In C language.

#include"lab5-q2.h"

#include

#include

#include

#include

#include

/* Initialize the tree with a root #1 */

/* Create an empty BTree first */

/* The root (key, value) is stored at (key[0], value[0]) */

/* If key is unused, set key = INT_MAX, value = -2100 */

void tree_init(BTree **T, int key, double value, int max_size){

// You code here

}

/* Initialize the tree with arrays #2 */

/* Create an empty BTree first */

/* n defines the number of (key,value) pairs of the array */

/* If key is unused, set key = INT_MAX, value = -2100 */

void tree_init_with_array(BTree **T, int *key, double *value, int n, int max_size){

// You code here

}

/* Initialize the empty tree with height of root #3 */

/* Based on the height, calculate the max_size */

/* Create an empty BTree with max_size */

/* If key is unused, set key = INT_MAX, value = -2100 */

void tree_init_with_height(BTree **T, int height){

// You code here

}

/* Get the index of parent #4 */

/* Return the index of the parent */

/* Return -2100 if the parent index is invalid or unused */

int tree_parent(BTree *T, int child_index){

// You code here

return 0;

}

/* Get the index of left child #5 */

/* Return the index of the left child */

/* Return -2100 if the left child index is invalid or unused */

int tree_lchild(BTree *T, int parent_index) {

// You code here

return 0;

}

/* Get the index of right child #6 */

/* Return the index of the right child */

/* Return -2100 if the right child index is invalid or unused */

int tree_rchild(BTree *T, int parent_index){

// You code here

}

/* Insert or update a node #7 */

/* If key exists in T, update the value */

/* If key not in T, insert (key, double) as left child of parent_index*/

/* If the left child cannot be inserted, then do nothing */

/* If the left child is used by other key, then do nothing */

void tree_insert_lchild(BTree *T, int parent_index, int key, double value){

// You code here

}

/* Insert or update a node #8 */

/* If key exists in T, update the value */

/* If key not in T, insert (key,double) as right child of parent_index*/

/* If the right child cannot be inserted, then do nothing */

/* If the right child is used by other key, then do nothing */

void tree_insert_rchild(BTree *T, int parent_index, int key, double value){

// You code here

}

/* Find the value based on the key in the tree T or not #9 */

/* If key in T, return the corresponding value */

/* If key not in T, return -2100.00 */

double tree_key_find(BTree *T, int key){

// You code here

return 0.;

}

/* Find the value based on the index in the tree T or not #10 */

/* If index is used, return the corresponding value */

/* If index is unused or exceeding the max_size, return -2100.00 */

double tree_index_find(BTree *T, int index){

// You code here

return 0.;

}

/* Free the tree *T, if *T is not NULL #11 */

/* Assign NULL to *T after free */

void tree_free(BTree **T){

// You code here

}

/* The print function print the tree in an output string using postorder traversal #12 */

/* The number in the bracket is key, number after bracket is value */

/* If the tree looks like */

/* (0)1.7 */

/* | \ */

/* (1)1.2 (2)1.8 */

/* | | \ */

/* (4)0 (3)2 (6)5 */

/* Then, the output string is "(4)0.00 (1)1.20 (3)2.00 (6)5.00 (2)1.80 (0)1.70 " */

/* You can assume the number of nodes is not more than 100 */

char *tree_print(BTree *T){

char *output = malloc(sizeof(char)*3000);

// You code here

return output;

}

Question 2: Binary Tree - Array Implementation (30\%) You are going to implement the binary tree abstract data type using array implementation. The header file "lab5-q2.h" and the description of the functions are as follows. Your program should not contain main(). Name your program as "lab5-q2.c