Updated check_bipartite_graph_dfs.py (#9525)

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* Delete greedy_methods/dijkstra_algorithm.py

* Update check_bipartite_graph_dfs.py

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* Update check_bipartite_graph_dfs.py

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* Update graphs/check_bipartite_graph_dfs.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update graphs/check_bipartite_graph_dfs.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update check_bipartite_graph_dfs.py

* Update check_bipartite_graph_dfs.py

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* Update check_bipartite_graph_dfs.py

* Update check_bipartite_graph_dfs.py

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* Update check_bipartite_graph_dfs.py

* Update check_bipartite_graph_dfs.py

* Update check_bipartite_graph_dfs.py

* Let's use self-documenting variable names

This is complex code so let's use self-documenting function and variable names to help readers to understand.

We should not shorten names to simplify the code formatting but use understandable name and leave to code formatting to psf/black.

I am not sure if `nbor` was supposed to be `neighbour`.  ;-)

* Update check_bipartite_graph_dfs.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

graphs/check_bipartite_graph_dfs.py

@@ -1,34 +1,55 @@
-# Check whether Graph is Bipartite or Not using DFS
+from collections import defaultdict
 
 
-# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
-# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
-# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
-# or u belongs to V and v to U. We can also say that there is no edge that connects
-# vertices of same set.
-def check_bipartite_dfs(graph):
-    visited = [False] * len(graph)
-    color = [-1] * len(graph)
+def is_bipartite(graph: defaultdict[int, list[int]]) -> bool:
+    """
+    Check whether a graph is Bipartite or not using Depth-First Search (DFS).
 
-    def dfs(v, c):
-        visited[v] = True
-        color[v] = c
-        for u in graph[v]:
-            if not visited[u]:
-                dfs(u, 1 - c)
+    A Bipartite Graph is a graph whose vertices can be divided into two independent
+    sets, U and V such that every edge (u, v) either connects a vertex from
+    U to V or a vertex from V to U. In other words, for every edge (u, v),
+    either u belongs to U and v to V, or u belongs to V and v to U. There is
+    no edge that connects vertices of the same set.
 
-    for i in range(len(graph)):
-        if not visited[i]:
-            dfs(i, 0)
+    Args:
+        graph: An adjacency list representing the graph.
 
-    for i in range(len(graph)):
-        for j in graph[i]:
-            if color[i] == color[j]:
-                return False
+    Returns:
+        True if there's no edge that connects vertices of the same set, False otherwise.
 
-    return True
+    Examples:
+        >>> is_bipartite(
+        ...     defaultdict(list, {0: [1, 2], 1: [0, 3], 2: [0, 4], 3: [1], 4: [2]})
+        ... )
+        False
+        >>> is_bipartite(defaultdict(list, {0: [1, 2], 1: [0, 2], 2: [0, 1]}))
+        True
+    """
+
+    def depth_first_search(node: int, color: int) -> bool:
+        visited[node] = color
+        return any(
+            visited[neighbour] == color
+            or (
+                visited[neighbour] == -1
+                and not depth_first_search(neighbour, 1 - color)
+            )
+            for neighbour in graph[node]
+        )
+
+    visited: defaultdict[int, int] = defaultdict(lambda: -1)
+
+    return all(
+        not (visited[node] == -1 and not depth_first_search(node, 0)) for node in graph
+    )
 
 
-# Adjacency list of graph
-graph = {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}
-print(check_bipartite_dfs(graph))
+if __name__ == "__main__":
+    import doctest
+
+    result = doctest.testmod()
+
+    if result.failed:
+        print(f"{result.failed} test(s) failed.")
+    else:
+        print("All tests passed!")