HDU 3549 Flow Problem（最大流）

HDU 3549 Flow Problem（最大流）

Time Limit: 5000/5000 MS (Java/Others)

Memory Limit: 65536/32768 K (Java/Others)

【Description】	【题目描述】
Network flow is a well-known difficult problem for ACMers. Given a graph, your task is to find out the maximum flow for the weighted directed graph.	网络流是ACMers众所周知的一个难题。给定一幅图，你的任务是找出这个加权有向图的最大流。

【Input】	【输入】
The first line of input contains an integer T, denoting the number of test cases. For each test case, the first line contains two integers N and M, denoting the number of vertexes and edges in the graph. (2 <= N <= 15, 0 <= M <= 1000) Next M lines, each line contains three integers X, Y and C, there is an edge from X to Y and the capacity of it is C. (1 <= X, Y <= N, 1 <= C <= 1000)	输入的第一行是一个整数T，表示测试用例的数量。 对于每个测试用例，第一行有两个整数N和M，表示图中顶点与边的数量。（2 <= N <= 15, 0 <= M <= 1000）接着M行，每行三个整数X,Y和C，有一条从X到Y的边，其容量为C。(1 <= X, Y <= N, 1 <= C <= 1000)

【Output】	【输出】
For each test cases, you should output the maximum flow from source 1 to sink N.	对于每个测试样例，输出从源点1到汇点N的最大流。

【Sample Input - 输入样例】	【Sample Output - 输出样例】
2 3 2 1 2 1 2 3 1 3 3 1 2 1 2 3 1 1 3 1	Case 1: 1 Case 2: 2

【题解】

最大流问题

题目描述得太简单，自己从来没做过，就去百度了一下大概的规则

然后……就当成水管来看吧…………

比较简单的方式的用DFS实现，注意处理好搜索与回溯即可。

搜索时可以每次只找一条1→N的路径，也可以在当前已走过的路径下尽可能地推送流量到N，即多条路径（不过这种方式比较费时，因为会在重复尝试一些无效的路径）

为了方便回溯，每次A→B推送的流量等于添加B→A的容量。

vector的查询速度并不是很快，多次使用的时候用指针或是继承可以提高速度，以及看/写起来舒服点……

【代码 C++】

 #include<cstdio>
 #include <cstring>
 #include <algorithm>
 #include <vector>
 int n;
 struct edge{
     int next, capacity, last_i;
 };
 std::vector<edge> data[];
 bool us[];
 void read(){
     int m, x, y, c, i, j, map[][];
     memset(map, , sizeof(map));
     scanf("%d%d", &n, &m);
     for (i = ; i <= n; ++i) data[i].clear();
     for (i = ; i < m; ++i) scanf("%d%d%d", &x, &y, &c), map[x][y] += c;
     edge temp = { , ,  };
     for (i = ; i < n; ++i){
         for (j = i + ; j <= n; ++j){
             if (map[i][j] + map[j][i] == ) continue;
             temp.next = j; temp.capacity = map[i][j]; temp.last_i = data[j].size();
             data[i].push_back(temp);
             temp.next = i; temp.capacity = map[j][i]; temp.last_i = data[i].size() - ;
             data[j].push_back(temp);
         }
     }
 }
 int send(int nowEdge, int flowWait){
     if (nowEdge == n) return flowWait;
     us[nowEdge] = ;
     int hadSend, temp, i, ed = data[nowEdge].size();
     for (i = hadSend = ; i < ed; ++i){
         edge &now = data[nowEdge][i];
         if (!us[now.next] && now.capacity){
             temp = send(now.next, std::min(now.capacity, flowWait - hadSend));
             if (temp){
                 hadSend += temp; now.capacity -= temp;
                 data[now.next][now.last_i].capacity += temp;
             }
         }
     }
     return hadSend;
 }
 int main(){
     int t, i, opt, temp;
     for (i = scanf("%d", &t); i <= t; ++i){
         printf("Case %d: ", i);
         read();
         for (opt = ; memset(us, , sizeof(us));){
             temp = send(, );
             if (temp) opt += temp;
             else break;
         }
         printf("%d\n", opt);
     }
     return ;
 }