# 15. Count all Possible Path

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/castle-run3644/1)

## My Approach

Check for the existence of an Eulerian cycle in the graph.

* If every node in the graph has an even degree, it implies the existence of an Eulerian cycle. To determine this, sum the elements in each vector in the input `paths`.
* If any vector accumulate an odd sum, the function returns `false`, indicating the absence of an Eulerian cycle.

#### Note:

To understand the Euler circuit please [refer to this](https://www.youtube.com/watch?v=xR4sGgwtR2I)

## Time and Auxiliary Space Complexity

* **Time Complexity** : `O(N*M)`, where `N` is the number of vectors in `paths` and `M` is the average number of elements in each vector.
* **Auxiliary Space Complexity** : `O(1)`, as we are not using any extra space except for some variables.

## Code (C++)

```cpp
class Solution {
public:
    int isPossible(vector<vector<int>> paths){
        for(auto i: paths){
            if(accumulate(i.begin(), i.end(), 0) % 2 != 0)
                return false;
        }
        return true;
    }
};
```

## Contribution and Support

For discussions, questions, or doubts related to this solution, please visit our [discussion section](https://github.com/getlost01/gfg-potd/discussions). We welcome your input and aim to foster a collaborative learning environment.

If you find this solution helpful, consider supporting us by giving a ⭐ star to the [getlost01/gfg-potd](https://github.com/getlost01/gfg-potd) repository.


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