# Find least common ancestor (lca) of 2 nodes in a binary search tree

### Write a program to find least common ancestor (lca) of 2 nodes in a binary search tree

The approach:-

1. Starting from the root node.
2. Check if the node key is between the two provided keys. If so, the current node is the least common ancestor.
3. If the two provided keys are greater than the current node then recursively search the right sub-tree.
4. If the two provided keys are less than the current node then recursively search the left sub-tree.

#### C++ program to find least common ancestor (lca) of 2 nodes in a binary search tree

`#include <iostream>#include <cstdlib>using namespace std;// Node classclass Node {public:Node() { mData = -1; mParent = NULL; mLeft = NULL; mRight = NULL; }~Node() {}int data() { return mData; }void setData(int data) { mData = data; }Node* left() { return mLeft; }void setLeft(Node* left) { mLeft = left; }Node* right() { return mRight; }void setRight(Node* right) { mRight = right; }Node* parent() { return mParent; }void setParent(Node* parent) { mParent = parent; }private:int mData;Node* mLeft;Node* mRight;Node* mParent;};// Tree classclass Tree {public:Tree() { mRoot = NULL; }~Tree() {}Node* root() { return mRoot; }void addNode(int data);Node* lca(Node* node, int data1, int data2);private:void addNode(Node* node, int data);private:Node* mRoot;};void Tree::addNode(int data) {if ( mRoot == NULL ) {Node* tmp = new Node();tmp->setData(data);mRoot = tmp;}else {addNode(mRoot, data);}}void Tree::addNode(Node* node, int data) {if ( data <= node->data() ) {if ( node->left() != NULL )addNode(node->left(), data);else {Node* tmp = new Node();tmp->setData(data);tmp->setParent(node);node->setLeft(tmp);}}else {if ( node->right() != NULL )addNode(node->right(), data);else {Node* tmp = new Node();tmp->setData(data);tmp->setParent(node);node->setRight(tmp);}}}Node* Tree::lca(Node* node, int data1, int data2) {if ( node ) {int data = node->data();if ( data1 < data && data2 > data )return node;else if ( data1 > data && data2 > data )return lca(node->right(), data1, data2);elsereturn lca(node->left(), data1, data2);}return NULL;}// Test programint main() {Tree* t = new Tree();t->addNode(500);t->addNode(300);t->addNode(600);t->addNode(550);t->addNode(700);t->addNode(750);t->addNode(200);t->addNode(150);t->addNode(250);t->addNode(350);t->addNode(800);cout << t->lca(t->root(), 150, 350)->data() << endl;delete t;}`

Output:-

`300`