Cod sursa(job #2940066)

Utilizator Giulian617Buzatu Giulian Giulian617 Data 14 noiembrie 2022 19:09:34
Problema Flux maxim Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.82 kb
///Max Flow Dinic's Algorithm with scaling
///O(N*N*M) on normal graphs
///O(sqrt(N)*M) on bipartite graphs
#include <bits/stdc++.h>
using namespace std;
ifstream f("maxflow.in");
ofstream g("maxflow.out");
const int NMAX=1005,INF=0x3F3F3F3F;
int n,m,x,y,c,maxx;
bool SCALING=1;
struct edge
{
    int node, flow, capacity, index;
};
vector<int>level,skip;
vector<edge>edges[NMAX];
bool bfs(int s,int t,int limit)
{
    level.assign(n+1,-1);
    level[s]=0;
    queue<int>q;
    q.push(s);
    while(!q.empty())
    {
        int node=q.front();
        q.pop();
        for(edge& link:edges[node])
            if(link.capacity-link.flow>0 && level[link.node]==-1 && (!SCALING || link.capacity-link.flow>=limit))///if I can still push flow and the next node is not visited
            {
                level[link.node]=level[node]+1;
                q.push(link.node);
            }
    }
    return level[t]!=-1;///if t was visited it will return 1,otherwise 0
}
int dfs(int node,int t,int cur_flow)
{
    if(node==t)
        return cur_flow;
    for(; skip[node]<edges[node].size(); skip[node]++)///we start from the pointer we have for this node
    {
        int next=edges[node][skip[node]].node;
        edge& link = edges[node][skip[node]];///for simplicity
        if(link.capacity-link.flow>0  && level[node]+1==level[next])///if I can still push flow and the node is not visited and we only go forward
        {
            int bottleNeck=dfs(next,t,min(cur_flow,link.capacity-link.flow));
            if(bottleNeck>0)
            {
                link.flow+=bottleNeck;///update on the normal edge
                edges[next][link.index].flow-=bottleNeck;///update on the reverse edge
                return bottleNeck;
            }
        }
    }
    return 0;
}
int maxflow(int s,int t)
{
    int max_flow=0;
    skip.resize(n+1);
    for(int limit=SCALING ? (1<<(int(log2(maxx)))):1; limit>0; limit=limit/2)
        while(bfs(s,t,limit))
        {
            fill(skip.begin(),skip.end(),0);///for pruning dead ends
            for(int new_flow=dfs(s,t,INF); new_flow!=0; new_flow=dfs(s,t,INF))///as long as we can find a new path we increase the max_flow
                max_flow+=new_flow;
        }
    return max_flow;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    f>>n>>m;
    for(int i=1; i<=m; i++)
    {
        f>>x>>y>>c;
        edges[x].push_back({y,0,c,0});///to node,flow,capacity,index
        edges[y].push_back({x,0,0,0});///reverse edge:to node,flow,capacity,index
        edges[x].back().index=edges[y].size()-1;///index from adjacency list of y
        edges[y].back().index=edges[x].size()-1;///index from adjacency list of x
        if(c>maxx)
            maxx=c;
    }
    g<<maxflow(1,n);///source, terminal
    return 0;
}