题解——洛谷 P2680 NOIP提高组 2015 运输计划

树上差分加上二分答案

详细题解待填坑

#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAXlog = 20;
const int MAXM = 711001;
const int MAXN = 400001;
int dep[MAXN],jump[MAXN][MAXlog+2];
int lcav[MAXM],cf[MAXN],fw[MAXN],lent[MAXN];
int uline[MAXM],vline[MAXM],wline[MAXM];
int cnt=0,u[MAXN*2],v[MAXN*2],w[MAXN*2],first[MAXN*2],next[MAXN*2];
int n,m;
void addline(int ux,int vx,int i){
    uline[i]=ux;
    vline[i]=vx;
    wline[i]=lent[ux]+lent[vx]-2*lent[lcav[i]];
}
void addedge(int ux,int vx,int wx){
    cnt++;
    u[cnt]=ux;
    v[cnt]=vx;
    w[cnt]=wx;
    next[cnt]=first[ux];
    first[ux]=cnt;
}
void dfs(int u,int f){
//    printf("u=%d f=%d\n",u,f);
    dep[u]=dep[f]+1;
    jump[u][0]=f;
//    printf("u=%d j=0 jump=%d\n",u,jump[u][0]);
    for(int i=1;i<=MAXlog;i++){
        jump[u][i]=jump[jump[u][i-1]][i-1];
//        printf("u=%d j=%d jump=%d\n",u,i,jump[u][i]);
        }
    for(int i=first[u];i;i=next[i])
        if(v[i]!=f)
            dfs(v[i],u);
}
void dfs2(int u,int f,int wk){
    fw[u]=wk;
    lent[u]=lent[f]+wk;
    for(int i=first[u];i;i=next[i])
        if(v[i]!=f)
            dfs2(v[i],u,w[i]);
}
int lca(int x,int y){
    if(dep[y]>dep[x])
        swap(x,y);
    for(int i=MAXlog;i>=0;i--)
        if(dep[x]-(1<<i)>=dep[y])
            x=jump[x][i];
    if(x==y)
        return x;
    for(int i=MAXlog;i>=0;i--)
        if(jump[x][i]!=jump[y][i]){
            x=jump[x][i];
            y=jump[y][i];
        }
    return jump[x][0];
}
void runcf(int l){
    cf[uline[l]]++;
    cf[vline[l]]++;
    cf[lcav[l]]-=2;
}
int maxlen=0;
void calcf(int u,int f,int num){
    for(int i=first[u];i;i=next[i]){
        if(v[i]==f)
            continue;
        calcf(v[i],u,num);
        cf[u]+=cf[v[i]];    
    }
    if(cf[u]==num&&fw[u]>maxlen)
        maxlen=fw[u];
}
bool check(int ans){
    int inq=0;
    int maxchain=0;
    maxlen=0;
//    printf("!ok\n");
    memset(cf,0,sizeof(cf));
    for(int i=1;i<=cnt;i++)
        if(wline[i]>ans){
            runcf(i);
            inq++;
            if(wline[i]>maxchain)
                maxchain=wline[i];
            }

    calcf(1,0,inq);
//    printf("*ok\n");
    if(maxchain-maxlen<=ans)
        return true;
    else
        return false;
}
int main(){
    scanf("%d %d",&n,&m);
    int maxt=0;
    for(int i=1;i<=n-1;i++){
        int a,b,t;
        scanf("%d %d %d",&a,&b,&t);
        addedge(a,b,t);
        addedge(b,a,t);
        maxt=max(maxt,t);
    }
    dep[0]=-1;
    dfs(1,0);
    dfs2(1,0,0);
    int maxline=0;
    for(int i=1;i<=m;i++){
        int um,vm;
        scanf("%d %d",&um,&vm);
//        if(jump[5][0]!=3)
//            printf("!\n");
        lcav[i]=lca(um,vm);
        addline(um,vm,i);
        if(wline[i]>maxline)
            maxline=wline[i];
    }
    /*for(int i=0;i<=n;i++){
        for(int j=0;j<=MAXlog;j++)
            printf("jump[%d][%d]=%d  \n",i,j,jump[i][j]);
        printf("\n");
    }*/
    /*for(int i=1;i<=m;i++){
        printf("u=%d v=%d lca=%d len=%d\n",uline[i],vline[i],lcav[i],wline[i]);
    }*/
    int l=maxline-maxt,r=maxline+1;
    while(l<r){
        int mid=(l+r)>>1;
        if(check(mid))
            r=mid;
        else
            l=mid+1;
    }
    printf("%d",r);
    return 0;
}