# 17. Minimum Number of Vertices to Reach All Nodes

Given a **directed acyclic graph**, with `n` vertices numbered from `0` to `n-1`, and an array `edges` where `edges[i] = [fromi, toi]` represents a directed edge from node `fromi` to node `toi`.

Find *the smallest set of vertices from which all nodes in the graph are reachable*. It's guaranteed that a unique solution exists.

Notice that you can return the vertices in any order.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/07/07/untitled22.png)

```
Input: n = 6, edges = [[0,1],[0,2],[2,5],[3,4],[4,2]]
Output: [0,3]
Explanation: It's not possible to reach all the nodes from a single vertex. From 0 we can reach [0,1,2,5]. From 3 we can reach [3,4,2,5]. So we output [0,3].
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/07/07/untitled.png)

```
Input: n = 5, edges = [[0,1],[2,1],[3,1],[1,4],[2,4]]
Output: [0,2,3]
Explanation: Notice that vertices 0, 3 and 2 are not reachable from any other node, so we must include them. Also any of these vertices can reach nodes 1 and 4.
```

## Solution: (Checking the Indegree of each vertices)

```cpp
class Solution
{
public:
    vector<int> findSmallestSetOfVertices(int n, vector<vector<int>> &edges)
    {
        vector<int> res;
        vector<int> inDeg(n, 0);
        for (int i = 0; i < edges.size(); i++)
        {
            inDeg[edges[i][1]]++;
        }

        for (int i = 0; i < n; i++)
        {
            if (inDeg[i] == 0)
            {
                res.push_back(i);
            }
        }

        return res;
    }
};
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://soumyajit4419.gitbook.io/ds-algo/graph/15.minimum-number-of-vertices-to-reach-all-nodes.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.