This is a C Program to find the Lowest Common Ancestor of a given tree.
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.
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 :
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.
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.
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.
/*
* C Program to Find Lowest Common Ancestor in a Binary Search Tree
*/
#include <stdio.h>
#include<stdlib.h>
struct node
{
int data;
struct node *left, *right;
};
/*
* Function to find the lowest common ancestor
*/
struct node *lca(struct node *root, int node_1, int node_2)
{
if (root != NULL)
{
if (root->data > node_1 && root->data > node_2)
{
return lca(root->left, node_1, node_2);
}
if (root->data < node_1 && root->data < node_2)
{
return lca(root->right, node_1, node_2);
}
return root;
}
}
struct node *newNode(int data)
{
struct node* p = (struct node*)malloc(sizeof(struct node));
p->data = data;
p->left = p->right = NULL;
return(p);
}
int main()
{
struct node *root = newNode(20);
root->left = newNode(8);
root->right = newNode(22);
root->left->left = newNode(4);
root->left->right = newNode(12);
root->left->right->left = newNode(10);
root->left->right->right = newNode(14);
/* Sample tree
* 20
* / \
* 8 22
* / \
* 4 12
* / \
* 10 14
*/
int node_1 = 10, node_2 = 14;
struct node *t = lca(root, node_1, node_2);
printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
node_1 = 14, node_2 = 8;
t = lca(root, node_1, node_2);
printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
node_1 = 10, node_2 = 22;
t = lca(root, node_1, node_2);
printf("LCA of %d and %d is %d \n", node_1, node_2, t->data);
return 0;
}
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.
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.
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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