Here is source code of the C Program to Find the Common Ancestor and Print the Path. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

/*
* C Program to Find the Common Ancestor and Print the Path
*
* 10
* / \
* 7 15
* / \ / \
* 6 8 12 18
* / \
* 5 9
* (Given Binary tree)
*/
#include <stdio.h>
#include <stdlib.h>

struct btnode
{
int value;
struct btnode *l;
struct btnode *r;
};

typedef struct btnode N;

N* new(int);
int count;

void create();
void preorder(N *t);
void ancestor(N *t);
int search(N *t, int, int);
void path(int, int, int);

N *root = NULL;

void main()
{
int choice;

create();
while (1)
{
printf("Enter the choice\n");
printf("1-Display : 2-path : 3-Exit\n");
scanf("%d", &choice);
switch (choice)
{
case 1:
printf("preorder display of tree elements\n");
preorder(root);
printf("\n");
break;
case 2:
ancestor(root);
break;
case 3:
exit(0);
default:
printf("Enter the right choice\n");
}
}
}

/* creating temporary node */
N* new(int data)
{
N* temp = (N*)malloc(sizeof(N));
temp->value = data;
temp->l = NULL;
temp->r = NULL;

return(temp);
}

/* Creating the binary search tree */
void create()
{
root = new(10);
root->l = new(7);
root->r = new(15);
root->l->l = new(6);
root->l->r = new(8);
root->r->l = new(12);
root->r->r = new(18);
root->r->r->r = new(20);
root->l->l->l = new(5);
root->l->r->r = new(9);
}

/* To display the preorder traversal of the tree */
void preorder(N *temp)
{
printf("%d->", temp->value);
if (temp->l != NULL)
preorder(temp->l);
if (temp->r != NULL)
preorder(temp->r);
}

/* to find common ancestor for given nodes */
void ancestor(N *temp)
{
int a, b, anc = 0;
count = 0;

printf("enter two node values to find common ancestor\n");
scanf("%d", &a);
scanf("%d", &b);
count = search(root, a, b);
if (count == 2)
{
while (temp->value != a && temp->value != b)
{
if ((temp->value > a)&&(temp->value > b))
{
anc = temp->value;
temp = temp->l;
}
else if ((temp->value < a)&&(temp->value < b))
{
anc = temp->value;
temp = temp->r;
}
else if ((temp->value > a)&&(temp->value < b))
{
anc = temp->value;
printf("anc = %d\n", anc);
break;
}
else if ((temp->value < a)&&(temp->value > b))
{
anc = temp->value;
temp = temp->r;
}
else
{
printf("common ancestor = %d\n", anc);
break;
}
}
path(anc, a, b);
}
else
printf("enter correct node values & do not enter root value\n");
}

/* to find whether given nodes are present in tree or not */
int search(N *temp, int a, int b)
{
if ((temp->value == a ||temp->value == b)&& (root->value != a&&root->value != b))
{
count++;
}
if (temp->l != NULL)
search(temp->l, a, b);
if (temp->r != NULL)
search(temp->r, a, b);
return count;
}

/* to print the path ancestor to given nodes */
void path(int anc, int c, int b)
{
N *temp = NULL;
int i = 0, a[2];
a[0] = c;
a[1] = b;

for (;i < 2;i++)
{
if (anc == root->value) // If ancestor is root
{
temp = root;
while (1)
{
printf("%d", temp->value);
if (a[i] < temp->value)
temp = temp->l;
else if (a[i] > temp->value)
temp = temp->r;
else
{
if (a[i] == temp->value)
{
break;
}
}
printf("->");
}
printf("\n");
}
else if (anc < root->value) //If ancestor is less than the root value
{
temp = root;
while (temp != NULL)
{
if (anc < temp->value)
temp = temp->l;
else if (anc > temp->value)
temp = temp->r;
else
{
while (1)
{
if (a[i] < temp->value)
{
printf("%d->", temp->value);
temp = temp->l;
}
else if (a[i] > temp->value)
{
printf("%d->", temp->value);
temp = temp->r;
}
else
{
printf("%d\n", temp->value);
break;
}
}
}
}
}
else //If ancestor greater than the root value
{
temp = root;
while (temp != NULL)
{
if (anc > temp->value)
temp = temp->r;
else if (anc < temp->value)
temp = temp->l;
else
{
while (1)
{
if (a[i] < temp->value)
{
printf("%d->", temp->value);
temp = temp->l;
}
else if (a[i] > temp->value)
{
printf("%d->", temp->value);
temp = temp->r;
}
else
{
printf("%d\n", temp->value);
break;
}
}
}
}
}
}
}



$ cc tree33.c
$ a.out
Enter the choice
1-Display : 2-path : 3-Exit
1
preorder display of tree elements
10->7->6->5->8->9->15->12->18->20
Enter the choice
1-Display : 2-path : 3-Exit
2
enter two node values to find common ancestor
6
8
anc = 7
7->6
7->8
Enter the choice
1-Display : 2-path : 3-Exit
2
enter two node values to find common ancestor
7
20
anc = 10
10->7
10->15->18->20
Enter the choice
1-Display : 2-path : 3-Exit
2
enter two node values to find common ancestor
12
20
anc = 15
15->12
15->18->20
Enter the choice
1-Display : 2-path : 3-Exit
2
enter two node values to find common ancestor
15
20
10->15
10->15->18->20
Enter the choice
1-Display : 2-path : 3-Exit
3