Added doctests to eulerian_path_and_circuit_for_undirected_graph.py (#11883)

* Added doc_tests to eulerian_path_and_circuit_for_undirected_graph.py

* Minor update to doctests, to meet ruff requirements

* Minor update to doctests, to meet ruff requirements

* updating DIRECTORY.md

* updating DIRECTORY.md

---------

Co-authored-by: Sinclo <Sinclo@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: Sinclo

graphs/eulerian_path_and_circuit_for_undirected_graph.py

@@ -5,8 +5,31 @@
 # space complexity is O(VE)
 
 
-# using dfs for finding eulerian path traversal
 def dfs(u, graph, visited_edge, path=None):
+    """
+    Using dfs for finding eulerian path traversal
+    Args:
+        u: The start_node
+        graph: The graph to check
+        visited_edge: Specify if a node has been visited or not
+        path: Optional path parameter
+
+    Returns:
+        Path
+
+    Example:
+        >>> visited_edge = [[False] * 11 for _ in range(11)]
+        >>> dfs(1, {1: [2, 3], 2: [1, 3], 3: [1, 2]}, visited_edge)
+        [1, 2, 3, 1]
+        >>> dfs(5, {1: [2, 3, 4], 2: [1, 3], 3: [1], 4: [1, 5], 5: [4]}, visited_edge)
+        [5, 4, 1]
+        >>> dfs(1, {1: [], 2: [], 3: [1, 2]}, visited_edge)
+        [1]
+        >>> dfs(1, {1: [], 2: []}, visited_edge)
+        [1]
+        >>> dfs(1, {1: [], 2: []}, visited_edge, [1, 3])
+        [1, 3, 1]
+    """
     path = (path or []) + [u]
     for v in graph[u]:
         if visited_edge[u][v] is False:
@@ -15,8 +38,29 @@ def dfs(u, graph, visited_edge, path=None):
     return path
 
 
-# for checking in graph has euler path or circuit
 def check_circuit_or_path(graph, max_node):
+    """
+    For checking in graph has euler path or circuit
+
+    Args:
+        graph: The graph to check
+        max_node: The maximum node to check
+
+    Returns:
+        Type of graph, and its circuit or path
+
+    Example:
+        >>> check_circuit_or_path({1: [2, 3], 2: [1, 3], 3: [1, 2]}, 10)
+        (1, -1)
+        >>> check_circuit_or_path({1: [2, 3, 4], 2: [], 3: [1, 2], 4: [], 5: [4]}, 10)
+        (2, 5)
+        >>> check_circuit_or_path({1: [2, 3, 1], 2: [2], 3: [1, 3], 4: [1], 5: []}, 10)
+        (3, 4)
+        >>> check_circuit_or_path({1: [], 2: [], 3: [1, 2]}, 10)
+        (1, -1)
+        >>> check_circuit_or_path({1: [], 2: []}, 10)
+        (1, -1)
+    """
     odd_degree_nodes = 0
     odd_node = -1
     for i in range(max_node):
@@ -33,6 +77,28 @@ def check_circuit_or_path(graph, max_node):
 
 
 def check_euler(graph, max_node) -> None:
+    """
+    Args:
+        graph: The graph to check
+        max_node: The maximum node to check
+
+    Example:
+        >>> check_euler({1: [2, 3], 2: [1, 3], 3: [1, 2]}, 10)
+        graph has a Euler cycle
+        [1, 2, 3, 1]
+        >>> check_euler({1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}, 10)
+        graph has a Euler path
+        [5, 4, 1, 2, 3, 1]
+        >>> check_euler({1: [2, 3, 1], 2: [2, 3, 4], 3: [1, 3], 4: [1], 5: []}, 10)
+        graph is not Eulerian
+        no path
+        >>> check_euler({1: [], 2: [], 3: [1, 2]}, 10)
+        graph has a Euler cycle
+        [1]
+        >>> check_euler({1: [], 2: []}, 10)
+        graph has a Euler cycle
+        [1]
+    """
     visited_edge = [[False for _ in range(max_node + 1)] for _ in range(max_node + 1)]
     check, odd_node = check_circuit_or_path(graph, max_node)
     if check == 3:
@@ -69,3 +135,7 @@ def main() -> None:
 
 if __name__ == "__main__":
     main()
+
+    import doctest
+
+    doctest.testmod()