Graph/Mst/Prim.h

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• Last update: 2025-06-11 15:37:14+07:00

Depends on

• DataStructure/DSU/Dsu.h
• template.h

Code

#include "../../template.h"
#include "../../DataStructure/DSU/Dsu.h"

struct Edge {
    int u, v, w;
    Edge() {}
    Edge(int _u, int _v, int _w): u(_u), v(_v), w(_w) {}
};

pair<ll, vector<Edge>> prim(int s, int n, vector<vector<pii>> &g) {
    ll ans = 0;
    vector<int> par(n+1);
    vector<Edge> MST;
    vector<int> vis(n+1);
    vector<ll> d(n+1, 1e18);
    priority_queue<pii, vector<pii>, greater<pii>> pq;
    d[s] = 0;
    pq.push({d[s], s});
    while (!pq.empty()) {
        auto [dist, u] = pq.top(); pq.pop();
        if (vis[u]) continue;
        vis[u] = 1;
        ans += dist;
        if (s != u) {
            MST.emplace_back(u, par[u], dist);
        }
        for (auto [v, w] : g[u]) {
            if (!vis[v] && d[v] > w) {
                d[v] = w;
                pq.push({d[v], v});
            }
        }
    }
    return {ans, MST};
}

#line 2 "template.h"

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define MOD (ll)(1e9+7)
#define all(x) (x).begin(),(x).end()
#define unique(x) x.erase(unique(all(x)), x.end())
#define INF32 ((1ull<<31)-1)
#define INF64 ((1ull<<63)-1)
#define inf (ll)1e18

#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second

const int mod = 998244353;

void solve();

int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);
    // cin.exceptions(cin.failbit);
    // int t; cin >> t;
    // while(t--)
        solve();
    cerr << "\nTime run: " << 1000 * clock() / CLOCKS_PER_SEC << "ms" << '\n';
    return 0;
}
#line 2 "DataStructure/DSU/Dsu.h"

/* Diff: different between a[u] and a[par[u]] */

struct Dsu {
    vector<int> par, sz;
    vector<ll> diff;

    Dsu() {}
    Dsu(int n): par(n+1), sz(n+1, 1), diff(n+1) {
        iota(all(par), 0);
    }

    int find(int v) {
        if (v == par[v]) return v;
        return par[v] = find(par[v]);
    }
    
    void merge(int a, int b) {
        a = find(a);
        b = find(b);
        if (a == b) return;
        if (sz[a] < sz[b]) swap(a, b);
        par[b] = a;
        sz[a] += sz[b];
    }

    bool same_component(int u, int v) {
        return find(u) == find(v);
    }

    int component_size(int u) {
        u = find(u);
        return sz[u];
    }

    /* https://judge.yosupo.jp/problem/unionfind_with_potential */
    int findPotential(int v, int mod) {
        if (v == par[v]) return v;
        int p = par[v];
        int root = findPotential(p, mod);
        diff[v] = (diff[v] + diff[p]) % mod;
        return par[v] = root;
    }

    bool mergePotential(int u, int v, int x, int mod) {
        int pu = findPotential(u, mod);
        int pv = findPotential(v, mod);
        if (pu == pv) {
            return (diff[u] - diff[v] + mod) % mod == x;
        }
        if(sz[pu] < sz[pv]) {
            swap(u, v);
            swap(pu, pv);
            x = (mod - x) % mod;
        }
        par[pv] = pu;
        sz[pu] += sz[pv];
        diff[pv] = ((diff[u] - diff[v] - x) % mod + mod) % mod;
        return true;
    }

    int getDiff(int u, int v, int mod) {
        int pu = findPotential(u, mod);
        int pv = findPotential(v, mod);
        if (pu != pv) return -1;
        return (diff[u] - diff[v] + mod) % mod;
    }
};
#line 3 "Graph/Mst/Prim.h"

struct Edge {
    int u, v, w;
    Edge() {}
    Edge(int _u, int _v, int _w): u(_u), v(_v), w(_w) {}
};

pair<ll, vector<Edge>> prim(int s, int n, vector<vector<pii>> &g) {
    ll ans = 0;
    vector<int> par(n+1);
    vector<Edge> MST;
    vector<int> vis(n+1);
    vector<ll> d(n+1, 1e18);
    priority_queue<pii, vector<pii>, greater<pii>> pq;
    d[s] = 0;
    pq.push({d[s], s});
    while (!pq.empty()) {
        auto [dist, u] = pq.top(); pq.pop();
        if (vis[u]) continue;
        vis[u] = 1;
        ans += dist;
        if (s != u) {
            MST.emplace_back(u, par[u], dist);
        }
        for (auto [v, w] : g[u]) {
            if (!vis[v] && d[v] > w) {
                d[v] = w;
                pq.push({d[v], v});
            }
        }
    }
    return {ans, MST};
}

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