C Program to Find the Lowest Common Ancestor of a Binary Search Tree

This is a C Program to find the Lowest Common Ancestor of a given tree.

Problem Description

We will be given a Binary Tree and we have to write a C program to find out the Lowest Common Ancestor of the two nodes of same tree taken as input from user.
Lowest Common Ancestor: In a given tree, the lowest common ancestor of two nodes node_1 and node_2 will be a node X such that node X will be the lowest node who has node_1 and node_2 as its descendants or children.

Expected Input and Output

Case 1. When both the nodes lie on same side of the root node and at same level:
For example :

If the input tree is 
             20
           /    \
          8     22
         /  \
        4   12
           /  \
          10  14
and the nodes are node_1 = 10, node_2 = 14,
then Output will be LCA = 12.

Case 2. When one of the nodes itself is a lowest common ancestor:
For example :

If the input tree is 
             20
           /    \
          8     22
         /  \
        4   12
           /  \
          10  14
and the nodes are node_1 = 14, node_2 = 8,
then Output will be LCA = 8.

Case 3. When the two nodes lie on different sides of root node:
For example :

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If the input tree is 
             20
           /    \
          8     22
         /  \
        4   12
           /  \
          10  14
and the nodes are node_1 = 10, node_2 = 22,
then Output will be LCA = 20.
Problem Solution

1. First we need to look for node_1 and node_2 in given tree. If they lie on different sides of root node, then the root itself will be the LCA of node_1 and node_2.
2. If root is greater than node_1 and node_2 then their LCA will lie on left subtree.
3. If root is less than node_1 and node_2, their LCA will lie on right subtree.

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Program/Source Code

Here is source code of the C Program for finding the lowest common ancestor of of nodes in a given binary search tree. The program is successfully compiled and tested using Codeblocks gnu/gcc compiler on windows 10. The program output is also shown below.

  1. /*
  2.  * C Program to Find Lowest Common Ancestor in a Binary Search Tree
  3.  */
  4. #include <stdio.h>
  5. #include<stdlib.h>
  6. struct node
  7. {
  8.     int data;
  9.     struct node *left, *right;
  10. };
  11. /*
  12.  * Function to find the lowest common ancestor
  13.  */
  14. struct node *lca(struct node *root, int node_1, int node_2)
  15. {
  16.     if (root != NULL)
  17.     {
  18.         if (root->data > node_1 && root->data > node_2)
  19.         {
  20.             return lca(root->left, node_1, node_2);
  21.         }
  22.         if (root->data < node_1 && root->data < node_2)
  23.         {
  24.             return lca(root->right, node_1, node_2);
  25.         }
  26.         return root;
  27.     }
  28. }
  29. struct node *newNode(int data)
  30. {
  31.     struct node* p = (struct node*)malloc(sizeof(struct node));
  32.     p->data = data;
  33.     p->left = p->right = NULL;
  34.     return(p); 
  35. }
  36. int main()
  37. {
  38.     struct node *root = newNode(20);
  39.     root->left = newNode(8);
  40.     root->right = newNode(22);
  41.     root->left->left = newNode(4);
  42.     root->left->right = newNode(12);
  43.     root->left->right->left = newNode(10);
  44.     root->left->right->right = newNode(14);
  45.     /* Sample tree
  46.      *        20
  47.      *      /    \
  48.      *     8     22
  49.      *    /  \
  50.      *   4   12
  51.      *      /  \
  52.      *     10  14
  53.      */
  54.     int node_1 = 10, node_2 = 14;
  55.     struct node *t = lca(root, node_1, node_2);
  56.     printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
  57.     node_1 = 14, node_2 = 8;
  58.     t = lca(root, node_1, node_2);
  59.     printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
  60.     node_1 = 10, node_2 = 22;
  61.     t = lca(root, node_1, node_2);
  62.     printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
  63.     return 0;
  64. }
Program Explanation

1. Here in this program we have written a function to find out the lowest common ancestor of two nodes in a given tree.
2. Function lca(root,node_1,node_2) takes in three parameters which are root node of the tree, node_1 and node_2 are the two nodes whose LCA is to be determined. Function LCA returns a node therefore it is of (struct node *) type.

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lca(root, node_1, node_2)
1. This function returns the lowest node who has node_1 and node_2 as its descendants or children.
2. If node_1 and node_2 lie on different sides of root i.e. (node_1 > root->data && node_2 < root->data) or vice versa, then the lca will be the root node itself.
3. In other cases such as when both node_1 and node_2 lie on left subtree i.e. (node_1 < root->data && node_2 < root->data), then the lca also lies on left subtree.
4. So as a result we recursively call the function by passing parameters as root->left, node_1 and node_2 now. By passing root->left as a parameter we go deeper and deeper inside the left subtree and return the smallest node which has both the nodes node_1 and node_2 as it’s children.
5. Similarly we do it for the right subtree by checking just one if condition and passing root->right as a parameter.

Runtime Test Cases
LCA of 10 and 14 is 12
LCA of 14 and 8 is 8
LCA of 10 and 22 is 20

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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