<=TT;++i)ans[i]=0x7fffffff;
        for(int i=1;i<=TT;++i)qs[i]=i;
        
        DivCon(1,1,n,m,1,TT);
        
        
        for(int i=1;i<=TT;++i)printf("%d
    ",ans[i]);
        return 0;
    }
    自己还是太辣鸡了
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  • 原文地址:https://www.cnblogs.com/zzyer/p/8598815.html
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