Lowest common ancestor added

pydatastructs/graphs/__init__.py

@@ -17,7 +17,8 @@
     shortest_paths,
     all_pair_shortest_paths,
     topological_sort,
-    topological_sort_parallel
+    topological_sort_parallel,
+    lowest_common_ancestor
 )
 
 __all__.extend(algorithms.__all__)

pydatastructs/graphs/algorithms.py

@@ -11,6 +11,7 @@
 from pydatastructs.graphs.graph import Graph
 from pydatastructs.linear_data_structures.algorithms import merge_sort_parallel
 from pydatastructs import PriorityQueue
+import math
 
 __all__ = [
     'breadth_first_search',
@@ -22,7 +23,8 @@
     'shortest_paths',
     'all_pair_shortest_paths',
     'topological_sort',
-    'topological_sort_parallel'
+    'topological_sort_parallel',
+    'lowest_common_ancestor'
 ]
 
 Stack = Queue = deque
@@ -993,3 +995,109 @@ def _job(graph: Graph, u: str):
     if len(L) != num_vertices:
         raise ValueError("Graph is not acyclic.")
     return L
+
+def lowest_common_ancestor(graph: Graph, vertex1: str, vertex2: str, algorithm: str) -> str:
+    """
+    Finds the lowest common ancestor of two vertices u and v of a directed acylic graph.
+    The LCA of two vertices u and v is defined as the vertex w which is an ancestor
+    of both u and v and is farthest from the root vertex.
+
+    Parameters
+    ==========
+
+    graph: Graph
+        The graph under consideration.
+    vertex1, vertex2: str
+        The names of the vertices in the graph whose lowest common
+        ancestor is to be found.
+    algorithm: str
+        The algorithm to be used.
+        Currently, following are supported,
+        'binary_lifting' -> Binary lifting algorithm as given in [1].
+
+    Returns
+    =======
+
+    str
+        The name of the vertex that is the lowest common ancestor of the two given
+        vertices in the given graph.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import Graph, AdjacencyListGraphNode, lowest_common_ancestor
+    >>> v_1 = AdjacencyListGraphNode('v_1')
+    >>> v_2 = AdjacencyListGraphNode('v_2')
+    >>> v_3 = AdjacencyListGraphNode('v_3')
+    >>> v_4 = AdjacencyListGraphNode('v_4')
+    >>> v_5 = AdjacencyListGraphNode('v_5')
+    >>> graph = Graph(v_1, v_2, v_3, v_4, v_5)
+    >>> graph.add_edge('v_1', 'v_2')
+    >>> graph.add_edge('v_1', 'v_3')
+    >>> graph.add_edge('v_3', 'v_4')
+    >>> graph.add_edge('v_3', 'v_5')
+    >>> lowest_common_ancestor(graph, 'v_5', 'v_2', 'binary_lifting')
+    'v_1'
+    >>> lowest_common_ancestor(graph, 'v_4', 'v_5', 'binary_lifting')
+    'v_3'
+
+    References
+    ==========
+
+    .. [1] https://www.geeksforgeeks.org/lca-in-a-tree-using-binary-lifting-technique/
+    """
+    import pydatastructs.graphs.algorithms as algorithms
+    func = "_" + algorithm + "_" + graph._impl
+    if not hasattr(algorithms, func):
+        raise NotImplementedError(
+            "Currently %s algorithm isn't implemented for "
+            "finding lowest common ancestor of two vertices in a %s graph." % (algorithm, graph._impl))
+    return getattr(algorithms, func)(graph, vertex1, vertex2)
+
+
+def _binary_lifting_adjacency_list(graph: Graph, vertex1: str, vertex2: str) -> list:
+    num_vertices = len(graph.vertices)
+    log_value = math.log2(num_vertices)
+    ancestor = {u: [""]*(int(log_value) + 1) for u in graph.vertices}
+    level = {u: 0 for u in graph.vertices}
+    def precompute(curr_node, next_node, ancestor, level):
+        if next_node != "" :
+            ancestor[next_node][0] = curr_node
+            level[next_node] = level[curr_node] + 1
+        return True
+
+    def _collect_source_nodes(graph: Graph) -> list:
+        S = []
+        in_degree = {u: 0 for u in graph.vertices}
+        for u in graph.vertices:
+            for v in graph.neighbors(u):
+                in_degree[v.name] += 1
+        for u in in_degree:
+            if in_degree[u] == 0:
+                S.append(u)
+        return list(S)
+
+    source = _collect_source_nodes(graph)[0]
+
+    depth_first_search(graph, source, precompute, ancestor, level)
+    for pow in range(1, int(log_value) + 1):
+        for vertex in graph.vertices:
+            if(ancestor[vertex][pow-1] != ""):
+                ancestor[vertex][pow] = ancestor[ancestor[vertex][pow - 1]][pow - 1]
+
+    if level[vertex1] > level[vertex2]:
+        vertex1, vertex2 = vertex2, vertex1
+
+    difference = level[vertex2] - level[vertex1]
+    while(difference > 0):
+        pow_of_two =int(math.log2(difference))
+        vertex2 = ancestor[vertex2][pow_of_two]
+        difference =- (1 << pow_of_two)
+    if vertex1 == vertex2:
+        return vertex1
+
+    for pow in range(int(log_value), -1, -1):
+        if ancestor[vertex1][pow] != "" and (ancestor[vertex1][pow] != ancestor[vertex2][pow]):
+            vertex1 = ancestor[vertex1][pow]
+            vertex2 = ancestor[vertex2][pow]
+    return ancestor[vertex1][0]

pydatastructs/graphs/tests/test_algorithms.py

@@ -1,8 +1,11 @@
+from math import exp
+from pydatastructs.linear_data_structures.algorithms import lower_bound
+from pydatastructs.graphs.algorithms import lowest_common_ancestor
 from pydatastructs import (breadth_first_search, Graph,
 breadth_first_search_parallel, minimum_spanning_tree,
 minimum_spanning_tree_parallel, strongly_connected_components,
 depth_first_search, shortest_paths, topological_sort,
-topological_sort_parallel)
+topological_sort_parallel, lowest_common_ancestor)
 from pydatastructs.utils.raises_util import raises
 
 def test_breadth_first_search():
@@ -369,3 +372,56 @@ def _test_topological_sort(func, ds, algorithm, threads=None):
 
     _test_topological_sort(topological_sort, "List", "kahn")
     _test_topological_sort(topological_sort_parallel, "List", "kahn", 3)
+
+def test_lowest_common_ancestor():
+    def _test_lowest_common_ancestor(ds):
+        import pydatastructs.utils.misc_util as utils
+        GraphNode = getattr(utils, "Adjacency" + ds + "GraphNode")
+
+        V1 = GraphNode(0)
+        V2 = GraphNode(1)
+        V3 = GraphNode(2)
+        V4 = GraphNode(3)
+        V5 = GraphNode(4)
+        V6 = GraphNode(5)
+        V7 = GraphNode(6)
+        V8 = GraphNode(7)
+
+        G1 = Graph(V1, V2, V3, V4, V5, V6, V7)
+
+        edges = [
+            (V1.name, V2.name),
+            (V1.name, V3.name),
+            (V3.name, V4.name),
+            (V3.name, V5.name),
+            (V5.name, V6.name),
+            (V5.name, V7.name),
+            (V2.name, V8.name)
+        ]
+
+        for edge in edges:
+            G1.add_edge(*edge)
+
+        lca = lowest_common_ancestor(G1, V6.name, V7.name)
+        expected_result = V5.name
+        assert(lca == expected_result)
+
+        lca2 = lowest_common_ancestor(G1, V4.name, V7.name)
+        expected_result = V3.name
+        assert(lca2 == expected_result)
+
+        lca3 = lowest_common_ancestor(G1, V7.name, V2.name)
+        expected_result = V1.name
+        assert(lca3 == expected_result)
+
+        lca4 = lowest_common_ancestor(G1, V1.name, V6.name)
+        expected_result = V1.name
+        assert(lca4 == expected_result)
+
+        lca5 = lowest_common_ancestor(G1, V3.name, V7.name)
+        expected_result = V3.name
+        assert(lca5 == expected_result)
+
+        lca6 = lowest_common_ancestor(G1, V7.name, V8.name)
+        expected_result = V1.name
+        assert(lca6 == expected_result)