#6122. 「网络流 24 题」航空路线

https://loj.ac/s/1578964

LibreOJ/6009/6009.cpp

@@ -0,0 +1,90 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <queue>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 25,
+          M = 105;
+const int INF = 0x3f3f3f3f;
+
+int n, m;
+std::array<int, M> a, b1, b2, f1, f2;
+std::array<int, 1 << N> dist;
+std::array<bool, 1 << N> vis;
+
+bool check(int s, int i) {
+    if ((b1[i] | s) != s) return false;
+    if (b2[i] & s) return false;
+
+    return true;
+}
+
+void spfa(int s) {
+    std::fill(dist.begin(), dist.end(), INF);
+
+    std::queue<int> q;
+    q.push(s);
+    dist[s] = 0;
+    vis[s] = true;
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+
+        for (int i = 1; i <= m; i++) {
+            if (!check(u, i)) continue;
+
+            int v = u ^ (u & f1[i]) | f2[i];
+
+            if (dist[u] + a[i] < dist[v]) {
+                dist[v] = dist[u] + a[i];
+
+                if (!vis[v]) {
+                    q.push(v);
+                    vis[v] = true;
+                }
+            }
+        }
+
+        vis[u] = false;
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1; i <= m; i++) {
+        std::string b, f;
+
+        cin >> a[i] >> b >> f;
+
+        for (int j = 0; j < b.size(); j++) {
+            if (b[j] == '+') {
+                b1[i] = b1[i] | 1 << j;
+            } else if (b[j] == '-') {
+                b2[i] = b2[i] | 1 << j;
+            }
+        }
+
+        for (int j = 0; j < f.size(); j++) {
+            if (f[j] == '-') {
+                f1[i] = f1[i] | 1 << j;
+            } else if (f[j] == '+') {
+                f2[i] = f2[i] | 1 << j;
+            }
+        }
+    }
+
+    spfa((1 << n) - 1);
+
+    cout << (dist[0] == INF ? 0 : dist[0]) << endl;
+
+    return 0;
+}

LibreOJ/6122/6122.cpp

@@ -0,0 +1,156 @@
+#include <cstring>
+#include <iostream>
+#include <map>
+#include <queue>
+#include <string>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 105,
+          M = 5005,
+          INF = 0x3f3f3f3f;
+
+int n, m, s, t, flow, cost;
+bool flag;
+std::map<std::string, int> map;
+std::string a[N];
+
+// Graph
+int idx, head[N], ver[M << 1], next[M << 1];
+std::pair<int, int> edge[M << 1];
+
+void add(int u, int v, int flow, int cost) {
+    next[idx] = head[u];
+    ver[idx] = v;
+    edge[idx] = std::make_pair(flow, cost);
+    head[u] = idx++;
+}
+
+// Dinic
+int dist[N];
+bool vis[N];
+
+bool spfa() {
+    memset(vis, 0x00, sizeof(vis));
+    memset(dist, 0x3f, sizeof(dist));
+
+    std::queue<int> q;
+    q.push(s);
+    dist[s] = 0;
+    vis[s] = true;
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+        vis[u] = false;
+
+        for (int i = head[u]; ~i; i = next[i]) {
+            int v = ver[i],
+                c = edge[i].first,
+                w = edge[i].second;
+
+            if (dist[v] > dist[u] + w && c > 0) {
+                dist[v] = dist[u] + w;
+                if (!vis[v]) {
+                    q.push(v);
+                    vis[v] = true;
+                }
+            }
+        }
+    }
+
+    return dist[t] != INF;
+}
+
+int dinic(int u, int limit) {
+    if (u == t) return limit;
+
+    int flow = 0;
+    vis[u] = true;
+    for (int i = head[u]; ~i && flow < limit; i = next[i]) {
+        int v = ver[i],
+            c = edge[i].first,
+            w = edge[i].second;
+
+        if (dist[v] == dist[u] + w && c && !vis[v]) {
+            int k = dinic(v, std::min(c, limit - flow));
+            if (!k) dist[v] = INF;
+            edge[i].first -= k;
+            edge[i ^ 1].first += k;
+            flow += k;
+            cost += k * w;
+        }
+    }
+    vis[u] = false;
+
+    return flow;
+}
+
+void dfs1(int u) {
+    vis[u] = true;
+    cout << a[u - n] << endl;
+    for (int i = head[u]; ~i; i = next[i]) {
+        if (ver[i] <= n && !edge[i].first) {
+            dfs1(ver[i] + n);
+            return;
+        }
+    }
+}
+
+void dfs2(int u) {
+    for (int i = head[u]; ~i; i = next[i]) {
+        if (ver[i] <= n && !edge[i].first && !vis[ver[i] + n]) {
+            dfs2(ver[i] + n);
+        }
+    }
+    cout << a[u - n] << endl;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+
+    memset(head, 0xff, sizeof(head));
+
+    cin >> n >> m;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+        map[a[i]] = i;
+        if (i == 1 || i == n) {
+            add(i, i + n, 2, 0);
+            add(i + n, i, 0, 0);
+        } else {
+            add(i, i + n, 1, 0);
+            add(i + n, i, 0, 0);
+        }
+    }
+
+    s = 1, t = n * 2;
+    for (int i = 1; i <= m; i++) {
+        std::string u, v;
+        cin >> u >> v;
+        int uu = map[u],
+            vv = map[v];
+        if (uu == 1 && vv == n) flag = true;
+        add(uu + n, vv, 1, -1);
+        add(vv, uu + n, 0, 1);
+    }
+
+    while (spfa()) flow += dinic(s, INF);
+
+    if (flow == 2) {
+        cout << -cost << endl;
+        dfs1(n + 1);
+        dfs2(n + 1);
+    } else if (!flag) {  // flow != 2
+        cout << "No Solution!" << endl;
+    } else {  // flow != 2 && flag
+        cout << 2 << endl
+             << a[1] << endl
+             << a[n] << endl
+             << a[1] << endl;
+    }
+
+    return 0;
+}

Luogu/P1642/P1642.cpp

@@ -0,0 +1,99 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <iomanip>
+#include <limits>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 105;
+const double eps = 1e-4;
+
+int n, m;
+std::array<int, N> siz;
+std::array<double, N> d;
+std::array<std::array<double, N>, N> f;
+std::array<std::vector<int>, N> g;
+std::array<std::pair<int, int>, N> a;
+
+void dfs(int u, int fa) {
+    f[u][0] = 0;
+    siz[u] = 1;
+
+    for (int v : g[u]) {
+        if (v == fa) continue;
+
+        dfs(v, u);
+
+        siz[u] += siz[v];
+
+        for (int i = std::min(siz[u], m); ~i; i--) {
+            for (int j = 0; j <= std::min(siz[v], i); j++) {
+                f[u][i] = std::max(f[u][i], f[u][i - j] + f[v][j]);
+            }
+        }
+    }
+
+    for (int i = std::min(m, siz[u]); i; i--) {
+        f[u][i] = f[u][i - 1] + d[u];
+    }
+}
+
+bool check(double mid) {
+    for (int i = 1; i <= n; i++) {
+        d[i] = static_cast<double>(a[i].first) - mid * a[i].second;
+    }
+
+    std::for_each(f.begin(), f.end(), [&](auto &x) {
+        std::fill(x.begin(), x.end(), std::numeric_limits<int>::min());
+    });
+
+    dfs(1, -1);
+
+    for (int i = 1; i <= n; i++) {
+        if (f[i][m] > -eps) return true;
+    }
+
+    return false;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    m = n - m;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i].first;
+    }
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i].second;
+    }
+
+    for (int i = 1, u, v; i < n; i++) {
+        cin >> u >> v;
+
+        g[u].emplace_back(v);
+        g[v].emplace_back(u);
+    }
+
+    double l = 0,
+           r = 10000;
+
+    while (r - l > eps) {
+        double mid = (l + r) / 2;
+
+        if (check(mid)) l = mid;
+        else r = mid;
+    }
+
+    cout << std::fixed << std::setprecision(1) << l << endl;
+
+    return 0;
+}

Luogu/P2761/P2761.cpp

@@ -0,0 +1,90 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <queue>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 22,
+          M = 105;
+const int INF = 0x3f3f3f3f;
+
+int n, m;
+std::array<int, M> a, b1, b2, f1, f2;
+std::array<int, 1 << N> dist;
+std::array<bool, 1 << N> vis;
+
+bool check(int s, int i) {
+    if ((b1[i] | s) != s) return false;
+    if (b2[i] & s) return false;
+
+    return true;
+}
+
+void spfa(int s) {
+    std::fill(dist.begin(), dist.end(), INF);
+
+    std::queue<int> q;
+    q.push(s);
+    dist[s] = 0;
+    vis[s] = true;
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+
+        for (int i = 1; i <= m; i++) {
+            if (!check(u, i)) continue;
+
+            int v = u ^ (u & f1[i]) | f2[i];
+
+            if (dist[u] + a[i] < dist[v]) {
+                dist[v] = dist[u] + a[i];
+
+                if (!vis[v]) {
+                    q.push(v);
+                    vis[v] = true;
+                }
+            }
+        }
+
+        vis[u] = false;
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1; i <= m; i++) {
+        std::string b, f;
+
+        cin >> a[i] >> b >> f;
+
+        for (int j = 0; j < b.size(); j++) {
+            if (b[j] == '+') {
+                b1[i] = b1[i] | 1 << j;
+            } else if (b[j] == '-') {
+                b2[i] = b2[i] | 1 << j;
+            }
+        }
+
+        for (int j = 0; j < f.size(); j++) {
+            if (f[j] == '-') {
+                f1[i] = f1[i] | 1 << j;
+            } else if (f[j] == '+') {
+                f2[i] = f2[i] | 1 << j;
+            }
+        }
+    }
+
+    spfa((1 << n) - 1);
+
+    cout << (dist[0] == INF ? 0 : dist[0]) << endl;
+
+    return 0;
+}

Luogu/P4322/P4322.cpp

@@ -0,0 +1,78 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <iomanip>
+#include <limits>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2505;
+const double eps = 1e-4;
+
+int k, n;
+std::array<int, N> siz;
+std::array<double, N> d;
+std::array<std::array<double, N>, N> f;
+std::array<std::vector<int>, N> g;
+std::array<std::pair<int, int>, N> a;
+
+void dfs(int u) {
+    f[u][1] = d[u];
+    siz[u] = 1;
+
+    for (int v : g[u]) {
+        dfs(v);
+
+        siz[u] += siz[v];
+
+        for (int i = std::min(siz[u], k + 1); i; i--) {
+            for (int j = 0; j <= std::min(siz[v], i - 1); j++) {
+                f[u][i] = std::max(f[u][i], f[u][i - j] + f[v][j]);
+            }
+        }
+    }
+}
+
+bool check(double mid) {
+    for (int i = 1; i <= n; i++) {
+        d[i] = static_cast<double>(a[i].second) - mid * a[i].first;
+    }
+
+    std::for_each(f.begin(), f.end(), [&](auto &x) {
+        std::fill(x.begin(), x.end(), std::numeric_limits<int>::min());
+    });
+
+    dfs(0);
+
+    return f[0][k + 1] >= 0;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> k >> n;
+
+    for (int i = 1, r; i <= n; i++) {
+        cin >> a[i].first >> a[i].second >> r;
+
+        g[r].emplace_back(i);
+    }
+
+    double l = 0,
+           r = 10000;
+
+    while (r - l > eps) {
+        double mid = (l + r) / 2;
+
+        if (check(mid)) l = mid;
+        else r = mid;
+    }
+
+    cout << std::fixed << std::setprecision(3) << l << endl;
+
+    return 0;
+}