[최소 신장 트리]12월 6일

[MST]1206/1774.cpp

@@ -0,0 +1,111 @@
+//
+// Created by LG on 2021-12-05.
+//
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <tuple>
+#include <cmath>
+
+using namespace std;
+
+typedef pair<int, int> ci;
+typedef tuple<double, int, int> tp;
+
+vector<int> parent;
+double sum;
+
+int findParent(int node){
+    if(parent[node] < 0)
+        return node;
+    return parent[node] = findParent(parent[node]);
+}
+
+bool unionInput(int x, int y){
+    int xp = findParent(x);
+    int yp = findParent(y);
+
+    if(xp == yp)
+        return false;
+    if(parent[xp] < parent[yp]){
+        parent[xp] += parent[yp];
+        parent[yp] = xp;
+    }
+    else{
+        parent[yp] += parent[xp];
+        parent[xp] = yp;
+    }
+    return true;
+}
+
+double kruskal(int v, priority_queue<tp, vector<tp>, greater<>> &pq){
+    int cnt = 0;
+
+    while(cnt < v-1){
+        double weight = get<0>(pq.top());
+        int x = get<1>(pq.top());
+        int y = get<2>(pq.top());
+        pq.pop();
+
+        if(unionInput(x, y)){
+            sum += weight;
+            cnt++;
+        }
+    }
+    return sum;
+}
+
+int main(){
+
+    int n, m;
+    cin >> n >> m;
+    parent.assign(n+1, -1);
+    priority_queue<tp, vector<tp>, greater<>> pq;
+    priority_queue<tp, vector<tp>, greater<>> pq_cycle;
+
+    vector<vector<bool>> connected(n+1, vector<bool>(n+1, false));
+    vector<ci> god(n+1);
+    for(int i=1; i<=n; i++){
+        cin >> god[i].first >> god[i].second;
+    }
+
+    int cnt = 0;
+    for(int i=0; i<m; i++){
+        int a, b;
+        cin >> a >> b;
+        connected[a][b] = true;
+
+        int xp = findParent(a);
+        int yp = findParent(b);
+
+        if(xp != yp){
+            if (parent[xp] < parent[yp]) {
+                parent[xp] += parent[yp];
+                parent[yp] = xp;
+            }
+            else {
+                parent[yp] += parent[xp];
+                parent[xp] = yp;
+            }
+            cnt++;
+        }
+    }
+
+    for(int i=1; i<n; i++){
+        for(int j=i+1; j<=n; j++){
+            double xd = god[i].first - god[j].first;
+            double yd = god[i].second - god[j].second;
+            if(connected[i][j] || connected[j][i])
+                continue;
+            else
+                pq.push({sqrt(xd*xd+yd*yd), i, j});
+        }
+    }
+
+    kruskal(n-cnt, pq);
+    cout << fixed;
+    cout.precision(2);
+    cout << sum;
+
+    return 0;
+}

[MST]1206/21924.cpp

@@ -0,0 +1,77 @@
+//
+// Created by LG on 2021-12-05.
+//
+#include <iostream>
+#include <vector>
+#include <tuple>
+#include <queue>
+
+using namespace std;
+typedef tuple<int, int, int> tp;
+
+vector<int> parent;
+
+int findParent(int node) {
+    if (parent[node] < 0)
+        return node;
+    return parent[node] = findParent(parent[node]);
+}
+
+bool unionInput(int x, int y) {
+    int xp = findParent(x);
+    int yp = findParent(y);
+
+    if (xp == yp)
+        return false;
+    if (parent[xp] < parent[yp]) {
+        parent[xp] += parent[yp];
+        parent[yp] = xp;
+    } else {
+        parent[yp] += parent[xp];
+        parent[xp] = yp;
+    }
+    return true;
+}
+
+long long kruskal(int v, priority_queue<tp, vector<tp>, greater<>> &pq){
+    int cnt = 0;
+    int sum = 0;
+
+    while(cnt < v-1){
+        if(pq.empty())
+            return 0;
+        int weight = get<0>(pq.top());
+        int x = get<1>(pq.top());
+        int y = get<2>(pq.top());
+        pq.pop();
+
+        if(unionInput(x, y)){
+            cnt++;
+            sum += weight;
+        }
+    }
+
+    return sum;
+}
+
+int main(){
+    int n, m, a, b, w;
+    cin >> n >> m;
+    priority_queue<tp, vector<tp>, greater<>> pq;
+
+    parent.assign(n+1, -1);
+    long long total = 0;
+    for(int i=0; i<m; i++){
+        cin >> a >> b >> w;
+        total += w;
+        pq.push({w, a, b});
+    }
+
+    long long cost = kruskal(n, pq);
+    if(cost == 0)
+        cout << -1;
+    else
+        cout << total - cost;
+
+    return 0;
+}