poj 1459 && zoj 1734 Power Network

題意：這題差不多是最大流的模版題。

分析：建圖時需要加入一個源點和匯點，然後把所有電站和源點相連，邊的容量就是電站的發電量；把所有消費者和匯點相連，邊的容量就是消費者的消費量。建好網絡以後直接跑求最大流的算法即可。這題用的是ford-fulkerson方法，剛開始用dfs最增廣路超時了，換成bfs找增廣路AC。

PS：現在才知道ford-fulkerson只是一種方法，而並不是一種算法。用bfs找增廣路就是Edmonds-Karp算法，簡稱EK。

以下附上代碼：

#include <algorithm>
#include <iostream>
#include <sstream>
#include <fstream>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cctype>
#include <cmath>
#include <stack>
#include <queue>
#include <list>
#include <map>
#include <set>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

const int maxn = 205;
const int inf = 1000000000;

struct arc
{
  int c,f;
};

int n,np,nc,m;
arc edge[maxn][maxn];
int al[maxn];
int p[maxn];
bool vis[maxn];


//這個網絡以n+1爲源點n爲匯點 
void input()
{
  int i,j;
  int u,v,c;
  for(i = 0; i <= n+1; i++){
    for(j = 0; j <= n+1; j++){
      edge[i][j].c = edge[i][j].f = 0;
    }
  }
  for(i = 0; i <= n+1; i++) vis[i] = 0;
  
  for(i = 0; i < m; i++){
    scanf(" (%d,%d)%d",&u,&v,&c);
    edge[u][v].c = c;
  }

  //源點 
  for(i = 0;i < np; i++){
    scanf(" (%d)%d",&u,&c);
    edge[n+1][u].c = c;
  }
  //匯點 
  for(i = 0; i < nc; i++){
    scanf(" (%d)%d",&u,&c);
    edge[u][n].c = c;
  }
}



int bfs()
{
  int i;
  int u,v;
  queue<int> q;
  fill(vis,vis+n+2,0);
  
  //bfs尋找增廣路 
  al[n+1] = inf;
  q.push(n+1);
  vis[n+1] = 1;
  while(!q.empty()){
    u = q.front(); q.pop();
    
    for(i = 0; i <= n; i++){
      if(vis[i]) continue;
      //正向且未滿 
      if(edge[u][i].c && edge[u][i].f < edge[u][i].c){
        vis[i] = 1;
        al[i] = min(al[u],edge[u][i].c - edge[u][i].f);
        p[i] = u;
        q.push(i);
      }
      //反向且有流量
      else if(edge[i][u].c && edge[i][u].f){
        vis[i] = 1;
        al[i] = min(al[u],edge[i][u].f);
        p[i] = -u;
        q.push(i);
      }
    }//for i
    
    if(vis[n]) break;
  }//while
  
  if(!vis[n]) return 0;
  
  //增廣
  int t = n;
  int alpha = al[n];
  while(t != n+1){
    if(p[t] >= 0) edge[p[t]][t].f += alpha;
    else edge[t][-p[t]].f -= alpha;
    t = abs(p[t]);
  }
  
  return alpha;
}

int solve()
{
  int maxFlow = 0;
  int flow;
  while(flow = bfs()) maxFlow += flow;
  return maxFlow;
}

int main()
{
  while(scanf("%d%d%d%d",&n,&np,&nc,&m) == 4){
    input();
    printf("%d\n",solve());
  } 
	return 0;
}