P3128 [USACO15DEC] Maximum Flow Max Flow (differential trees)

Title Description

Farmer John has installed a new system of $\leq N \leq 50,0002≤N≤50,000), conveniently numbered 1 \ldots N1…N. Each pipe connects a pair of stalls, and all stalls are connected to each-other via paths of pipes.$

FJ is pumping milk between $\leq K \leq 100,0001≤K≤100,000). For the iith such pair, you are told two stalls s_isi and t_iti, endpoints of a path along which milk is being pumped at a unit rate. FJ is concerned that some stalls might end up overwhelmed with all the milk being pumped through them, since a stall can serve as a waypoint along many of the KK paths along which milk is being pumped. Please help him determine the maximum amount of milk being pumped through any stall. If milk is being pumped along a path from s_isi to t_iti, then it counts as being pumped through the endpoint stalls s_isi and$

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

Input Format

The first line of the input contains

The next $\ne yx≠y) describing a pipe$

between stalls

The next

stalls of a path through which milk is being pumped.

Output Format

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

barn.

Sample input and output

Input # 1

Output # 1

Ideas:

For several revisions to ask a path of trees statistical problems we can solve any problem directly to a tree difference can be the difference between the two points into u-> lca (u, v) lca (u, v) -> v difference can be divided point differential and differential side only difference lies in the different operations lca this problem is clear that we can modify each point differential maintains an array of statistics over the last dfs sweep to answer. (This question card out vector (I wrote defect may be a re wa mle there ..) with the chain before the star can live)

Property ( real weight is the weight of a point within a point after all differential and tree )

#include<bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int N = 5e4+7;
const int inf = 0x3f3f3f3f;
const double eps = 1e-6;
typedef long long ll;
const ll mod = 1e9+7;
struct edge{
    int next,v;
};
edge e[N<<1];
int head[N],cnt,f[N][30],d[N];
int val[N];
void add(int u,int v){
    e[++cnt]=(edge){head[u],v};
    head[u]=cnt;
}
int T;
void dfs(int u,int fa){
    d[u]=d[fa]+1; 
    for(int i=head[u];i;i=e[i].next){
        int v=e[i].v;
        if(v==fa) continue;
        f[v][0]=u;
        for(int j=1;j<=T;j++)
            f[v][j]=f[f[v][j-1]][j-1];
        dfs(v,u);
    }
}
int lca(int x,int y){
    if(d[x]>d[y]) swap(x,y);
    for(int i=T;i>=0;i--)
        if(d[f[y][i]]>=d[x]) y=f[y][i];
    if(x==y) return x;
    for(int i=T;i>=0;i--)
        if(f[x][i]!=f[y][i]) x=f[x][i],y=f[y][i];
    return f[x][0];
}
int ans=-inf;
void solve(int u,int fa){
    for(int i=head[u];i;i=e[i].next){
        int v=e[i].v;
        if(v==fa) continue;
        solve(v,u);
        val[u]+=val[v];
    }
    ans=max(ans,val[u]);
}
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    int n,k; cin>>n>>k;
    T=log2(n)+1;
    for(int i=1;i<n;i++){
        int u,v; cin>>u>>v;
        add(u,v); add(v,u);
    }
    dfs(1,0);
    for(int i=1;i<=k;i++){
        int s,t; cin>>s>>t;
        int LCA=lca(s,t);
        val[s]++; val[t]++; val[LCA]--; val[f[LCA][0]]--;
    }
    solve(1,0);
    cout<<ans<<endl;
}

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