Complete each of the functions below in C language.

The text is below for reference:

// lab7-q2.h

// Cannot modify this file

typedef struct ds {

int size; /* size of disjoint set */

int *parent; /* parent of each element */

int *tree_size; /* size of a tree in the disjoint set */

} DS;

/* Init a disjoint set with a given size #1 #2 */

/* All node should point to itself */

DS* ds_init(int size);

/* Find the root of node x #3 */

/* Path compression is needed */

/* Return the root of node x */

int ds_find_set(DS *S, int x);

/* Check if x and y belong to the same set #4 */

/* Return 1 if they are belong to the same set */

/* Return 0 if they are not belong to the same set */

int ds_same_set(DS* S, int x, int y);

/* Union the set containing x and the set containing y #5 #6 */

/* Put the set containing y as the subtree of the set of containing x */

/* If both sets have the same set, put set containing y as the subtree of set containing x */

/* You need to update tree_size */

void ds_union(DS *S, int x, int y);

/* Union the set containing x and the set containing y #7 #8 */

/* Put the smaller set as the subtree of the larger set */

/* Remember to update tree_size */

void ds_union_by_size(DS *S, int x, int y);

/* Free the disjoint set */

/* Return NULL pointer */

DS *ds_free(DS *S);

You are going to implement the disjoint set abstract data type using forest implementation. The header file "lab7-92.h" and the description of the functions are as follows. Your program should not contain main().Name your program as lab7-92.c". // lab7-92.h // Cannot modify this file typedef struct ds { int size; /* size of disjoint set */ int *parent; 1* parent of each element */ int *tree_size; /* size of a tree in the disjoint set */ } DS; /* Init a disjoint set with a given size #1 #2 */ /* All node should point to itself */ DS* ds_init(int size); /* Find the root of node * #3 */ /* Path compression is needed */ /* Return the root of node x */ int ds_find_set(DS *5, int x); 1* Check if x and y belong to the same set #4 */ /* Return 1 if they are belong to the same set */ /* Return 0 if they are not belong to the same set */ int ds_same_set(DS* S, int x, int y); /* Union the set containing x and the set containing y #5 #6 */ /* Put the set containing y as the subtree of the set of containing x */ 1* If both sets have the same set, put set containing y as the subtree of set containing x */ /* You need to update tree_size */ void ds_union(DS *s, int x, int y); 1* Union the set containing x and the set containing y #7 #8 */ 1* Put the smaller set as the subtree of the larger set */ 1* Remember to update tree_size */ void ds_union_by_size(DS *5, int x, int y); /* Free the disjoint set */ /* Return NULL pointer */ DS *ds_free (DS *5)