This algorithm checks whether an undirected graph contains an odd-length cycle by performing a BFS (Breadth-First Search) traversal from each unvisited vertex. It uses a coloring array to keep track of the vertices and their colors during the traversal. Initially, all vertices are uncolored (-1). When a vertex is visited, it is colored with either 0 or 1.

Time Complexity: O(m+n), where m is the number of edges and n is the number of vertices

            bool oddCycle(vector<vector<in>> & graph) {
              vector <int> coloringArray;
              coloringArray.resize(graph.size(), -1);
            
              for (int j = 0; j <graph.size(); j++) {
                if (coloringArray[j] == -1) {

                  coloringArray.at(j) = 1;
                  queue <int> queue;
                  queue.push(j);

                  while (!queue.empty()) {

                    int currentVertix = queue.front();
                    queue.pop();
                    
                    if (graph.at(currentVertix).at(currentVertix) == 1) {
                      return true;
                    }
                    for (int i = 0; i<graph.size(); i++) {
                      if (graph.at(currentVertix).at(i)) {
                        if (coloringArray[i] == -1) {

                          coloringArray[i] = 1 - coloringArray[currentVertix];
                          queue.push(i);
                          
                        } else if (coloringArray[i] == coloringArray[currentVertix]) {
                          return true;
                        }
                      }
                    }
                  }
                }
              }
              return false;
            }