Add a MST problem.

I need to give a class about mst and dsu, so I guess I had to find some
problems to do about it.

CSES Problem Set/Road Reparation-kruskal.cpp

@@ -0,0 +1,131 @@
+/* Problem URL: https://cses.fi/problemset/task/1675 */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+vi dsu;
+ll cost;
+int c;
+
+int find_p(int i)
+{
+    if (i == dsu[i]) {
+        return i;
+    }
+    return dsu[i] = find_p(dsu[i]);
+}
+
+void make_pair(int a, int b, ll v)
+{
+    a = find_p(a);
+    b = find_p(b);
+
+    if (a == b) {
+        return;
+    }
+
+    cost += v;
+    c--;
+
+    dsu[b] = a;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, m;
+    cin >> n >> m;
+
+    dsu.resize(n);
+    rep(i, n) {
+        dsu[i] = i;
+    }
+    c = n;
+
+    V<tuple<ll, int, int>> edges(m);
+    for (auto &[v, x, y] : edges) {
+        cin >> x >> y >> v;
+        x--, y--;
+    }
+
+    sortv(edges);
+
+    for (auto &[v, x, y] : edges) {
+        make_pair(x, y, v);
+    }
+
+    if (c != 1) {
+        cout << "IMPOSSIBLE\n";
+        return 0;
+    }
+
+    cout << cost << '\n';
+}

CSES Problem Set/Road Reparation-prim.cpp

@@ -0,0 +1,128 @@
+/* Problem URL: https://cses.fi/problemset/task/1675 */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+V<V<pair<int, ll>>> graph;
+
+ll prim()
+{
+    priority_queue<pair<ll, int>, V<pair<ll, int>>, greater<>> pq;
+    V<bool> vis(graph.size(), false);
+    int remaining = vis.size();
+    ll cost = 0;
+
+    pq.emplace(0, 0);
+
+    while (!pq.empty()) {
+        auto [v, u] = pq.top(); pq.pop();
+
+        if (vis[u]) {
+            continue;
+        }
+
+        vis[u] = true;
+        remaining--;
+        cost += v;
+
+        for (auto [x, cos] : graph[u]) {
+            if (!vis[x]) {
+                pq.emplace(cos, x);
+            }
+        }
+    }
+
+    return remaining == 0 ? cost : -1;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, m;
+    cin >> n >> m;
+
+    graph.resize(n);
+    while (m--) {
+        ll a, b, v;
+        cin >> a >> b >> v;
+        a--, b--;
+
+        graph[a].emplace_back(b, v);
+        graph[b].emplace_back(a, v);
+    }
+
+    ll ans = prim();
+    if (ans == -1) {
+        cout << "IMPOSSIBLE\n";
+        return 0;
+    }
+    cout << ans << '\n';
+}