如何保存 Edmonds-Karp 算法的最后一个 BFS？

Question

我已经实现了以下 C++ Edmonds-Karp 算法：

#include <iostream>
// Part of Cosmos by  OpenGenus Foundation //
#include <limits.h>
#include <string.h>
#include <queue>
using namespace std;
#define V 6
/* Returns true if there is a path from source 's' to sink 't' in
 * residual graph. Also fills parent[] to store the path */
bool bfs(int rGraph[V][V], int s, int t, int parent[])
{
    // Create a visited array and mark all vertices as not visited
    bool visited[V];
    memset(visited, 0, sizeof(visited));
    // Create a queue, enqueue source vertex and mark source vertex
    // as visited
    queue <int> q;
    q.push(s);
    visited[s] = true;
    parent[s] = -1;
    // Standard BFS Loop
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        for (int v = 0; v < V; v++)
            if (visited[v] == false && rGraph[u][v] > 0)
            {
                q.push(v);
                parent[v] = u;
                visited[v] = true;
            }
    }
    // If we reached sink in BFS starting from source, then return
    // true, else false
    return visited[t] == true;
}
// Returns tne maximum flow from s to t in the given graph
int fordFulkerson(int graph[V][V], int s, int t)
{
    int u, v;
    // Create a residual graph and fill the residual graph with
    // given capacities in the original graph as residual capacities
    // in residual graph
    int rGraph[V][V]; // Residual graph where rGraph[i][j] indicates
                      // residual capacity of edge from i to j (if there
                      // is an edge. If rGraph[i][j] is 0, then there is not)
    for (u = 0; u < V; u++)
        for (v = 0; v < V; v++)
            rGraph[u][v] = graph[u][v];
    int parent[V];  // This array is filled by BFS and to store path
    int max_flow = 0;  // There is no flow initially
    // Augment the flow while tere is path from source to sink
    while (bfs(rGraph, s, t, parent))
    {
        // Find minimum residual capacity of the edges along the
        // path filled by BFS. Or we can say find the maximum flow
        // through the path found.
        int path_flow = INT_MAX;
        for (v = t; v != s; v = parent[v])
        {
            u = parent[v];
            path_flow = min(path_flow, rGraph[u][v]);
        }
        // update residual capacities of the edges and reverse edges
        // along the path
        for (v = t; v != s; v = parent[v])
        {
            u = parent[v];
            rGraph[u][v] -= path_flow;
            rGraph[v][u] += path_flow;
        }
        // Add path flow to overall flow
        max_flow += path_flow;
    }
    // Return the overall flow
    return max_flow;
}

（来源：https://iq.opengenus.org/edmonds-karp-algorithm-for-maximum-flow/）

我想保存算法的最后一个 BFS，这样我就可以打印最小切割（即 {last BFS} {everything else not found in the last BFS}）

我该怎么做？

我尝试在每次调用 bfs 函数时创建一个 BFS 向量，并重新设置它，但不知怎么的，它似乎并没有像我想象的那样工作：

在 bfs 函数中：

bool bfs(int rGraph[V][V], int s, int t, int parent[], vector<int>& search)
{
...

 while (!q.empty())
    {
        int u = q.front();
        search.push_back(u);        
        q.pop();
...

在 fordFulkerson 部分：

vector<int>tempsearch;
vector<int>search;
 while (bfs(rGraph, s, t, parent, search))
    {

...
     tempsearch.resize(search);
     tempsearch = search     //this is now a pseudo-code variant
     search.resize(0);
    }
//at this point tempsearch or search should be the last bfs, no?
return max_flow;

Answer 1

好的，所以我找到了解决方案。我们需要将 visited 数组作为全局数组（或者您可以通过每个参数列表传递它）。这样每次刷新数组的时候，在整个程序中也保存了。

从那里开始，我们所要做的就是编写最小割的输出函数：

void printMinCut(){
    for(int i = 0; i < visited.size(); i++){
         if(visited[i] == true) cout << i;
    }
    cout << endl;
    for(int i = 0; i < visited.size(); i++){
         if(visited[i] == false) cout << i;
    }
}

给你！

如何保存 Edmonds-Karp 算法的最后一个 BFS？

How to save last BFS of Edmonds-Karp algorithm?

c++

graph

breadth-first-search

ford-fulkerson

edmonds-karp