LCA : lowest common ancestor

tree_node_type *LowestCommonAncestor( tree_node_type *root , tree_node_type *p , tree_node_type *q) { tree_node_type *l , *r , *temp; if(root==NULL) { return NULL; }

if(root->left==p || root->left==q || root->right ==p || root->right ==q)
{
return root;
}
else
{
l=LowestCommonAncestor(root->left , p , q);
r=LowestCommonAncestor(root->right , p, q);

if(l!=NULL && r!=NULL)
{
return root;
}
else
{
temp = (l!=NULL)?l:r;
return temp;
}
}
}
====================================================

Good and easy solution

Algorithm:
The main idea of the solution is — While traversing Binary Search Tree from top to bottom, the first node n we encounter with value between n1 and n2, i.e., n1 < n < n2 is the Lowest or Least Common Ancestor(LCA) of n1 and n2 (where n1 < n2). So just traverse the BST in pre-order, if you find a node with value in between n1 and n2 then n is the LCA, if it's value is greater than both n1 and n2 then our LCA lies on left side of the node, if it's value is smaller than both n1 and n2 then LCA lies on right side.

Implementation:

#include
#include

/* A binary tree node has data, pointer to left child
and a pointer to right child */
struct node
{
int data;
struct node* left;
struct node* right;
};

struct node* newNode(int );

/* Function to find least comman ancestor of n1 and n2 */
int leastCommanAncestor(struct node* root, int n1, int n2)
{
/* If we have reached a leaf node then LCA doesn't exist
If root->data is equal to any of the inputs then input is
not valid. For example 20, 22 in the given figure */
if(root == NULL || root->data == n1 || root->data == n2)
return -1;

/* If any of the input nodes is child of the current node
we have reached the LCA. For example, in the above figure
if we want to calculate LCA of 12 and 14, recursion should
terminate when we reach 8*/
if((root->right != NULL) &&
(root->right->data == n1 || root->right->data == n2))
return root->data;
if((root->left != NULL) &&
(root->left->data == n1 || root->left->data == n2))
return root->data;

if(root->data > n1 && root->data < n2)
return root->data;
if(root->data > n1 && root->data > n2)
return leastCommanAncestor(root->left, n1, n2);
if(root->data < n1 && root->data < n2)
return leastCommanAncestor(root->right, n1, n2);
}

/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
struct node* newNode(int data)
{
struct node* node = (struct node*)
malloc(sizeof(struct node));
node->data = data;
node->left = NULL;
node->right = NULL;

return(node);
}

====================================================
http://goursaha.freeoda.com/DataStructure/LowestCommonAncestor.html

Find Lowest Common Ancestor in Binary Tree

Question:-You have a Binary Tree and Two node p , q.
You have to find the first common parent of p and q.


tree_node_type *LowestCommonAncestor(
tree_node_type *root , tree_node_type *p , tree_node_type *q)
{
tree_node_type *l , *r , *temp;
if(root==NULL)
{
return NULL;
}

if(root->left==p || root->left==q || root->right ==p || root->right ==q)
{
return root;
}
else
{
l=LowestCommonAncestor(root->left , p , q);
r=LowestCommonAncestor(root->right , p, q);

if(l!=NULL && r!=NULL)
{
return root;
}
else
{
temp = (l!=NULL)?l:r;
return temp;
}
}
}