[最大权闭合子图][最小割] BZOJ 4873：寿司餐厅

Solution

对于(i,j)新建一个点，点权为di,j−ai[i=j]。
就是一个最大权闭合子图的模型，最小割即可。
刚开始忘掉写当前弧优化了。。。

#include <bits/stdc++.h>using namespace std;const int N = 211;const int INF = 1 << 28;inline char get(void) {  static char buf[100000], *S = buf, *T = buf;  if (S == T) {    T = (S = buf) + fread(buf, 1, 100000, stdin);    if (S == T) return EOF;  }  return *S++;}template<typename T>inline void read(T &x) {  static char c; x = 0; int sgn = 0;  for (c = get(); c < '0' || c > '9'; c = get()) if (c == '-') sgn = 1;  for (; c >= '0' && c <= '9'; c = get()) x = x * 10 + c - '0';  if (sgn) x = -x;}int n, m, S, T, cnt, Gcnt, clc, ans, mx;int a[N], w[N * 10], usd[N * 10];int d[N][N], id[N][N];struct edge {  int to, next, flow;  edge(int t = 0, int n = 0, int f = 0):to(t), next(n), flow(f) {}};edge G[N * N * N];int head[N * N], cur[N * N];int dis[N * N], vis[N * N];queue<int> Q;inline void AddEdge(int from, int to, int flow) {  G[++Gcnt] = edge(to, head[from], flow); head[from] = Gcnt;  G[++Gcnt] = edge(from, head[to], 0); head[to] = Gcnt;}inline bool bfs(int S, int T) {  vis[S] = ++clc; Q.push(S); dis[S] = 0;  while (!Q.empty()) {    int x = Q.front(); Q.pop();    for (int i = head[x]; i; i = G[i].next) {      edge &e = G[i];      if (e.flow && vis[e.to] != clc) {    dis[e.to] = dis[x] + 1;    vis[e.to] = clc; Q.push(e.to);      }    }  }  return vis[T] == clc;}inline int dfs(int u, int a) {  if (u == T || !a) return a;  int f, flow = 0;  for (int &i = cur[u]; i; i = G[i].next) {    edge &e = G[i];    if (e.flow && dis[e.to] == dis[u] + 1    && (f = dfs(e.to, min(e.flow, a))) > 0) {      e.flow -= f; G[i ^ 1].flow += f;      flow += f; a -= f; if (!a) break;    }  }  return flow;}inline int MaxFlow(int S, int T) {  int flow = 0;  while (bfs(S, T)) {    for (int i = 0; i <= cnt; i++) cur[i] = head[i];    flow += dfs(S, INF);  }  return flow;}int main(void) {  freopen("1.in", "r", stdin);  freopen("1.out", "w", stdout);  read(n); read(m); Gcnt = 1;  for (int i = 1; i <= n; i++) {    read(a[i]); mx = max(mx, a[i]);  }  for (int i = 1; i <= n; i++)    for (int j = i; j <= n; j++) {      read(d[i][j]); id[i][j] = ++cnt;    }  for (int i = 1; i <= 1000; i++) w[i] = ++cnt;  S = ++cnt; T = ++cnt;  for (int i = 1; i <= n; i++) {    for (int j = i; j <= n; j++) {      if (i == j) {    d[i][j] -= a[i];    AddEdge(id[i][i], w[a[i]], INF);      } else {    AddEdge(id[i][j], id[i + 1][j], INF);    AddEdge(id[i][j], id[i][j - 1], INF);      }      if (d[i][j] < 0) AddEdge(id[i][j], T, -d[i][j]);      else AddEdge(S, id[i][j], d[i][j]);      if (d[i][j] > 0) ans += d[i][j];    }    if (!usd[a[i]]) {      usd[a[i]] = 1;      AddEdge(w[a[i]], T, a[i] * a[i] * m);    }  }  printf("%d\n", ans - MaxFlow(S, T));  return 0;}