我尝试使用C++ implementation的Dinic算法解决最大流量问题。在该C ++代码中，假定所有参数都是整数。我尝试将代码转换为等效的代码，其中边的容量可以是连续的（非整数）。这是我的代码：
// C++ implementation of Dinic's Algorithm
// #include "HEADERS.h"
#include<bits/stdc++.h>
using namespace std;
double EPSILON = 1e-6 ;
// A structure to represent a edge between
// two vertex
struct Edge
{
int v ; // Vertex v (or "to" vertex)
// of a directed edge u-v. "From"
// vertex u can be obtained using
// index in adjacent array.
double flow ; // flow of data in edge
double C; // capacity
int rev ; // To store index of reverse
// edge in adjacency list so that
// we can quickly find it.
};
// Residual Graph
class Graph
{
int V; // number of vertex
int *level ; // stores level of a node
vector< Edge > *adj;
public :
Graph(int V)
{
adj = new vector<Edge>[V];
this->V = V;
level = new int[V];
}
// add edge to the graph
void addEdge(int u, int v, double C)
{
// Forward edge : 0 flow and C capacity
Edge a{v, 0, C, static_cast<int> (adj[v].size()) };
// Back edge : 0 flow and 0 capacity
Edge b{u, 0, 0, static_cast<int> (adj[u].size()) };
adj[u].push_back(a);
adj[v].push_back(b); // reverse edge
}
bool BFS(int s, int t);
int sendFlow(int s, double flow, int t, int ptr[]);
double DinicMaxflow(int s, int t);
};
// Finds if more flow can be sent from s to t.
// Also assigns levels to nodes.
bool Graph::BFS(int s, int t)
{
for (int i = 0 ; i < V ; i++)
level[i] = -1;
level[s] = 0; // Level of source vertex
// Create a queue, enqueue source vertex
// and mark source vertex as visited here
// level[] array works as visited array also.
list< int > q;
q.push_back(s);
vector<Edge>::iterator i ;
while (!q.empty())
{
int u = q.front();
q.pop_front();
for (i = adj[u].begin(); i != adj[u].end(); i++)
{
Edge &e = *i;
if (level[e.v] < 0 && e.flow < e.C)
{
// Level of current vertex is,
// level of parent + 1
level[e.v] = level[u] + 1;
q.push_back(e.v);
}
}
}
// IF we can not reach to the sink we
// return false else true
return level[t] < 0 ? false : true ;
}
// A DFS based function to send flow after BFS has
// figured out that there is a possible flow and
// constructed levels. This function called multiple
// times for a single call of BFS.
// flow : Current flow send by parent function call
// start[] : To keep track of next edge to be explored.
// start[i] stores count of edges explored
// from i.
// u : Current vertex
// t : Sink
int Graph::sendFlow(int u, double flow, int t, int start[])
{
// Sink reached
if (u == t)
return flow;
// Traverse all adjacent edges one -by - one.
for ( ; start[u] < static_cast <int> (adj[u].size()) ; start[u]++)
{
// Pick next edge from adjacency list of u
Edge &e = adj[u][start[u]];
if (level[e.v] == level[u]+1 && e.flow < e.C)
{
// find minimum flow from u to t
double curr_flow = min(flow, e.C - e.flow);
double temp_flow = sendFlow(e.v, curr_flow, t, start);
// flow is greater than zero
if (temp_flow > 0)
{
// add flow to current edge
e.flow += temp_flow;
// subtract flow from reverse edge
// of current edge
adj[e.v][e.rev].flow -= temp_flow;
return temp_flow;
}
}
}
return 0;
}
// Returns maximum flow in graph
double Graph::DinicMaxflow(int s, int t)
{
// Corner case
if (s == t)
return -1;
double total = 0; // Initialize result
// Augment the flow while there is path
// from source to sink
while (BFS(s, t) == true)
{
// store how many edges are visited
// from V { 0 to V }
int *start = new int[V+1];
double flow = sendFlow(s, INT_MAX, t, start) ;
// while flow is not zero in graph from S to D
while (flow > EPSILON )
{
// Add path flow to overall flow
total += flow;
flow = sendFlow(s, INT_MAX, t, start) ;
}
}
// return maximum flow
return total;
}
// Driver program to test above functions
int main()
{
Graph g(6);
g.addEdge(0, 1, 16 );
g.addEdge(0, 2, 13 );
g.addEdge(1, 2, 10 );
g.addEdge(1, 3, 12 );
g.addEdge(2, 1, 4 );
g.addEdge(2, 4, 14);
g.addEdge(3, 2, 9 );
g.addEdge(3, 5, 20 );
g.addEdge(4, 3, 7 );
g.addEdge(4, 5, 4);
// next exmp
/*g.addEdge(0, 1, 3 );
g.addEdge(0, 2, 7 ) ;
g.addEdge(1, 3, 9);
g.addEdge(1, 4, 9 );
g.addEdge(2, 1, 9 );
g.addEdge(2, 4, 9);
g.addEdge(2, 5, 4);
g.addEdge(3, 5, 3);
g.addEdge(4, 5, 7 );
g.addEdge(0, 4, 10);
// next exp
g.addEdge(0, 1, 10);
g.addEdge(0, 2, 10);
g.addEdge(1, 3, 4 );
g.addEdge(1, 4, 8 );
g.addEdge(1, 2, 2 );
g.addEdge(2, 4, 9 );
g.addEdge(3, 5, 10 );
g.addEdge(4, 3, 6 );
g.addEdge(4, 5, 10 ); */
cout << "Maximum flow " << g.DinicMaxflow(0, 5) << endl ;
return 0;
}
在这段代码中，我将flow和C的类型更改为double。我还更改了代码的某些部分，以使其适应这种新的double类型。该代码仅在某些情况下起作用！它输出正确的输出Maximum flow 23或引发Segmentation fault (core dumped)错误。我真的不知道这段代码有什么问题。有什么想法吗？
答案 0 :(得分：2)
我不知道该算法是否正确，但是假设是正确的，那么链接上的代码会出现几个问题。
#include<bits/stdc++.h>标头的用法。首先，应使用bits/stdc++.h should be avoided，并使用正确的#include文件。
第二，使用std::vector可以解决内存泄漏问题。该代码在某些地方使用std::vector，但完全拒绝在其他地方使用。例如：
int *start = new int[V+1];
应替换为：
std::vector<int> start(V+1);
由于代码中缺少delete [] start;，前者导致内存泄漏。使用std::vector，内存泄漏消失了。
一旦引入std::vector，就不需要V类中的Graph成员变量来跟踪顶点数量。原因是vector成员的大小被设置为V个顶点，并且vector已经通过使用vector::size()成员函数知道自己的大小。因此V成员变量是多余的，可以删除。
最后可以进行的更改是在struct Edge类内移动Graph。
考虑到所有提及的更改，这是一个清理的版本，当使用在main()函数中设置的测试图运行时，它返回的结果与原始代码相同：
#include <vector>
#include <list>
#include <algorithm>
#include <iostream>
#include <climits>
class Graph
{
struct Edge
{
int v;
int flow;
int C;
int rev;
};
std::vector<int> level;
std::vector<std::vector< Edge >> adj;
public:
Graph(int V) : level(V), adj(V) {}
void addEdge(int u, int v, int C)
{
adj[u].push_back({ v, 0, C, static_cast<int>(adj[v].size()) });
adj[v].push_back({ u, 0, 0, static_cast<int>(adj[u].size()) });
}
bool BFS(int s, int t);
int sendFlow(int s, int flow, int t, std::vector<int>& ptr);
int DinicMaxflow(int s, int t);
};
bool Graph::BFS(int s, int t)
{
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
std::list< int > q;
q.push_back(s);
std::vector<Edge>::iterator i;
while (!q.empty())
{
int u = q.front();
q.pop_front();
for (i = adj[u].begin(); i != adj[u].end(); i++)
{
Edge &e = *i;
if (level[e.v] < 0 && e.flow < e.C)
{
level[e.v] = level[u] + 1;
q.push_back(e.v);
}
}
}
return level[t] < 0 ? false : true;
}
int Graph::sendFlow(int u, int flow, int t, std::vector<int>& start)
{
if (u == t)
return flow;
for (; start[u] < static_cast<int>(adj[u].size()); start[u]++)
{
// Pick next edge from adjacency list of u
Edge &e = adj[u][start[u]];
if (level[e.v] == level[u] + 1 && e.flow < e.C)
{
int curr_flow = std::min(flow, e.C - e.flow);
int temp_flow = sendFlow(e.v, curr_flow, t, start);
if (temp_flow > 0)
{
e.flow += temp_flow;
adj[e.v][e.rev].flow -= temp_flow;
return temp_flow;
}
}
}
return 0;
}
int Graph::DinicMaxflow(int s, int t)
{
if (s == t)
return -1;
int total = 0;
while (BFS(s, t) == true)
{
std::vector<int> start(level.size() + 1);
while (int flow = sendFlow(s, INT_MAX, t, start))
total += flow;
}
return total;
}
测试功能如下：
int main()
{
Graph g(6);
g.addEdge(0, 1, 16 );
g.addEdge(0, 2, 13 );
g.addEdge(1, 2, 10 );
g.addEdge(1, 3, 12 );
g.addEdge(2, 1, 4 );
g.addEdge(2, 4, 14);
g.addEdge(3, 2, 9 );
g.addEdge(3, 5, 20 );
g.addEdge(4, 3, 7 );
g.addEdge(4, 5, 4);
std::cout << "Maximum flow " << g.DinicMaxflow(0, 5);
}
现在，如果要查看使用double而不是int作为流量会发生什么，最简单的方法是根据上述代码创建模板类。目标是使用int，而不是用模板参数（例如int）来代替double和int。结果代码如下：
T #include <vector>
#include <list>
#include <algorithm>
#include <iostream>
#include <climits>
template <typename T>
class Graph
{
struct Edge
{
int v;
T flow;
T C;
int rev;
};
std::vector<int> level;
std::vector<std::vector<Edge>> adj;
public:
Graph(int V) : level(V), adj(V) {}
void addEdge(int u, int v, T C)
{
adj[u].push_back({ v, T(), C, static_cast<int>(adj[v].size())});
adj[v].push_back({ u, T(), T(), static_cast<int>(adj[u].size())}); // reverse edge
}
bool BFS(int s, int t);
T sendFlow(int s, T flow, int t, std::vector<int>& ptr);
T DinicMaxflow(int s, int t);
};
template <typename T>
bool Graph<T>::BFS(int s, int t)
{
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
std::list< int > q;
q.push_back(s);
typename std::vector<Edge>::iterator i;
while (!q.empty())
{
int u = q.front();
q.pop_front();
for (i = adj[u].begin(); i != adj[u].end(); i++)
{
Edge &e = *i;
if (level[e.v] < 0 && e.flow < e.C)
{
level[e.v] = level[u] + 1;
q.push_back(e.v);
}
}
}
return level[t] < 0 ? false : true;
}
template <typename T>
T Graph<T>::sendFlow(int u, T flow, int t, std::vector<int>& start)
{
if (u == t)
return flow;
for (; start[u] < static_cast<int>(adj[u].size()); start[u]++)
{
Edge &e = adj[u][start[u]];
if (level[e.v] == level[u] + 1 && e.flow < e.C)
{
T curr_flow = std::min(flow, e.C - e.flow);
T temp_flow = sendFlow(e.v, curr_flow, t, start);
if (temp_flow > 0)
{
e.flow += temp_flow;
adj[e.v][e.rev].flow -= temp_flow;
return temp_flow;
}
}
}
return 0;
}
template <typename T>
T Graph<T>::DinicMaxflow(int s, int t)
{
if (s == t)
return -1;
T total = 0;
while (BFS(s, t) == true)
{
std::vector<int> start(level.size() + 1);
while (T flow = sendFlow(s, INT_MAX, t, start))
total += flow;
}
return total;
}
测试示例将简单地使用main或Graph<double>而不是简单地使用Graph<int>-Graph函数中的所有其他内容保持不变
现在该函数是模板，支持创建与main或int相同操作的任何数字类型都可以通过仅创建double来轻松替换。