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#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;
}

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#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;
}

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#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;
}

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Luogu/P2761/P2761.cpp Normal file
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#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;
}

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Luogu/P4322/P4322.cpp Normal file
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#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;
}