Added LCA and tests

pydatastructs/trees/binary_trees.py

@@ -415,6 +415,126 @@ def rank(self, x):
             walk = p
         return r
 
+    def _simple_path(self, key, root, path):
+        """
+        Utility funtion to find the simple path between root and node.
+        """
+        if root is None:
+            return False
+        path.append(root)
+        if self.tree[root].key == key:
+            return True
+
+        if self._simple_path(key, self.tree[root].left, path) or \
+            self._simple_path(key, self.tree[root].right, path):
+            return True
+
+        path.pop()
+        return False
+
+    def simple_path(self, key):
+        """
+        Return the intermediate nodes between root and node with given key
+
+        Parameters
+        ==========
+
+        key: Node.key
+            key of the node for which path to be found
+
+        Returns
+        =======
+
+        list
+            List of intermediate nodes.
+            Empty list if node is not present.
+
+        """
+        path = []
+        self._simple_path(key, self.root_idx, path)
+        return path
+
+    def lowest_common_ancestor(self, j, k, algorithm=1):
+
+        """
+        Computes the lowest common ancestor of two nodes.
+
+        Parameters
+        ==========
+
+        j: Node.key
+            key of first node
+        k: Node.key
+            key of second node
+        algorithm: int
+            The algorithm to be used for computing the
+            lowest common ancestor.
+            Optional, by default uses algorithm 1.
+
+            1 -> Determines the lowest common ancestor by finding
+                    the first intersection of the paths from v and w
+                    to the root.
+
+            2 -> Modifed version of the algorithm given in the
+                    following publication,
+                    D. Harel. A linear time algorithm for the
+                    lowest common ancestors problem. In 21s
+                    Annual Symposium On Foundations of
+                    Computer Science, pages 308-319, 1980.
+
+        Returns
+        =======
+
+        int
+            The index of the lowest common ancestor in the tree.
+            if both the nodes are present in the tree.
+        None
+            In all other cases.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Lowest_common_ancestor
+
+        .. [2] https://pdfs.semanticscholar.org/e75b/386cc554214aa0ebd6bd6dbdd0e490da3739.pdf
+
+        """
+        if algorithm == 1:
+            curr_root = self.root_idx
+            u, v = self.search(j), self.search(k)
+            if (u is None) or (v is None):
+                return None
+            u_left = self.comparator(self.tree[u].key, self.tree[curr_root].key)
+            v_left = self.comparator(self.tree[v].key, self.tree[curr_root].key)
+            while not (u_left ^ v_left):
+                if u_left and v_left:
+                    curr_root = self.tree[curr_root].left
+                else:
+                    curr_root = self.tree[curr_root].right
+                if curr_root == u or curr_root == v:
+                    return curr_root
+                u_left = self.comparator(self.tree[u].key, self.tree[curr_root].key)
+                v_left = self.comparator(self.tree[v].key, self.tree[curr_root].key)
+            return curr_root
+        else:
+            root = self.root_idx
+            path1 = self.simple_path(j)
+            path2 = self.simple_path(k)
+            print(path1, path2)
+            if not path1 or not path2:
+                return None
+
+            n, m = len(path1), len(path2)
+            i = j = 0
+            while i < n and j < m:
+                if path1[i] != path2[j]:
+                    return path1[i - 1]
+                i += 1
+                j += 1
+            if path1 < path2:
+                return path1[-1]
+            return path2[-1]
+
 class AVLTree(BinarySearchTree):
     """
     Represents AVL trees.

pydatastructs/trees/tests/test_binary_trees.py

@@ -54,6 +54,33 @@ def test_BinarySearchTree():
     assert b.delete(-10) is True
     assert b.delete(-3) is True
     assert b.delete(-13) is None
+    bl = BST()
+    nodes = [50, 30, 90, 70, 100, 60, 80, 55, 20, 40, 15, 10, 16, 17, 18]
+    for node in nodes:
+        bl.insert(node, node)
+    assert bl.tree[bl.lowest_common_ancestor(80, 55, 2)].key == 70
+    assert bl.tree[bl.lowest_common_ancestor(60, 70, 2)].key == 70
+    assert bl.tree[bl.lowest_common_ancestor(18, 18, 2)].key == 18
+    assert bl.tree[bl.lowest_common_ancestor(40, 90, 2)].key == 50
+    assert bl.lowest_common_ancestor(60, 200, 2) is None
+    assert bl.lowest_common_ancestor(200, 60, 2) is None
+    assert bl.tree[bl.lowest_common_ancestor(18, 10, 2)].key == 15
+    assert bl.tree[bl.lowest_common_ancestor(55, 100, 2)].key == 90
+    assert bl.tree[bl.lowest_common_ancestor(16, 80, 2)].key == 50
+    assert bl.lowest_common_ancestor(-3, 4, 2) is None
+    assert bl.tree[bl.lowest_common_ancestor(30, 55, 2)].key == 50
+
+    assert bl.tree[bl.lowest_common_ancestor(80, 55, 1)].key == 70
+    assert bl.tree[bl.lowest_common_ancestor(60, 70, 1)].key == 70
+    assert bl.lowest_common_ancestor(-3, 4, 1) is None
+    assert bl.tree[bl.lowest_common_ancestor(18, 18, 1)].key == 18
+    assert bl.tree[bl.lowest_common_ancestor(40, 90, 1)].key == 50
+    assert bl.lowest_common_ancestor(60, 200, 1) is None
+    assert bl.lowest_common_ancestor(200, 60, 1) is None
+    assert bl.tree[bl.lowest_common_ancestor(18, 10, 1)].key == 15
+    assert bl.tree[bl.lowest_common_ancestor(55, 100, 1)].key == 90
+    assert bl.tree[bl.lowest_common_ancestor(16, 80, 1)].key == 50
+    assert bl.tree[bl.lowest_common_ancestor(30, 55, 1)].key == 50
     raises(ValueError, lambda: BST(root_data=6))
 
 def test_BinaryTreeTraversal():