[최소 신장 트리] 5월 30일

#18 0530_최소_신장_트리/BOJ_1244_sample.cpp

@@ -0,0 +1,57 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+//남학생의 스위치 바꾸기
+vector<int> changeSwitchBoy(int n, int number, vector<int> switches) {
+    for (int i = number; i <= n; i += number) { //배수에 있는 스위치 바꾸기
+        switches[i] = !switches[i];
+    }
+    return switches;
+}
+
+//여학생의 스위치 바꾸기
+vector<int> changeSwitchGirl(int n, int number, vector<int> switches) {
+    switches[number] = !switches[number];
+    for (int i = 1; i < number; i++) {
+        if ((number + i > n) || (switches[number - i] != switches[number + i])) { //스위치 범위 넘어가거나 좌우 대칭이 아니면
+            break;
+        }
+        switches[number - i] = !switches[number - i];
+        switches[number + i] = !switches[number + i];
+    }
+    return switches;
+}
+
+int main() {
+    int n, m;
+    int student, number;
+
+    //입력
+    cin >> n;
+    vector<int> switches(n + 1, 0);
+    for (int i = 1; i <= n; i++) {
+        cin >> switches[i];
+    }
+
+    //입력 & 연산
+    cin >> m;
+    while (m--) {
+        cin >> student >> number;
+        if (student == 1) {
+            switches = changeSwitchBoy(n, number, switches);
+        } else {
+            switches = changeSwitchGirl(n, number, switches);
+        }
+    }
+
+    //출력
+    for (int i = 1; i <= n; i++) {
+        cout << switches[i] << ' ';
+        if (i % 20 == 0) {
+            cout << '\n';
+        }
+    }
+    return 0;
+}

#18 0530_최소_신장_트리/BOJ_16202_sample.cpp

@@ -0,0 +1,79 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <tuple>
+
+using namespace std;
+typedef tuple<int, int, int> tp;
+
+vector<int> parent;
+
+//Find 연산
+int findParent(int x) {
+    if (parent[x] < 0) {
+        return x;
+    }
+    return parent[x] = findParent(parent[x]);
+}
+
+//Union 연산
+bool unionNodes(int x, int y) {
+    int px = findParent(x);
+    int py = findParent(y);
+
+    if (px == py) {
+        return false;
+    }
+    if (parent[px] < parent[py]) { //새로운 루트 px
+        parent[px] += parent[py];
+        parent[py] = px;
+    } else { //새로운 루트 py
+        parent[py] += parent[px];
+        parent[px] = py;
+    }
+    return true;
+}
+
+int kruskal(int n, int idx, vector<tp> &edge) {
+    int cnt = 0, sum = 0;
+    for (int i = idx; i < edge.size(); i++) {
+        int dist = get<0>(edge[i]);
+        int x = get<1>(edge[i]);
+        int y = get<2>(edge[i]);
+        if (!unionNodes(x, y)) {
+            continue;
+        }
+        sum += dist;
+        cnt++;
+        if (cnt == n - 1) {
+            return sum;
+        }
+    }
+    return 0; //mst를 만들 수 없음
+}
+
+int main() {
+    int n, m, k, x, y;
+
+    cin >> n >> m >> k;
+    vector<tp> edge;
+    for (int i = 1; i <= m; i++) {
+        cin >> x >> y;
+        edge.push_back({i, x, y});
+    }
+
+    bool flag = false;
+    for (int i = 0; i < k; i++) {
+        if (flag) { //더이상 mst를 만들 수 없음
+            cout << 0 << ' ';
+            continue;
+        }
+        parent.assign(n + 1, -1); //초기화
+        int ans = kruskal(n, i, edge);
+        if (ans == 0) {
+            flag = true;
+        }
+        cout << ans << ' ';
+    }
+    return 0;
+}

#18 0530_최소_신장_트리/BOJ_1647_sample.cpp

@@ -0,0 +1,73 @@
+#include <iostream>
+#include <vector>
+#include <tuple>
+#include <algorithm>
+
+using namespace std;
+typedef tuple<int, int, int> tp;
+
+vector<int> parent;
+
+//Find 연산
+int findParent(int x) {
+    if (parent[x] < 0) {
+        return x;
+    }
+    return parent[x] = findParent(parent[x]);
+}
+
+//Union 연산
+bool unionNodes(int x, int y) {
+    int px = findParent(x);
+    int py = findParent(y);
+
+    if (px == py) {
+        return false;
+    }
+    if (parent[px] < parent[py]) { //새로운 루트 px
+        parent[px] += parent[py];
+        parent[py] = px;
+    } else { //새로운 루트 py
+        parent[py] += parent[px];
+        parent[px] = py;
+    }
+    return true;
+}
+
+int kruskal(int n, vector<tp> &edge) {
+    int sum = 0, cnt = 0;
+    for (int i = 0; i < edge.size(); i++) {
+        int w = get<0>(edge[i]);
+        int u = get<1>(edge[i]);
+        int v = get<2>(edge[i]);
+        if (!unionNodes(u, v)) {
+            continue;
+        }
+        sum += w;
+        cnt++;
+        if (cnt == n - 1) {
+            return sum;
+        }
+    }
+    return 0;
+}
+
+int main() {
+    int n, m, a, b, c;
+
+    //입력
+    cin >> n >> m;
+    vector<tp> edge;
+    parent.assign(n + 1, -1);
+    while (m--) {
+        cin >> a >> b >> c;
+        edge.push_back({c, a, b});
+    }
+
+    //연산
+    sort(edge.begin(), edge.end());
+
+    //연산&출력
+    cout << kruskal(n - 1, edge);
+    return 0;
+}

#18 0530_최소_신장_트리/BOJ_1774_sample.cpp

@@ -0,0 +1,95 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <tuple>
+#include <cmath>
+
+using namespace std;
+typedef tuple<double, int, int> tp;
+typedef pair<double, double> ci;
+
+vector<int> parent;
+
+//Find 연산
+int findParent(int x) {
+    if (parent[x] < 0) {
+        return x;
+    }
+    return parent[x] = findParent(parent[x]);
+}
+
+//Union 연산
+bool unionNodes(int x, int y) {
+    int px = findParent(x);
+    int py = findParent(y);
+
+    if (px == py) {
+        return false;
+    }
+    if (parent[px] < parent[py]) { //새로운 루트 px
+        parent[px] += parent[py];
+        parent[py] = px;
+    } else { //새로운 루트 py
+        parent[py] += parent[px];
+        parent[px] = py;
+    }
+    return true;
+}
+
+double kruskal(int v, vector<tp> &edge) {
+    double sum = 0;
+    int cnt = 0;
+
+    for (int i = 0; i < edge.size(); i++) {
+        double cost = get<0>(edge[i]);
+        int x = get<1>(edge[i]);
+        int y = get<2>(edge[i]);
+
+        if (!unionNodes(x, y)) {
+            continue;
+        }
+        sum += cost;
+        cnt++;
+        if (cnt == v - 1) {
+            return sum;
+        }
+    }
+    return 0;
+}
+
+int main() {
+    int n, m, a, b, v = 0;
+    double x, y;
+
+    //입력
+    cin >> n >> m;
+    parent.assign(n + 1, -1);
+    vector<tp> edge;
+    vector<ci> star(n + 1);
+
+    for (int i = 1; i <= n; i++) {
+        cin >> x >> y;
+        for (int j = 1; j < i; j++) {
+            //임의의 두 별에 대한 거리(간선) 모두 구하기
+            double dx = x - star[j].first;
+            double dy = y - star[j].second;
+            edge.push_back({sqrt(dx * dx + dy * dy), i, j});
+        }
+        star[i] = {x, y};
+    }
+
+    //연산
+    while (m--) {
+        cin >> a >> b;
+        if (unionNodes(a, b)) { //이미 연결된 통로
+            v++;
+        }
+    }
+    sort(edge.begin(), edge.end());
+
+    //연산 & 출력
+    cout << fixed;
+    cout.precision(2);
+    cout << kruskal(n - v, edge);
+    return 0;
+}