Ombrophobic Bovines POJ - 2391 Floyd+ 二分+最大流

最新推荐文章于 2019-08-14 23:51:30 发布

转载最新推荐文章于 2019-08-14 23:51:30 发布 · 329 阅读

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本文介绍了一种结合Floyd算法、二分查找及最大流算法的综合应用案例，通过解决一个具体的流量分配问题来展示这些算法如何协同工作。文中详细解释了如何构造图模型、进行最短路径计算、以及如何使用Dinic算法求解最大流等问题。

Floyd+ 二分+最大流

vj挂了，不知道对不对

#include<iostream>
#include<string>
#include<cstring>
#include<algorithm>
#include<cstdio>
#include<vector>
#include<queue>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a));
#define sf scanf
#define pf printf
#define LL long long
#define bug1  cout<<"bug1"<<endl;
#define bug2  cout<<"bug2"<<endl;
#define bug3  cout<<"bug3"<<endl;
#define mem(a,b) memset(a,b,sizeof(a));
#define inf 0x3f3f3f3f
const int maxn=2205;
const int INF=1e9+5;

struct Edge {
  int from, to, cap, flow;
};

bool operator < (const Edge& a, const Edge& b) {
  return a.from < b.from || (a.from == b.from && a.to < b.to);
}

struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;
  vector<int> G[maxn];
  bool vis[maxn];
  int d[maxn];
  int cur[maxn];

  void init(int n) {
    for(int i = 0; i < n; i++) G[i].clear();
    edges.clear();
  }

  void ClearFlow() {
    for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;
  }

  void addedge(int from, int to, int cap) {
    edges.push_back((Edge){from, to, cap, 0});
    edges.push_back((Edge){to, from, 0, 0});
    m = edges.size();
    G[from].push_back(m-2);
    G[to].push_back(m-1);
  }

  bool BFS() {
    memset(vis, 0, sizeof(vis));
    queue<int> Q;
    Q.push(s);
    vis[s] = 1;
    d[s] = 0;
    while(!Q.empty()) {
      int x = Q.front(); Q.pop();
      for(int i = 0; i < G[x].size(); i++) {
        Edge& e = edges[G[x][i]];
        if(!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = 1;
          d[e.to] = d[x] + 1;
          Q.push(e.to);
        }
      }
    }
    return vis[t];
  }

  int DFS(int x, int a) {
    if(x == t || a == 0) return a;
    int flow = 0, f;
    for(int& i = cur[x]; i < G[x].size(); i++) {
      Edge& e = edges[G[x][i]];
      if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i]^1].flow -= f;
        flow += f;
        a -= f;
        if(a == 0) break;
      }
    }
    return flow;
  }

  int maxflow(int s, int t) {
    this->s = s; this->t = t;
    int flow = 0;
    while(BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }

  vector<int> Mincut() {
    vector<int> ans;
    for(int i = 0; i < edges.size(); i++) {
      Edge& e = edges[i];
      if(vis[e.from] && !vis[e.to] && e.cap > 0) ans.push_back(i);
    }
    return ans;
  }

  void Reduce() {
    for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;
  }
};

Dinic g;

int f,p;

int d[maxn][maxn];
struct OP{
    int c,d;
}op[maxn];
int main(){
    //OP op[maxn];
    while(~sf("%d%d",&f,&p)){
        int s=0,t=2*f+1;
        g.init(t+1);
        int sum=0;
        for(int i=1;i<=f;++i){
            int a,b;
            sf("%d%d",&a,&b);
            op[i].c=a;op[i].d=b;
            //cout<<op[i].c<<' '<<op[i].d<<endl;//怎么回事。。居然输出不了。。
            sum+=a;
        }
        mem(d,inf);
        for(int i=1;i<=p;++i){
            int a,b,c;
            sf("%d%d%d",&a,&b,&c);
            if(d[a][b]>c){
                d[a][b]=d[b][a]=c;
            }
        }
        for(int k=1;k<=f;++k){
            for(int i=1;i<=f;++i){
                for(int j=1;j<=f;++j){
                    if(i==j)d[i][j]=0;
                    d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
                }
            }
        }
        int l=0,r=INF;
        while(l<r){
            int mid=(l+r)>>1;
            g.init(t+1);
            for(int i=1;i<=f;++i){
                g.addedge(s,i,op[i].c);
                g.addedge(i,i+f,op[i].d);
                g.addedge(i+f,t,op[i].d);
            }
            for(int i=1;i<=f;++i){
                for(int j=1;j<=f;++j){
                    if(d[i][j]<=mid){
                        g.addedge(i,j+f,INF);
                    }
                }
            }
            int tmp=g.maxflow(s,t);
            if(tmp==sum)r=mid;
            else l=mid+1;
        }
        pf("%d\n",r);


    }



}

#include<iostream>
#include<string>
#include<cstring>
#include<algorithm>
#include<cstdio>
#include<vector>
#include<queue>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a));
#define sf scanf
#define pf printf
#define LL long long
#define bug1  cout<<"bug1"<<endl;
#define bug2  cout<<"bug2"<<endl;
#define bug3  cout<<"bug3"<<endl;
#define mem(a,b) memset(a,b,sizeof(a));
#define inf 0x3f3f3f3f
const int maxn=2205;
const int INF=1e9+5;

struct Edge {
  int from, to, cap, flow;
};

bool operator < (const Edge& a, const Edge& b) {
  return a.from < b.from || (a.from == b.from && a.to < b.to);
}

struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;
  vector<int> G[maxn];
  bool vis[maxn];
  int d[maxn];
  int cur[maxn];

  void init(int n) {
    for(int i = 0; i < n; i++) G[i].clear();
    edges.clear();
  }

  void ClearFlow() {
    for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;
  }

  void addedge(int from, int to, int cap) {
    edges.push_back((Edge){from, to, cap, 0});
    edges.push_back((Edge){to, from, 0, 0});
    m = edges.size();
    G[from].push_back(m-2);
    G[to].push_back(m-1);
  }

  bool BFS() {
    memset(vis, 0, sizeof(vis));
    queue<int> Q;
    Q.push(s);
    vis[s] = 1;
    d[s] = 0;
    while(!Q.empty()) {
      int x = Q.front(); Q.pop();
      for(int i = 0; i < G[x].size(); i++) {
        Edge& e = edges[G[x][i]];
        if(!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = 1;
          d[e.to] = d[x] + 1;
          Q.push(e.to);
        }
      }
    }
    return vis[t];
  }

  int DFS(int x, int a) {
    if(x == t || a == 0) return a;
    int flow = 0, f;
    for(int& i = cur[x]; i < G[x].size(); i++) {
      Edge& e = edges[G[x][i]];
      if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i]^1].flow -= f;
        flow += f;
        a -= f;
        if(a == 0) break;
      }
    }
    return flow;
  }

  int maxflow(int s, int t) {
    this->s = s; this->t = t;
    int flow = 0;
    while(BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }

  vector<int> Mincut() {
    vector<int> ans;
    for(int i = 0; i < edges.size(); i++) {
      Edge& e = edges[i];
      if(vis[e.from] && !vis[e.to] && e.cap > 0) ans.push_back(i);
    }
    return ans;
  }

  void Reduce() {
    for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;
  }
};

Dinic g;

int f,p;

int d[maxn][maxn];
struct OP{
    int c,d;
}op[maxn];
int main(){
    //OP op[maxn];
    while(~sf("%d%d",&f,&p)){
        int s=0,t=2*f+1;
        g.init(t+1);
        int sum=0;
        for(int i=1;i<=f;++i){
            int a,b;
            sf("%d%d",&a,&b);
            op[i].c=a;op[i].d=b;
            //cout<<op[i].c<<' '<<op[i].d<<endl;//怎么回事。。居然输出不了。。
            sum+=a;
        }
        mem(d,inf);
        for(int i=1;i<=p;++i){
            int a,b,c;
            sf("%d%d%d",&a,&b,&c);
            if(d[a][b]>c){
                d[a][b]=d[b][a]=c;
            }
        }
        for(int k=1;k<=f;++k){
            for(int i=1;i<=f;++i){
                for(int j=1;j<=f;++j){
                    if(i==j)d[i][j]=0;
                    d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
                }
            }
        }
        int l=0,r=INF;
        while(l<r){
            int mid=(l+r)>>1;
            g.init(t+1);
            for(int i=1;i<=f;++i){
                g.addedge(s,i,op[i].c);
                g.addedge(i,i+f,op[i].d);
                g.addedge(i+f,t,op[i].d);
            }
            for(int i=1;i<=f;++i){
                for(int j=1;j<=f;++j){
                    if(d[i][j]<=mid){
                        g.addedge(i,j+f,INF);
                    }
                }
            }
            int tmp=g.maxflow(s,t);
            if(tmp==sum)r=mid;
            else l=mid+1;
        }
        pf("%d\n",r);


    }



}