USACO 2015 Dec Platinum 1.Max Flow

Description

Farmer John has installed a new system of

pipes to transport milk betweenthe stalls in his barn (), conveniently numbered. Each pipe connects a pair of stalls, and all stalls areconnected to each-other via paths of pipes.

FJ is pumping milk between

pairs of stalls (). Fortheth such pair, you are told two stallsand, endpoints of apath along which milk is being pumped at a unit rate. FJ is concerned that somestalls might end up overwhelmed with all the milk being pumped through them,since a stall can serve as a waypoint along many of thepaths along whichmilk is being pumped. Please help him determine the maximum amount of milkbeing pumped through any stall. If milk is being pumped along a path fromto, then it counts as being pumped through the endpoint stallsand

, as well as through every stall along the path between them.

Input

The first line of the input contains

and .

The next

lines each contain two integers and() describing a pipebetween stalls and

.

The next

lines each contain two integers and

describing the endpointstalls of a path through which milk is being pumped.

Output

An integer specifying the maximum amount of milk pumped through any stall in thebarn.

Sample Input

5 103 41 54 25 45 45 43 54 34 31 33 55 41 53 4

Sample Output

9

#include<stdio.h>int n,k,x,y,s,t,r,ans,idx,point[500001],next[1000001],v[1000001],h[500001],fa[500001],sum[500001],size[500001],f[500001][21];void addedge(int x,int y){    next[++idx]=point[x];    point[x]=idx;    v[idx]=y;}int max(int a,int b){    if(a>b)    return a;    return b;}void swap(int &m,int &k){    int o=m;    m=k;    k=o;}void dfs(int x,int y,int deep){    h[x]=deep;    fa[x]=y;    for (int i=1;i<17;i++)        f[x][i]=f[f[x][i-1]][i-1];    for(int i=point[x];i;i=next[i])        if (v[i]!=y)        {            f[v[i]][0]=x;            dfs(v[i],x,deep+1);        }}int lca(int x,int y){    if(h[x]<h[y])    swap(x,y);    for(int i=17;i>=0;i--)        while (h[f[x][i]]>=h[y])            x=f[x][i];    if(x==y) return x;    for(int i=17;i>=0;i--)        if(f[x][i]!=f[y][i])            x=f[x][i],y=f[y][i];    return f[x][0];}void dfs2(int x,int fa){    size[x]=sum[x];    for(int i=point[x];i;i=next[i])        if(v[i]!=fa)        {            dfs2(v[i],x);            size[x]+=size[v[i]];        }    ans=max(ans,size[x]);}int main(){    scanf("%d%d",&n,&k);    for(int i=1;i<n;i++)    {        scanf("%d%d",&x,&y);        addedge(x,y);        addedge(y,x);    }    dfs(1,0,1);    for(int i=1;i<=k;i++)    {        scanf("%d%d",&s,&t);        r=lca(s,t);        sum[s]++;        sum[t]++;        sum[r]--;        if(r!=1)        sum[fa[r]]--;    }    dfs2(1,0);    printf("%d\n",ans);}