<p>There are a total of <code>numCourses</code> courses you have to take, labeled from <code>0</code> to <code>numCourses - 1</code>. You are given an array <code>prerequisites</code> where <code>prerequisites[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that you <strong>must</strong> take course <code>b<sub>i</sub></code> first if you want to take course <code>a<sub>i</sub></code>.</p>

<ul>
	<li>For example, the pair <code>[0, 1]</code>, indicates that to take course <code>0</code> you have to first take course <code>1</code>.</li>
</ul>

<p>Return <code>true</code> if you can finish all courses. Otherwise, return <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0]]
<strong>Output:</strong> true
<strong>Explanation:</strong> There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> numCourses = 2, prerequisites = [[1,0],[0,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> There are a total of 2 courses to take. 
To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= numCourses &lt;= 2000</code></li>
	<li><code>0 &lt;= prerequisites.length &lt;= 5000</code></li>
	<li><code>prerequisites[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; numCourses</code></li>
	<li>All the pairs prerequisites[i] are <strong>unique</strong>.</li>
</ul>

const int N = 2005;
vector<int>ad_list[N];
int col[N];
bool cycle;
void detectCycle(int u)
{
    col[u] = 1;
    for(auto &j:ad_list[u])
    {
        if(!col[j])
            detectCycle(j);
        else if(col[j] == 1)
            cycle = true;
    }
    col[u] = 2;
}
class Solution {
public:
    bool canFinish(int n, vector<vector<int>>& vc) {
        cycle = false;
        for(int i = 0;i < n;i++)
        {
            col[i] = 0;
            ad_list[i].clear();
        }
        for(int i = 0;i < vc.size();i++)
        {
            int u = vc[i][0];
            int v = vc[i][1];
            ad_list[u].push_back(v);
        }
        for(int i = 0;i < n;i++)
        {
            if(!col[i] and !cycle)
                detectCycle(i);
        }
        if(cycle)
            return false;
        return true;
    }
};
16900