网络流(一)----最大流Ford-Fulkerson算法

感谢YB大神的总结.

 

以HDU1532为例的Ford_Fulkerson算法

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>

using namespace std;

const int inf = 0x3f;
const int INF = 0x3f3f3f3f;
const int maxn = 1005;

struct Node
{
    int to, flow, next;
}edge[maxn * maxn];

int n, m; //顶点数,   边数
int S, T; //源点, 汇点
int tot; //记录邻接表边数
int s[maxn];//DFS保存 结点的  栈
int pre[maxn], rec[maxn], mins[maxn], head[maxn];

void Add_edge(int a, int b, int c)
{
    edge[tot].to = b; edge[tot].flow = c; edge[tot].next = head[a];
    head[a] = tot++;
    edge[tot].to = a; edge[tot].flow = 0; edge[tot].next = head[b];
    head[b] = tot++;
}

void Init()
{
    tot = 0;
    memset(head, -1, sizeof(head));
}

inline int DFS()
{
    int top = 1; 
    memset(pre, -1, sizeof(pre));
    s[top] = S;
    pre[S] = S;
    mins[S] = INF;
    while(top)
    {
        int v = s[top--];
        for(int i = head[v]; i != -1; i = edge[i].next)
        {
            int u = edge[i].to;
            if(pre[u] == -1 && edge[i].flow > 0)
            {
                pre[u] = v;
                rec[u] = i;
                mins[u] = min(mins[v], edge[i].flow);
                s[++top] = u;
            }
        }
        
        if(pre[T] != -1)  //直到找到了汇点
            return mins[T];//每次返回增广路径中容量最小的
    }
    return -1; // 不存在增广路径
}

int Ford_Fulkerson()
{
    int add, Maxflow = 0;

    while((add = DFS()) != -1)
    {//算法知道无法找到增广路径才停止
        Maxflow += add;
        for(int i = T; i != S; i = pre[i]) //修改残余网络
        {
            edge[rec[i]].flow -= add; //正向减去流量
            edge[rec[i]^1].flow += add;//反向增加流量
        }
    }
    return Maxflow;
}
int main()
{
    while(~scanf("%d %d", &n, &m))
    {
        int i, j, k, s, e, c;
        Init();
        for(int i = 0; i < n; i++)
        {
            cin >> s >> e >> c;
            Add_edge(s, e, c);
        }
        S = 1; T = m;
        cout << Ford_Fulkerson() << endl;
    }
    return 0;
}

　　下面是Edmonds-Karp算法代码的实现，bfs使得找到的增广路节点数最少，和上面dfs版本代码的唯一不同就是把保存节点的栈改成了队列：

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>

using namespace std;

const int inf = 0x3f;
const int INF = 0x3f3f3f3f;
const int maxn = 1005;

struct Node
{
    int to, flow, next;
}edge[maxn * maxn];

int n, m; //顶点数,   边数
int S, T; //源点, 汇点
int tot; //记录邻接表边数
int q[maxn];//DFS保存 结点的  栈
int pre[maxn], rec[maxn], mins[maxn], head[maxn];

void Add_edge(int a, int b, int c)
{
    edge[tot].to = b; edge[tot].flow = c; edge[tot].next = head[a];
    head[a] = tot++;
    edge[tot].to = a; edge[tot].flow = 0; edge[tot].next = head[b];
    head[b] = tot++;
}

void Init()
{
    tot = 0;
    memset(head, -1, sizeof(head));
}


inline int bfs()  //bfs寻找增广路
{
	int h,t;
	h=t=0;
	memset(pre,-1,sizeof(pre));
	q[h]=S;
	pre[S]=S;
	mins[S]=INF;
	while(h<=t)
	{
		int v=q[h++];
		for(int i=head[v];i!=-1;i=edge[i].next)
		{
			int u=edge[i].to;
			if(pre[u]==-1 && edge[i].flow>0)
			{
				pre[u]=v;
				rec[u]=i;
				mins[u]=min(mins[v],edge[i].flow);
				q[++t]=u;
			}
		}	
		if(pre[T]!=-1) //直到找到了汇点T
		return mins[T];//每次返回增广路径中，容量最小的值
	}
	return -1; // 不存在增广路径
}

int Edmonds_Karp()   
{
	int add,Maxflow=0;
	while((add=bfs())!=-1) //算法直到无法找到增广路径时才停止
	{
		Maxflow+=add;
		for(int i=T;i!=S;i=pre[i])  //修改残留网络
		{
			edge[rec[i]].flow-=add; //正向减去流量
			edge[rec[i]^1].flow+=add;//反向增加流量
		}
	}
	return Maxflow;
}

int main()
{
    while(~scanf("%d %d", &n, &m))
    {
        int i, j, k, s, e, c;
        Init();
        for(int i = 0; i < n; i++)
        {
            cin >> s >> e >> c;
            Add_edge(s, e, c);
        }
        S = 1; T = m;
        cout << Edmonds_Karp() << endl;
    }
    return 0;
}