343E - Pumping Stations - CodeForces Solution

#include <bits/stdc++.h>
using namespace std;
const int N = 205, B = 2005, I = 1e9;
int s, t, n, m, as[N], sum;
struct flow 
{
    int h[N], tot = 1, d[N], cur[N], a[N]; 
    queue<int> q; 
    struct edge 
    {
        int to, val, nxt; 
    }e[B << 1];
    void add(int u, int v, int w) 
    {
        e[++tot] = {v, w, h[u]}; h[u] = tot; 
        e[++tot] = {u, 0, h[v]}; h[v] = tot;
    }
    bool bfs() 
    {
        while(q.size()) q.pop();
        for(int i = 1; i <= n; i++) cur[i] = h[i], d[i] = 0;
        q.push(s); d[s] = 1;
        while(q.size()) 
        {
            int u = q.front(); q.pop();
            for(int i = h[u]; i; i = e[i].nxt)
            {
                int v = e[i].to; 
                if(e[i].val && !d[v]) 
                {
                    d[v] = d[u] + 1;
                    if(v == t) return 1;
                    q.push(v);
                }
            }
        }
        return 0;
    }
    int dfs(int u, int sum) 
    {
        if(u == t) return sum;
        int res = sum; 
        for(int &i = cur[u]; i; i = e[i].nxt)
        {
            int v = e[i].to, w = e[i].val;
            if(w == 0 || d[v] != d[u] + 1) continue;
            int k = dfs(v, min(res, w)); 
            if(k == 0) d[v] = 0;
            else 
            {
                e[i].val -= k, e[i ^ 1].val += k; res -= k;
                if(res == 0) break;
            }
        }
        return sum - res;
    }
    void undo() 
    {
        for(int i = 2; i <= tot; i += 2)
        {
            e[i].val += e[i ^ 1].val;
            e[i ^ 1].val = 0;
        }
    }
    int dinic() 
    {
        int sum = 0; undo();
        while(bfs()) sum += dfs(s, I);
        return sum; 
    }
    int ta[N], fa[N], ct;
    vector<int> g[N];
    struct node 
    {
        int u, v, w; 
        friend bool operator < (node a, node b) {return a.w > b.w;}
    }ed[N];
    int find(int x) {return x == fa[x] ? x : fa[x] = find(fa[x]);}
    void merge(int x, int y) 
    {
        x = find(x), y = find(y);
        if(x == y) return;
        fa[x] = y; g[y].insert(begin(g[y]), begin(g[x]), end(g[x]));
    }
    void solve(int l, int r) 
    {
        if(l == r) return;
        s = a[l], t = a[r]; ed[++ct] = {s, t, dinic()};
        int na = 0, mid = l - 1;
        for(int i = l; i <= r; i++) 
        {
            if(d[a[i]]) a[++mid] = a[i];
            else ta[++na] = a[i]; 
        }
        for(int i = 1; i <= na; i++) a[i + mid] = ta[i];
        solve(l, mid); solve(mid + 1, r);
    }   
    void solve() 
    {
        for(int i = 1; i <= n; i++) a[i] = i, fa[i] = i, g[i].push_back(i);
        solve(1, n); sort(ed + 1, ed + ct + 1);
        for(int i = 1; i <= ct; i++) 
        {
            sum += ed[i].w;
            merge(ed[i].u, ed[i].v);
        }
        int u = find(1);
        for(int i = 1; i <= n; i++) as[i] = g[u][i - 1];
    }
}f;
int u, v, w;
int main()
{
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= m; i++)
    {
        scanf("%d%d%d", &u, &v, &w);
        f.add(u, v, w), f.add(v, u, w);
    }
    f.solve();
    printf("%d\n", sum);
    for(int i = 1; i <= n; i++) printf("%d ", as[i]);
    printf("\n");
    return 0;
}