What is the problem with breadth and depth traversal?

Question

C++ / C#

There is a program that performs breadth and depth traversal to find a path between vertices.

#include <vector>
#include <locale.h>
#include <queue>
#include <Windows.h>
#include <set>
#include <iostream>
#include <fstream>

using namespace std;

UINT BFS(UINT begin, UINT vertex, UINT n,  const vector<vector<int>> &graph)
{
   queue<int> q;
   q.push(begin);


   set<int> gray;

   while (!q.empty())
   {
      UINT v = q.front();
      q.pop();
      gray.insert(v);

      if (v == vertex)
         return 1;

      for (UINT i = 0; i < n; i++)
         if (graph[v][i])
            q.push(i);
      
      if (q.empty())
         return 0;
   }
   for (UINT j : gray);
}



UINT DFS(UINT u, UINT vertex, UINT n,  const vector<vector<int>> &graph, set<int> &gray, set<int> &black)
{
   gray.insert(u);

   for (UINT i = 0; i < n; i++)
      if (graph[u][i])
      {
         if (i == vertex)
            return 1;


        int is_black = black.count(i), is_gray = gray.count(i), is_white = 0;
         
        if (!is_black || !is_gray)
            is_white = 1;


         if (is_white)
            if (DFS(i, vertex, n, graph, gray, black))
               return 1;
      }
   
   gray.erase(u);
   black.insert(u);

   return 0;
}



void main()
{
   UINT one = 0, two = 0;
   setlocale(LC_ALL, "");

   ifstream get_content("in.txt");

   if (get_content)
   {
      UINT vertex, edge;
      get_content >> vertex >> edge;
      vector<vector<int>> graph;
      graph.assign(vertex, vector<int>(vertex));;

      UINT one, two;

      for (UINT i = 0; i < edge; i++)
      {
         UINT one, two;
         get_content >> one >> two;
         graph[one][two] = 1;
      }
      


      printf_s("Введите две вершины: ");

      cin >> one;
      cin >> two;

      set<int> gray, black;


      UINT b = DFS(one, two, vertex, graph, gray, black);
      
      b ? printf_s("Путь есть\n") : printf_s("Пути нет\n");


      b = BFS(one, two, vertex, graph);


      b ? printf_s("Путь есть\n") : printf_s("Пути нет\n");

   }
   else
      printf_s("Не удалось открыть файл");

   return;
}

The number of vertices and edges is written to the in.txt file in the first line, then the paths from one vertex to another are written.
During testing, it was found that when entering in in.txt:
4 4 //4 vertices and 4 edges
0 1
1 2
2 0
2 3
When searching for a path from vertex 0 to vertex 3 (there is a path), the program gives an error. What could be the problem? I will be grateful for the provision of the corrected code section

Answer 1

In BFS, you don't check that a vertex is labeled, and you always queue the vertex. And there is some unnecessary left cycle at the end. The search loops endlessly and eats up all the memory. DFS seems to be correct (there are many complaints about the style, really).