NOIP2012 T3开车旅行 set+倍增

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70分做法：
先预处理出所有点的最近和次近（O(n^2)一遍就OK）
然后暴力求出每个解（O(nm)）

//By SiriusRen#include <cstdio>#include <cstring>#include <algorithm>#define inf 0x3fffffffusing namespace std;int n,x,rech=0x3fffffff,rec,s,m;double ans=0x3fffffff;struct Path{int to,weight,to2,weight2;void init(){weight=inf,weight2=inf,to=-1,to2=-1;}}path[100050];struct Node{int position,height;}node[100050];bool cmp(Node a,Node b){return a.height<b.height;}int main(){    scanf("%d",&n);    for(int i=1;i<=n;i++){        node[i].position=i;        scanf("%d",&node[i].height);    }    for(int i=1;i<=n;i++){        path[i].init();        for(int j=i+1;j<=n;j++){            if(path[i].weight2>abs(node[j].height-node[i].height)){                path[i].weight2=abs(node[j].height-node[i].height);                path[i].to2=node[j].position;            }            else if(path[i].weight2==abs(node[j].height-node[i].height)&&node[j].height<node[i].height){                path[i].to2=node[j].position;            }            if(path[i].weight2<path[i].weight){                swap(path[i].weight2,path[i].weight);                swap(path[i].to,path[i].to2);            }            else if(path[i].weight2==path[i].weight&&node[j].height<node[i].height){                swap(path[i].to,path[i].to2);            }        }    }    scanf("%d",&x);    for(int i=1;i<=n;i++){        int wei1=0,wei2=0,f=1;        for(int j=i;;){            if(f){                if(wei1+wei2+path[j].weight2<=x)                    wei2+=path[j].weight2;                else break;                j=path[j].to2;            }            else{                if(wei1+wei2+path[j].weight<=x)                    wei1+=path[j].weight;                else break;                j=path[j].to;            }            f^=1;        }        if(wei1&&(ans>1.0*wei2/wei1||(ans==1.0*wei2/wei1&&rech<node[i].height))){            ans=1.0*wei2/wei1;            rec=i;            rech=node[i].height;        }    }    printf("%d\n",rec);    scanf("%d",&m);    for(int i=1;i<=m;i++){        scanf("%d%d",&s,&x);        int wei1=0,wei2=0,f=1;        for(int j=s;;){            if(f){                if(wei1+wei2+path[j].weight2<=x)                    wei2+=path[j].weight2;                else break;                j=path[j].to2;            }            else{                if(wei1+wei2+path[j].weight<=x)                    wei1+=path[j].weight;                else break;                j=path[j].to;            }            f^=1;        }        printf("%d %d\n",wei2,wei1);     }}

100分做法：
先用set 从后向前插入，取出左边两个点和右边两个点（如果有的话），排个序。
O(nlogn)求出最近和次近。
然后呢用倍增求距离
g[i][j]表示从i出发走2^j轮到的地方
f[i][j][0]表示从i出发走2^j轮A走了多少
f[i][j][1]表示从i出发走2^j轮B走了多少
预处理出走一轮到哪儿
g[i][0]=edge[edge[i].to2].to;
f[i][0][0]=edge[i].weight2;
f[i][0][1]=edge[edge[i].to2].weight;

倍增就好了…
g[i][j]=g[g[i][j-1]][j-1];
f[i][j][0]=f[g[i][j-1]][j-1][0]+f[i][j-1][0];
f[i][j][1]=f[g[i][j-1]][j-1][1]+f[i][j-1][1];

//By SiriusRen#include <set>#include <cstdio>#include <cstring>#include <algorithm>#define int long longusing namespace std;int n,xx,x,m,g[100050][20],f[100050][20][2],rech,rec;double ans=0x3fffffff;struct Node{int height,position;}node[100050];struct Node2{int height,Short,position;}jy;struct Edge{int to,to2,weight,weight2;void init(){weight=weight2=0x3fffffff;}}edge[100050];set<Node>s;set<Node2>p;bool operator < (Node a,Node b){return a.height<b.height;}bool operator < (Node2 a,Node2 b){    if(a.Short!=b.Short)return a.Short<b.Short;    else return a.height<b.height;}void init(){    for(int i=n;i>=1;i--){        p.clear();edge[i].init();        s.insert(node[i]);        set<Node>::iterator it=s.find(node[i]),it2=it;        if((++it)!=s.end()){            jy.height=(*it).height;            jy.position=(*it).position;            jy.Short=abs((*it).height-node[i].height);            p.insert(jy);        }        else goto deal1;        if((++it)!=s.end()){            jy.height=(*it).height;            jy.position=(*it).position;            jy.Short=abs((*it).height-node[i].height);            p.insert(jy);        }        deal1:if(it2==s.begin())goto deal;        if((--it2)==s.begin()){            jy.height=(*it2).height;            jy.position=(*it2).position;            jy.Short=abs((*it2).height-node[i].height);            p.insert(jy);            goto deal;        }        else        {            jy.height=(*it2).height;            jy.position=(*it2).position;            jy.Short=abs((*it2).height-node[i].height);            p.insert(jy);        }        it2--;        jy.height=(*it2).height;        jy.position=(*it2).position;        jy.Short=abs((*it2).height-node[i].height);        p.insert(jy);        deal:set<Node2>::iterator itp=p.begin();        if(itp!=p.end()){            edge[i].weight=(*itp).Short;            edge[i].to=(*itp).position;            if((++itp)!=p.end()){                edge[i].weight2=(*itp).Short;                edge[i].to2=(*itp).position;            }        }    }}signed main(){    scanf("%lld",&n);    for(int i=1;i<=n;i++){        scanf("%lld",&node[i].height);        node[i].position=i;    }    init();    for(int i=1;i<=n;i++){        g[i][0]=edge[edge[i].to2].to;        f[i][0][0]=edge[i].weight2;        f[i][0][1]=edge[edge[i].to2].weight;    }    for(int j=1;j<=18;j++){        for(int i=1;i<=n;i++){            g[i][j]=g[g[i][j-1]][j-1];            f[i][j][0]=f[g[i][j-1]][j-1][0]+f[i][j-1][0];            f[i][j][1]=f[g[i][j-1]][j-1][1]+f[i][j-1][1];        }    }    scanf("%lld%lld",&x,&m);    for(int i=1;i<=n;i++){        int wei1=0,wei2=0,S=i,temp=x;        for(int j=17;j>=0;j--){            if(temp>=f[S][j][0]+f[S][j][1]&&g[S][j]){                wei1+=f[S][j][0];                wei2+=f[S][j][1];                temp=temp-(f[S][j][0]+f[S][j][1]);                S=g[S][j];            }        }        if(temp>=edge[S].weight2&&edge[S].to2){            temp-=edge[S].weight2;            wei1+=edge[S].weight2;        }        if(wei2&&(ans>1.0*wei1/wei2||(ans==1.0*wei1/wei2&&rech<node[i].height))){            rech=node[i].height;            rec=i;            ans=1.0*wei1/wei2;        }    }    printf("%lld\n",rec);    for(int i=1;i<=m;i++){        scanf("%lld%lld",&xx,&x);        int wei1=0,wei2=0,S=xx,temp=x;        for(int j=17;j>=0;j--){            if(temp>=f[S][j][0]+f[S][j][1]&&g[S][j]){                wei1+=f[S][j][0];                wei2+=f[S][j][1];                temp=temp-(f[S][j][0]+f[S][j][1]);                S=g[S][j];            }        }        if(temp>=edge[S].weight2&&edge[S].to2){            temp-=edge[S].weight2;            wei1+=edge[S].weight2;        }        printf("%lld %lld\n",wei1,wei2);    }}

这里写图片描述

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