Given a Directed Acyclic Graph of **n** nodes (numbered from 1 to n) and **m** edges. The task is to find the number of sink nodes. A sink node is a node such that no edge emerges out of it.

**Examples:**

Input : n = 4, m = 2 Edges[] = {{2, 3}, {4, 3}} Output : 2 Only node 1 and node 3 are sink nodes. Input : n = 4, m = 2 Edges[] = {{3, 2}, {3, 4}} Output : 3

The idea is to iterate through all the edges. And for each edge, mark the source node from which the edge emerged out. Now, for each node check if it is marked or not. And count the unmarked nodes.

Algorithm:

1. Make any array A[] of size equal to the number of nodes and initialize to 1. 2. Traverse all the edges one by one, say, u -> v. (i) Mark A[u] as 1. 3. Now traverse whole array A[] and count number of unmarked nodes.

Below is implementation of this approach:

## C++

`// C++ program to count number if sink nodes ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Return the number of Sink NOdes. ` `int` `countSink(` `int` `n, ` `int` `m, ` `int` `edgeFrom[], ` ` ` `int` `edgeTo[]) ` `{ ` ` ` `// Array for marking the non-sink node. ` ` ` `int` `mark[n]; ` ` ` `memset` `(mark, 0, ` `sizeof` `mark); ` ` ` ` ` `// Marking the non-sink node. ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `mark[edgeFrom[i]] = 1; ` ` ` ` ` `// Counting the sink nodes. ` ` ` `int` `count = 0; ` ` ` `for` `(` `int` `i = 1; i <= n ; i++) ` ` ` `if` `(!mark[i]) ` ` ` `count++; ` ` ` ` ` `return` `count; ` `} ` ` ` `// Driven Program ` `int` `main() ` `{ ` ` ` `int` `n = 4, m = 2; ` ` ` `int` `edgeFrom[] = { 2, 4 }; ` ` ` `int` `edgeTo[] = { 3, 3 }; ` ` ` ` ` `cout << countSink(n, m, edgeFrom, edgeTo) << endl; ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to count number if sink nodes ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Return the number of Sink NOdes. ` `static` `int` `countSink(` `int` `n, ` `int` `m, ` ` ` `int` `edgeFrom[], ` `int` `edgeTo[]) ` `{ ` ` ` `// Array for marking the non-sink node. ` ` ` `int` `[]mark = ` `new` `int` `[n + ` `1` `]; ` ` ` ` ` `// Marking the non-sink node. ` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++) ` ` ` `mark[edgeFrom[i]] = ` `1` `; ` ` ` ` ` `// Counting the sink nodes. ` ` ` `int` `count = ` `0` `; ` ` ` `for` `(` `int` `i = ` `1` `; i <= n ; i++) ` ` ` `if` `(mark[i] == ` `0` `) ` ` ` `count++; ` ` ` ` ` `return` `count; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `n = ` `4` `, m = ` `2` `; ` ` ` `int` `edgeFrom[] = { ` `2` `, ` `4` `}; ` ` ` `int` `edgeTo[] = { ` `3` `, ` `3` `}; ` ` ` ` ` `System.out.println(countSink(n, m, ` ` ` `edgeFrom, edgeTo)); ` `} ` `} ` ` ` `// This code is contributed by 29AjayKumar ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program to count number if sink nodes ` ` ` `# Return the number of Sink NOdes. ` `def` `countSink(n, m, edgeFrom, edgeTo): ` ` ` ` ` `# Array for marking the non-sink node. ` ` ` `mark ` `=` `[` `0` `] ` `*` `(n ` `+` `1` `) ` ` ` ` ` `# Marking the non-sink node. ` ` ` `for` `i ` `in` `range` `(m): ` ` ` `mark[edgeFrom[i]] ` `=` `1` ` ` ` ` `# Counting the sink nodes. ` ` ` `count ` `=` `0` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `): ` ` ` `if` `(` `not` `mark[i]): ` ` ` `count ` `+` `=` `1` ` ` ` ` `return` `count ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `n ` `=` `4` ` ` `m ` `=` `2` ` ` `edgeFrom ` `=` `[` `2` `, ` `4` `] ` ` ` `edgeTo ` `=` `[` `3` `, ` `3` `] ` ` ` ` ` `print` `(countSink(n, m, edgeFrom, edgeTo)) ` ` ` `# This code is contributed by PranchalK ` |

*chevron_right*

*filter_none*

## C#

`// C# program to count number if sink nodes ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Return the number of Sink NOdes. ` `static` `int` `countSink(` `int` `n, ` `int` `m, ` ` ` `int` `[]edgeFrom, ` ` ` `int` `[]edgeTo) ` `{ ` ` ` `// Array for marking the non-sink node. ` ` ` `int` `[]mark = ` `new` `int` `[n + 1]; ` ` ` ` ` `// Marking the non-sink node. ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `mark[edgeFrom[i]] = 1; ` ` ` ` ` `// Counting the sink nodes. ` ` ` `int` `count = 0; ` ` ` `for` `(` `int` `i = 1; i <= n ; i++) ` ` ` `if` `(mark[i] == 0) ` ` ` `count++; ` ` ` ` ` `return` `count; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `n = 4, m = 2; ` ` ` `int` `[]edgeFrom = { 2, 4 }; ` ` ` `int` `[]edgeTo = { 3, 3 }; ` ` ` ` ` `Console.WriteLine(countSink(n, m, ` ` ` `edgeFrom, edgeTo)); ` `} ` `} ` ` ` `// This code is contributed by PrinciRaj1992 ` |

*chevron_right*

*filter_none*

**Output:**

2

**Time Complexity:** O(m + n) where n is number of nodes and m is number of edges.

**Related Article:**

The Celebrity Problem

This article is contributed by **Anuj Chauhan**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Determine whether a universal sink exists in a directed graph
- Detect cycle in the graph using degrees of nodes of graph
- Maximize count of nodes disconnected from all other nodes in a Graph
- Maximum number of edges that N-vertex graph can have such that graph is Triangle free | Mantel's Theorem
- Calculate number of nodes between two vertices in an acyclic Graph by Disjoint Union method
- Maximize number of nodes which are not part of any edge in a Graph
- Maximum number of nodes which can be reached from each node in a graph.
- Calculate number of nodes between two vertices in an acyclic Graph by DFS method
- Minimum number of Nodes to be removed such that no subtree has more than K nodes
- Graph implementation using STL for competitive programming | Set 2 (Weighted graph)
- Convert the undirected graph into directed graph such that there is no path of length greater than 1
- Convert undirected connected graph to strongly connected directed graph
- Sum of degrees of all nodes of a undirected graph
- Kth largest node among all directly connected nodes to the given node in an undirected graph
- Check if given path between two nodes of a graph represents a shortest paths
- Largest component size in a graph formed by connecting non-co-prime nodes
- Maximum sum of values of nodes among all connected components of an undirected graph
- Minimum nodes to be colored in a Graph such that every node has a colored neighbour
- Nodes with prime degree in an undirected Graph
- Difference Between sum of degrees of odd and even degree nodes in an Undirected Graph