bzoj 2304 [Apio 2011 path] 分类： bzoj...

最新推荐文章于 2017-05-04 10:17:02 发布
转载最新推荐文章于 2017-05-04 10:17:02 发布 · 175 阅读
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原文链接：http://www.cnblogs.com/dashgua/p/4723031.html
本文深入探讨了使用Dijkstra算法结合堆实现最短路径求解的方法，并通过具体代码示例详细介绍了如何构建图模型，特别提及了APIO2011寻路问题的解决方案。
喜闻乐见的最短路。
关于如何求最短路，dijstra+heap
关于如何构图，详见《APIO2011寻路解题报告》
代码很长，勿喷。。。
感觉map不靠谱，手写点离散化。
然后居然冲进第一版了。。。
vfk似乎说过这道题代码超过6k的都是弱菜，所以我是大蒟蒻。
#include<map>
#include<stack>
#include<queue>
#include<ctime>
#include<cmath>
#include<string>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<utility>
#include<iostream>
#include<algorithm>

const int MAXN = 1005,Nya = -1, SIZE = 2e9+2,INF = 0x3f3f3f3f, NodeNum = MAXN*12;
const long long LINF = 1e14;
struct Point{int x,y;Point(){}Point(int x,int y):x(x),y(y){}}ptmp;
struct Square{int id,xl,xr,yl,yr;Square(){}Square(int id,int xl,int xr,int yl,int yr):id(id),xl(xl),xr(xr),yl(yl),yr(yr){}};
struct SqSide{Point up[2],down[2],left[2],right[2];};
struct Edge{int v,next;long long w;Edge(){}Edge(int v,long long w,int next):v(v),w(w),next(next){}};
bool cmpl(const Square &a,const Square &b){return a.xl < b.xl;}
bool cmpr(const Square &a,const Square &b){return a.xr < b.xr;}
bool cmpu(const Square &a,const Square &b){return a.yr < b.yr;}
bool cmpd(const Square &a,const Square &b){return a.yl < b.yl;}
bool cmpi(const Square &a,const Square &b){return a.id < b.id;}
bool cmpx(const Point &a,const Point &b){if(a.x!=b.x)return a.x < b.x;else return a.y < b.y;}
bool cmpy(const Point &a,const Point &b){if(a.y!=b.y)return a.y < b.y;else return a.x < b.x;}
#define Trans(x,y) ((long long)(x)*SIZE+(y))
#define Find(x) (std::lower_bound(nd+1,nd+dl+1,(x))-nd)
#define Mp(x,y) std::make_pair(x,y)


int n;Point S,T;
Square ss[MAXN];

SqSide sq[MAXN];

int sn[MAXN<<1],sl;
long long nd[NodeNum];int dl; 

int head[NodeNum],el;
Edge edge[NodeNum<<2];

void NewEdge(int u,int v,long long w)
{
    ++el, edge[el] = Edge(v,w,head[u]), head[u] = el;
}
long long GetDist(const Point &a,const Point &b)
{
    return (long long)abs(a.x-b.x)+abs(a.y-b.y);
}
namespace osq
{
    int head[MAXN], el;
    Point v[NodeNum];
    int next[NodeNum];  

    int blen;
    Point bowl[NodeNum];

    void Clear()
    {
        el = 0;
        memset(head,0,sizeof(head));
        memset(next,0,sizeof(next));
        memset(v,0,sizeof(v));
    }
    void Add(int u,const Point &val)
    {
        ++el, next[el] = head[u], v[el] = val, head[u] = el;
    }
    void Solve()
    {
        std::sort(ss+1,ss+n+1,cmpi);
        for(int i = 1; i <= n; i++)
        {
          blen = 0; 
         for(int j = head[i]; j ; j = next[j])
            bowl[++blen] = v[j];    

          std::sort(bowl+1,bowl+blen+1,cmpx);

          for(int k = 1,s1,s2; k < blen; k++)
            if(bowl[k].x == bowl[k+1].x)
              if(bowl[k].x == ss[i].xl || bowl[k].x == ss[i].xr)
                if(bowl[k].y != bowl[k+1].y)
                {
                    s1 = Find(Trans(bowl[k].x,bowl[k].y));
                    s2 = Find(Trans(bowl[k+1].x,bowl[k+1].y));
                    long long dist = GetDist(bowl[k],bowl[k+1]);
                    NewEdge(s1,s2,dist), NewEdge(s2,s1,dist);
                }

          std::sort(bowl+1,bowl+blen+1,cmpy);   

          for(int k = 1,s1,s2; k < blen; k++)
            if(bowl[k].y == bowl[k+1].y)
             if(bowl[k].y == ss[i].yl || bowl[k].y == ss[i].yr)
               if(bowl[k].x != bowl[k+1].x)
                {
                    s1 = Find(Trans(bowl[k].x,bowl[k].y));
                    s2 = Find(Trans(bowl[k+1].x,bowl[k+1].y));
                    long long dist = GetDist(bowl[k],bowl[k+1]);
                    NewEdge(s1,s2,dist), NewEdge(s2,s1,dist);
                }
        }
    }
}

int tree[MAXN<<3],nn;
namespace seg
{
    #define L(x) ((x)<<1)
    #define R(x) ((x)<<1|1)
    void PushDown(int x)
    {
        if(tree[x] != Nya)
        {
            tree[L(x)] = tree[R(x)] = tree[x];
            tree[x] = Nya;
        }
    }
    int GetColor(int ll,int rr,int k,int si)
    {
        if(ll == rr) return tree[si];
        else
        {
            int mid = (ll+rr)>>1;

            PushDown(si);
            if(k <= mid) return GetColor(ll,mid,k,L(si));
            else  return GetColor(mid+1,rr,k,R(si));
        }
    }
    void Color(int ll,int rr,int l,int r,int si,int col)
    {
        if(ll == l && rr == r) tree[si] = col;
        else
        {
            int mid = (ll+rr)>>1;

            PushDown(si);

            if(r <= mid) Color(ll,mid,l,r,L(si),col);
            else if(l > mid) Color(mid+1,rr,l,r,R(si),col);
            else 
            {
             Color(ll,mid,l,mid,L(si),col);
             Color(mid+1,rr,mid+1,r,R(si),col);
            }
        }
    }

}

namespace copy
{
#define Sfind(x) (std::lower_bound(sn+1,sn+nn+1,(x))-sn)
#define Gain(P,E,F) sq[ss[i].id].P = ptmp = Point(E,F), osq::Add(ss[tmp].id,ptmp)
    void LeftSolve()
    {
        tree[1] = sl = 0; 
        std::sort(ss+1,ss+n+1,cmpl);

        for(int i = 1; i <= n; i++)
          sn[++sl] = ss[i].yl, sn[++sl] = ss[i].yr;

        std::sort(sn+1,sn+sl+1);
        nn = std::unique(sn+1,sn+sl+1)-(sn+1);

        for(int i = 1,s1,s2,tmp; i <= n; i++)
        { 
            s1 = Sfind(ss[i].yl);
            tmp = seg::GetColor(1,nn,s1,1); 
            if(tmp) Gain(left[0],ss[tmp].xr,ss[i].yl);

            s2 = Sfind(ss[i].yr);
            tmp = seg::GetColor(1,nn,s2,1);
            if(tmp) Gain(left[1],ss[tmp].xr,ss[i].yr); 

            seg::Color(1,nn,s1,s2,1,i);
        }  
    }
    void RightSolve()
    {
        tree[1] = sl = 0; 
        std::sort(ss+1,ss+n+1,cmpr);

        for(int i = 1; i <= n; i++)
          sn[++sl] = ss[i].yl, sn[++sl] = ss[i].yr;

        std::sort(sn+1,sn+sl+1);
        nn = std::unique(sn+1,sn+sl+1)-(sn+1);

        for(int i = n,s1,s2,tmp; i >= 1; i--)
        { 
            s1 = Sfind(ss[i].yl);
            tmp = seg::GetColor(1,nn,s1,1); 
            if(tmp) Gain(right[0],ss[tmp].xl,ss[i].yl);

            s2 = Sfind(ss[i].yr);
            tmp = seg::GetColor(1,nn,s2,1);
            if(tmp) Gain(right[1],ss[tmp].xl,ss[i].yr); 

            seg::Color(1,nn,s1,s2,1,i);
        }  
    }
    void UpSolve()
    {   
        tree[1] = sl = 0; 
        std::sort(ss+1,ss+n+1,cmpu);

        for(int i = 1; i <= n; i++)
          sn[++sl] = ss[i].xl, sn[++sl] = ss[i].xr;

        std::sort(sn+1,sn+sl+1);
        nn = std::unique(sn+1,sn+sl+1)-(sn+1);

        for(int i = n,s1,s2,tmp; i >= 1; i--)
        { 
            s1 = Sfind(ss[i].xl);
            tmp = seg::GetColor(1,nn,s1,1); 
            if(tmp) Gain(up[0],ss[i].xl,ss[tmp].yl);

            s2 = Sfind(ss[i].xr);
            tmp = seg::GetColor(1,nn,s2,1);
            if(tmp) Gain(up[1] ,ss[i].xr,ss[tmp].yl);

            seg::Color(1,nn,s1,s2,1,i);
        }
    }
    void DownSolve()
    {
        tree[1] = sl = 0; 
        std::sort(ss+1,ss+n+1,cmpu);

        for(int i = 1; i <= n; i++)
          sn[++sl] = ss[i].xl, sn[++sl] = ss[i].xr;

        std::sort(sn+1,sn+sl+1);
        nn = std::unique(sn+1,sn+sl+1)-(sn+1);

        for(int i = 1,s1,s2,tmp; i <= n; i++)
        { 
            s1 = Sfind(ss[i].xl);
            tmp = seg::GetColor(1,nn,s1,1); 
            if(tmp) Gain(down[0] ,ss[i].xl,ss[tmp].yr);

            s2 = Sfind(ss[i].xr);
            tmp = seg::GetColor(1,nn,s2,1);
            if(tmp) Gain(down[1] ,ss[i].xr,ss[tmp].yr);

            seg::Color(1,nn,s1,s2,1,i);
        }
    }
}

#define Insert(g)   if(g[0].x != INF) nd[++dl] = Trans(g[0].x,g[0].y);\
                    if(g[1].x != INF) nd[++dl] = Trans(g[1].x,g[1].y);


void GetAllNode()
{
    std::sort(ss+1,ss+n+1,cmpi);
    for(int i = 1; i <= n; i++)
    {
        Insert(sq[i].up);
        Insert(sq[i].down);
        Insert(sq[i].left);
        Insert(sq[i].right);

        nd[++dl] = Trans(ss[i].xl,ss[i].yl),
        nd[++dl] = Trans(ss[i].xl,ss[i].yr),
        nd[++dl] = Trans(ss[i].xr,ss[i].yl),
        nd[++dl] = Trans(ss[i].xr,ss[i].yr);
    }
    std::sort(nd+1,nd+dl+1);
    dl = std::unique(nd+1,nd+dl+1)-(nd+1);
}

#define Connect(g)                                      \
        if(g.x != INF)                                  \
        {                                               \
         s2 = Find(Trans(g.x,g.y));                     \
         dist = GetDist(ptmp,g);                        \
         NewEdge(s1,s2,dist),NewEdge(s2,s1,dist);       \
        }

void BuildGraph()
{
    std::sort(ss+1,ss+n+1,cmpi);
    for(int i = 1,s1,s2; i <= n; i++)
    {
        long long dist; 
        ptmp = Point(ss[i].xl,ss[i].yr);
        s1 = Find(Trans(ss[i].xl,ss[i].yr));

        Connect(sq[i].up[0]);
        Connect(sq[i].left[1]);

        ptmp = Point(ss[i].xr,ss[i].yl);
        s1 = Find(Trans(ss[i].xr,ss[i].yl));

        Connect(sq[i].down[1]);
        Connect(sq[i].right[0]);

        ptmp = Point(ss[i].xl,ss[i].yl);
        s1 = Find(Trans(ss[i].xl,ss[i].yl));

        Connect(sq[i].down[0]);
        Connect(sq[i].left[0]);

        ptmp = Point(ss[i].xr,ss[i].yr);
        s1 = Find(Trans(ss[i].xr,ss[i].yr));

        Connect(sq[i].up[1]);
        Connect(sq[i].right[1]);
    }

    for(int i = 1; i <= n; i++)
    {
        ptmp = Point(ss[i].xl,ss[i].yl),osq::Add(ss[i].id,ptmp);
        ptmp = Point(ss[i].xr,ss[i].yl),osq::Add(ss[i].id,ptmp);
        ptmp = Point(ss[i].xl,ss[i].yr),osq::Add(ss[i].id,ptmp);
        ptmp = Point(ss[i].xr,ss[i].yr),osq::Add(ss[i].id,ptmp);
    }
    osq::Solve();
}
typedef std::pair<long long,int> HeapNode;
std::priority_queue<HeapNode,std::vector<HeapNode>,std::greater<HeapNode> >  heap;
bool flag[NodeNum];

#define num second
long long Dijstra(int s,int t)
{
    static long long dist[NodeNum];
    memset(flag,false,sizeof(flag));

    for(int i = 1; i <= dl; i++)
      dist[i] = LINF;
    dist[s] = 0;
    heap.push(Mp(0,s));

    while(!heap.empty())
    {
        int x = heap.top().num;
        heap.pop();
        if(flag[x])continue;

        flag[x] = true;

        for(int i = head[x]; i ; i = edge[i].next)
        {
            int p = edge[i].v;long long tmp = dist[x] + edge[i].w;
            if(tmp < dist[p]) dist[p] = tmp, heap.push(Mp(dist[p],p));
        }
    }
    return dist[t];
}

void Solve()
{
    copy::UpSolve();
    copy::DownSolve();
    copy::LeftSolve();
    copy::RightSolve();

    GetAllNode();

    BuildGraph();

    int st = Find(Trans(S.x,S.y)),ed = Find(Trans(T.x,T.y));
    long long ans = Dijstra(st,ed);

    if(ans < LINF)
      printf("%lld\n",ans);
    else 
      puts("No Path");  
}

void Clear()
{
    dl = el = 0;
    memset(sq,0x3f3f3f3f,sizeof(sq));
    memset(head,0,sizeof(head));
    osq::Clear();
}

void Init()
{
    scanf("%d%d%d%d",&S.x,&S.y,&T.x,&T.y);

    scanf("%d",&n);
    for(int i = 1,x1,y1,x2,y2; i <= n; i++)
    {
      scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
      if(x1 > x2) std::swap(x1,x2);
      if(y1 > y2) std::swap(y1,y2);
      ss[i] = Square(i,x1,x2,y1,y2);
    }
    ss[n+1] = Square(n+1,S.x,S.x,S.y,S.y);
    ss[n+2] = Square(n+2,T.x,T.x,T.y,T.y);
    n += 2;
}

int main()
{
    int Case;

#ifndef ONLINE_JUDGE
    freopen("path.in","r",stdin);
    freopen("path.out","w",stdout);
#endif

    scanf("%d",&Case);

    while(Case--)
    {
      Clear();

      Init();

      Solve();          
    }

#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
#endif
}