Added LCA algorithms (#88)

Two algorithms for finding lowest common ancestor have been added.

pydatastructs/trees/binary_trees.py

@@ -415,6 +415,143 @@ def rank(self, x):
             walk = p
         return r
 
+    def _simple_path(self, key, root):
+        """
+        Utility funtion to find the simple path between root and node.
+
+        Parameter
+        =========
+
+        key: Node.key
+            Key of the node to be searched
+
+        Returns
+        =======
+
+        path: list
+        """
+
+        stack = Stack()
+        stack.push(root)
+        path = []
+        node_idx = -1
+
+        while not stack.is_empty:
+            node = stack.pop()
+            if self.tree[node].key == key:
+                node_idx = node
+                break
+            if self.tree[node].left:
+                stack.push(self.tree[node].left)
+            if self.tree[node].right:
+                stack.push(self.tree[node].right)
+
+        if node_idx == -1:
+            return path
+
+        while node_idx != 0:
+            path.append(node_idx)
+            node_idx = self.tree[node_idx].parent
+        path.append(0)
+        path.reverse()
+
+        return path
+
+    def _lca_1(self, j, k):
+        root = self.root_idx
+        path1 = self._simple_path(j, root)
+        path2 = self._simple_path(k, root)
+        if not path1 or not path2:
+            raise ValueError("One of two path doesn't exists. See %s, %s"
+                             %(path1, path2))
+
+        n, m = len(path1), len(path2)
+        i = j = 0
+        while i < n and j < m:
+            if path1[i] != path2[j]:
+                return self.tree[path1[i - 1]].key
+            i += 1
+            j += 1
+        if path1 < path2:
+            return self.tree[path1[-1]].key
+        return self.tree[path2[-1]].key
+
+    def _lca_2(self, j, k):
+        curr_root = self.root_idx
+        u, v = self.search(j), self.search(k)
+        if (u is None) or (v is None):
+            raise ValueError("One of the nodes with key %s "
+                             "or %s doesn't exits"%(j, k))
+        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:
+                if curr_root is None:
+                    return None
+                return self.tree[curr_root].key
+
+            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)
+
+        if curr_root is None:
+            return curr_root
+        return self.tree[curr_root].key
+
+    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
+        =======
+
+        Node.key
+            The key of the lowest common ancestor in the tree.
+            if both the nodes are present in the tree.
+
+        References
+        ==========
+
+        .. [1] https://en.wikipedia.org/wiki/Lowest_common_ancestor
+
+        .. [2] https://pdfs.semanticscholar.org/e75b/386cc554214aa0ebd6bd6dbdd0e490da3739.pdf
+
+        """
+        return getattr(self, "_lca_"+str(algorithm))(j, k)
+
 class AVLTree(BinarySearchTree):
     """
     Represents AVL trees.

pydatastructs/trees/tests/test_binary_trees.py

@@ -54,7 +54,38 @@ def test_BinarySearchTree():
     assert b.delete(-10) is True
     assert b.delete(-3) is True
     assert b.delete(-13) is None
-    raises(ValueError, lambda: BST(root_data=6))
+    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.lowest_common_ancestor(80, 55, 2) == 70
+    assert bl.lowest_common_ancestor(60, 70, 2) == 70
+    assert bl.lowest_common_ancestor(18, 18, 2) == 18
+    assert bl.lowest_common_ancestor(40, 90, 2) == 50
+
+    assert bl.lowest_common_ancestor(18, 10, 2) == 15
+    assert bl.lowest_common_ancestor(55, 100, 2) == 90
+    assert bl.lowest_common_ancestor(16, 80, 2) == 50
+    assert bl.lowest_common_ancestor(30, 55, 2) == 50
+
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(60, 200, 2))
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(200, 60, 2))
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(-3, 4, 2))
+
+    assert bl.lowest_common_ancestor(80, 55, 1) == 70
+    assert bl.lowest_common_ancestor(60, 70, 1) == 70
+    assert bl.lowest_common_ancestor(18, 18, 1) == 18
+    assert bl.lowest_common_ancestor(40, 90, 1) == 50
+
+    assert bl.lowest_common_ancestor(18, 10, 1) == 15
+    assert bl.lowest_common_ancestor(55, 100, 1) == 90
+    assert bl.lowest_common_ancestor(16, 80, 1) == 50
+    assert bl.lowest_common_ancestor(30, 55, 1) == 50
+
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(60, 200, 1))
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(200, 60, 1))
+    assert raises(ValueError, lambda: bl.lowest_common_ancestor(-3, 4, 1))
 
 def test_BinaryTreeTraversal():
     BST = BinarySearchTree