solved 'Course Schedule' on LeetCode https://leetcode.com/problems/course-schedule/

has_cycles.cpp

class Solution {
 public:
  // Use DFS to find cycles.
  bool canFinish(int numCourses, vector<pair<int, int>> &prerequisites) {
    // Init the graph.
    adjacency_list_ = vector<vector<int>>(numCourses);
    visited_ = vector<bool>(numCourses);
    visited_in_recursion_ = vector<bool>(numCourses);
    for (const auto &edge : prerequisites) {
      adjacency_list_[edge.second].push_back(edge.first);
    }

    bool has_back_edge = false;
    for (int i = 0; i < numCourses; ++i) {
      if (!visited_[i]) {
        has_back_edge = hasBackEdge(i);
        if (has_back_edge) {
          break;
        }
      }
    }
    // Having back edges means there are cycles, thus
    // impossible to finish the courses.
    return !has_back_edge;
  }
 private:
  // Looking for back edges using DFS.
  bool hasBackEdge(int v) {
    visited_[v] = true;
    visited_in_recursion_[v] = true;
    for (int neighbor : adjacency_list_[v]) {
      if (visited_in_recursion_[neighbor] ||
          (!visited_[neighbor] && hasBackEdge(neighbor))) {
        // Found a back edge. Note the DFS happens 
        // in the second condition.
        return true;
      }
    }
    // Unmark the recursion records.
    visited_in_recursion_[v] = false;
    return false;
  }

  vector<vector<int>> adjacency_list_;
  vector<bool> visited_;
  vector<bool> visited_in_recursion_;
};