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Happy Vertices

Problem

Editorial

Analytics

You are given a graph with $$N$$ vertices and $$M$$ edges. Master parent is the vertex which has no parent but may have 0 or more children. In any connected component of the graph,vertex with the lowest value in that component serves as the master parent.

A vertex is called happy if it has more children than its parent. Count the number of happy vertices in the given graph.The graph has no cycles or self loops.

**Input Format**:

First line consists of two space separated integers denoting $$N$$ and $$M$$ and the following $$M$$ lines consist of two space separated integers $$X$$ and $$Y$$ denoting there is an edge between vertices $$X$$ and $$Y$$.

**Output Format**:

Print the number of happy vertices in the graph.

**Constraints**:

$$ 1 \le N \le 100000$$

$$ 0 \le M \le N-1 $$

$$ 1 \le X, Y \le N $$

Explanation

In this graph, we have vertices 1,2,3 and 4. Since 1 is the lowest among these, so it becomes the master vertex. Now, 1 has only 1 child while 2 has two children.So, 2 is a happy vertex. There are no more happy vertices in the graph.

Time Limit:
1.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

Marking Scheme:
Marks are awarded when all the testcases pass.

Allowed Languages:
C,
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JavaScript(Node.js),
Julia,
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PHP,
Python,
Python 3,
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Ruby,
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Initializing Code Editor...

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{}

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