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Tree.c
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Tree.c
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// Timothy Stephenson June 14th 2021
// Implementation for binary Tree
// all keys must be reprsented by a void pointer, with inputed compare function upon initialization of tree
// all values must be void pointers
// max number of elements in a given TREE is the max value of a unsigned int (4,294,967,295)
//Will use AVL Rebalancing to keep the Binary Search Tree balanced
// the term height refers to the the longest path from a given node to a empty node
// ie a "NULL" node has a hieght of 0, a leaf node has a height of 1, and the height of any given node is
// the max height of its two children + 1
#include <stdlib.h>
#include <assert.h>
#include <stdbool.h>
#include "Tree.h"
typedef struct node node;
struct node{
unsigned int size;
unsigned short int height;
void *key;
void *val;
node *l;
node *r;
};
void node_Free(node *n , void (*free_key) (void*) , void (*free_val) (void*) ) {
if(n!=NULL){
node_Free(n->l , free_key , free_val);
node_Free(n->r , free_key , free_val);
(*free_key)(n->key);
(*free_val)(n->val);
free(n);
}
return;
}
node *node_Leaf(void *k , void *v ){
node *n = (node*) malloc( sizeof(node) );
n->size = 1;
n->height = 1;
n->key = k;
n->val = v;
n->l = NULL;
n->r = NULL;
return n;
}
unsigned int node_Size(node *n){
if (n==NULL) return 0;
return n->size;
}
unsigned short int node_Height(node *n){
if(n==NULL) return 0;
return n->height;
}
// assuming childrens nodes sizes are correct, fix the size of node *n
void node_FixSize(node *n){
n->size = 1 + node_Size(n->l) + node_Size(n->r);
return;
}
//assuming childrens heights are correct, fix the height of node *n
void node_FixHeight(node *n){
unsigned short int left_height = node_Height(n->l) , right_height = node_Height(n->r) ;
// left child's node has a greater height:
if(left_height > right_height) n->height = left_height + 1;
// right child's node has a greater or equal height:
else n->height = right_height + 1;
return;
}
//postive for left-heavy , negative for right-heavy
short int node_HeightDiffernce(node *n){
assert(n!=NULL);
return node_Height(n->l) - node_Height(n->r);
}
void node_FillKeys(node *n, void **key_list){
if(n==NULL) return;
// element itself
unsigned items_leftward = node_Size(n->l);
key_list[items_leftward] = n->key;
// fill left
node_FillKeys(n->l,key_list);
// fill right
node_FillKeys(n->r, key_list + (items_leftward+1) );
return;
}
void *node_Search(node *n, void *k, int (*cmp) (void*,void*) ){
if(n==NULL) return NULL;
int i = (*cmp)(k,n->key);
//Equal
if(i==0) return n->val;
// Less
if(i<0) return node_Search(n->l , k ,cmp);
// Greater (i>0)
return node_Search(n->r , k, cmp);
}
// to call function, call node_AverageDepth(n , n->size, 1)
double node_AverageDepth(node *n, unsigned int TotalSize, unsigned short int depth){
if(n==NULL) return 0;
return ( (double) depth / TotalSize ) + node_AverageDepth(n->l,TotalSize,depth+1) + node_AverageDepth(n->r,TotalSize,depth+1) ;
}
void node_Assign(node *n , void *k , void *v, int (*cmp) (void*,void*), void (*free_key) (void*) , void (*free_val) (void*) ){
assert(n!=NULL);
int i = (*cmp)(k,n->key);
// found the key value pair
if(i==0){
(*free_key)(n->key);
(*free_val)(n->val);
n->key = k;
n->val = v;
}
// Less tthan
if(i<0) node_Assign(n->l , k , v, cmp, free_key, free_val);
// greater than
if(i>0) node_Assign(n->r , k , v, cmp, free_key, free_val);
return;
}
//precondition n->r != NULL
node* node_LeftRotate(node *n){
assert(n->r != NULL);
node *n_right = n->r;
n->r = n_right->l ;
node_FixSize(n);
node_FixHeight(n);
n_right->l = n;
node_FixSize(n_right);
node_FixHeight(n_right);
return n_right;
}
//precondition n->l != NULL
node* node_RightRotate(node *n){
assert(n->l != NULL);
node *n_left = n->l;
n->l = n_left->r ;
node_FixSize(n);
node_FixHeight(n);
n_left->r = n;
node_FixSize(n_left);
node_FixHeight(n_left);
return n_left;
}
node* node_ChildDirection(node *n, bool go_right){ assert(n!=NULL); if(go_right) return(n->r); return(n->l); }
//allocate space for min_max_child to store one node pointer, and free it afterwards
//precondition:
// the mix or max will not be the head of the intial function call
node *node_RemoveMinMax(node *n, bool go_right, void **to_fix, node **min_max_child){
assert(n!=NULL);
if(go_right && n->r == NULL){
*(min_max_child) = n->l;
n->l = NULL;
node_FixSize(n);
node_FixHeight(n);
return n;
}
if(!go_right && n->l == NULL){
*(min_max_child) = n->r;
n->r = NULL;
node_FixSize(n);
node_FixHeight(n);
return n;
}
node *min_max = node_RemoveMinMax(node_ChildDirection(n,go_right) , go_right , to_fix , min_max_child);
//the child of n is the min/max
if(min_max == node_ChildDirection(n,go_right) ){
if(go_right) n->r = *(min_max_child);
else n->l = *(min_max_child);
*(to_fix) = n->key;
}
node_FixSize(n);
node_FixHeight(n);
return min_max;
}
//will merge two nodes who's heights differ by no more than +=1 (ie two previous children of a now deleted parent)
// the outputed node's height out will be <= 1 + max( node_Height(left) , node_Height(right) )
//Precondition:
// ( left !=NULL || right != NULL ) aka do not call merge on two empty nodes, as there is nothing for to_fix to be pointed at
node* node_Merge(node *left , node *right, void **to_fix){
assert( left !=NULL || right != NULL );
if (left==NULL){
*(to_fix) = right->key;
return right;
}
if (right==NULL){
*(to_fix) = left->key;
return left;
}
if (left->r ==NULL){
left->r = right;
node_FixSize(left);
node_FixHeight(left);
*(to_fix) = left->key;
return left;
}
if (right->l==NULL){
right->l = left;
node_FixSize(right);
node_FixHeight(right);
*(to_fix) = right->key;
return right;
}
node *new_root;
node **temp = (node**) malloc(1 * sizeof(node*) );
bool random_bool = (bool) rand()%2 ;
if(left->height > right->height || (left->height==right->height && random_bool) ){
new_root = node_RemoveMinMax(left , true , to_fix , temp );
}
else{
new_root = node_RemoveMinMax(right , false , to_fix , temp );
}
free(temp);
new_root->l = left;
new_root->r = right;
node_FixSize(new_root);
node_FixHeight(new_root);
return new_root;
}
//prconditions:
// a node with void *k exists in the tree with n at the root
// the node that the inputted void *k corresponds too and all of its parents, may be unbalanced by at most one
// (either doubley left/right heavy, never tripley left/right heavy or more)
// all other nodes are balanced
node* node_RebalanceDirectionAVL(node *n, void *k, int (*cmp) (void*,void*) ){
if(n==NULL) return NULL; //maybe assert(n!=NULL)
int i = (*cmp)(k,n->key);
// k is to the left
if(i<0) n->l = node_RebalanceDirectionAVL(n->l , k, cmp);
// k is to the right
if(i>0) n->r = node_RebalanceDirectionAVL(n->r , k, cmp);
node_FixHeight(n);
if( node_HeightDiffernce(n) < -1 || 1 < node_HeightDiffernce(n) ){
assert( node_HeightDiffernce(n) == -2 || node_HeightDiffernce(n) == 2 ); //for testing, should only be possible to get messed up by one height differnce
//doubly left heavy:
if(node_HeightDiffernce(n)==2){
//n->l is balanced or left heavy:
if( 0 <= node_HeightDiffernce(n->l) ) return node_RightRotate(n);
//n->l is right heavy:
else{
n->l = node_LeftRotate(n->l);
node_FixHeight(n);
return node_RightRotate(n);
}
}
//doubly right heavy:
if(node_HeightDiffernce(n)==-2){
//n->r is balanced or right heavy:
if( node_HeightDiffernce(n->r) <= 0 ) return node_LeftRotate(n);
//n->r is left heavy:
else{
n->r = node_RightRotate(n->r);
node_FixHeight(n);
return node_LeftRotate(n);
}
}
}
return n;
}
// inserts the key val pair to the node tree
// precondition: n is a valid node, void *k does not exist in the tree
void node_Insert(node *n, void *k, void *v, int (*cmp) (void*,void*) ){
assert(n!=NULL);
int i = (*cmp)(k,n->key);
// Less
if(i<0){
if(n->l==NULL) n->l = node_Leaf(k,v);
else node_Insert(n->l , k , v, cmp);
}
// greater
if(i>0){
if(n->r==NULL) n->r = node_Leaf(k,v);
else node_Insert(n->r , k , v, cmp);
}
// precondition assures i==0 is not a possiblity
node_FixSize(n);
node_FixHeight(n);
return;
}
//remove the node with the void *k from the tree
//precondition:
// node_Search(n , k) != NULL
// on the intial call on the root of the tree, n->size >= 2 (there must be a node left once the specified node is deleted)
//points the string pointer to_fix to the node to call node_RebalanceDirectionAVL on in order to maintain AVL property
// the only nodes that have potentially changed heights are "to_fix" and its parents
node *node_Remove(node *n, void *k, void **to_fix, int (*cmp) (void*,void*) , void (*free_key) (void*) , void (*free_val) (void*) ){
assert(n!=NULL);
int i = (*cmp)(k,n->key);
node *to_return = n;
//at the node to remove
if(i==0){
if(n->l==NULL && n->r==NULL) to_return = NULL;
else to_return = node_Merge(n->l,n->r , to_fix);
(*free_key)(n->key);
(*free_val)(n->val);
free(n);
}
else{
// in case n->l or n->r is a leaf of only the node we want to delete, we save its parents key as the node to starting fixing from
*(to_fix) = n->key;
if(i<0) n->l = node_Remove(n->l , k , to_fix, cmp , free_key , free_val );
if(i>0) n->r = node_Remove(n->r , k , to_fix, cmp , free_key , free_val );
node_FixSize(n);
node_FixHeight(n);
}
return to_return;
}
// precondition 0<= i < n->size
//to call from head node, give 0 as nodes_leftward : node_nth( head_node , i , 0) where i is the index of desired node
void *node_nth(node *n, unsigned i, unsigned nodes_leftward){
assert(n!=NULL);
unsigned true_nodes_leftward = nodes_leftward + node_Size(n->l);
//are at nodes where exactly i nodes are "left" of it, thus 0-indexed, it is in the i'th spot
if(i==true_nodes_leftward) return n->key;
// too many nodes leftward (past index i)
if(i<true_nodes_leftward) return node_nth(n->l , i , nodes_leftward);
//too few nodes leftward (before index i) (i>true_nodes_leftward)
return node_nth(n->r , i, true_nodes_leftward+1 );
}
unsigned node_Position( node *n , void *k , int (*cmp) (void*,void*) ){
if(n==NULL) return 0;
int i = (*cmp)(k , n->key);
// are at the given node
if (i==0) return node_Size(n->l);
//go left
if(i<0) return node_Position(n->l , k, cmp);
//go right (i>0)
return 1 + node_Size(n->l) + node_Position(n->r , k, cmp);
}
void node_ValidHelper(node*n){
if(n==NULL) return;
assert(n->size == 1 + node_Size(n->l) + node_Size(n->r) );
assert(n->key!=NULL);
assert(n->val!=NULL);
assert( node_Height(n) == node_Height(n->r) + 1 || node_Height(n) == node_Height(n->l) + 1 );
//AVL Property:
assert( -1 <= node_HeightDiffernce(n) && node_HeightDiffernce(n) <= 1 );
node_ValidHelper(n->l);
node_ValidHelper(n->r);
// for(int i = 0; i<10; i+= 1) i -= 1;
return;
}
void node_Valid(node *n, int (*cmp) (void*,void*) ){
if(n==NULL) return;
node_ValidHelper(n);
//make sure keys are in correct sorted order, and tests out some functions
void **key_list = (void**) malloc(n->size * sizeof(void*) );
node_FillKeys(n , key_list);
int i = 0;
for(i=0; i< n->size ; i+=1){
if (i!= n->size -1) assert( (*cmp)(key_list[i] , key_list[i+1]) < 0 );
assert(node_Position(n,key_list[i], cmp) == i );
assert(node_nth(n,i,0)==key_list[i]);
}
free(key_list);
return;
}
struct TREE{
node *head;
int (*cmp) (void* , void*);
void (*free_key) (void*);
void (*free_val) (void*);
};
void TREE_Valid(TREE *d){
// Goes through a O(n) validation checker, would make O(log n) function like Add and delete O(n) if they validated the tree every time
// only comment in for testing with smaller datasets
node_Valid(d->head, d->cmp);
return;
}
// returns a empty Tree
TREE* TREE_Empty( int (*cmp) (void*, void*) , void (*free_key) (void*) , void (*free_val) (void*) ){
TREE *d = (TREE*) malloc( sizeof(TREE) );
d->head = NULL;
d->cmp = cmp;
d->free_key = free_key;
d->free_val = free_val;
TREE_Valid(d);
return d;
}
// Free's a given Tree
void TREE_Free(TREE *d){
node_Free(d->head , d->free_key , d->free_val);
free(d);
return;
}
// adds a given: void *key, void *val pair,
// if the key already exists in the tree, the inputed val replaces one previously stored (frees the previously stored val)
// uses the callers key in the TREE (DO NOT FREE IT AFTER CALLING)
void TREE_Add(TREE *d , void *k , void *v){
assert(v!=NULL);
assert(k!=NULL);
// currently empty
if(d->head==NULL){
d->head = node_Leaf(k,v);
}
else{
// key does not exist already
if( node_Search(d->head ,k, d->cmp)==NULL ){
node_Insert(d->head , k , v, d->cmp);
d->head = node_RebalanceDirectionAVL(d->head , k, d->cmp);
}
//key does already exist
else{
node_Assign(d->head , k , v , d->cmp , d->free_key, d->free_val);
}
}
TREE_Valid(d);
return;
}
// returns the void pointer associated with the given void* key in the TREE if it exists, returns NULL if it doesn't
// does not free in inputted void pointer key
void* TREE_Search(TREE *d , void *k){ return node_Search(d->head , k, d->cmp); }
// removes (and frees) the key val pair associated with the inputted void *key
// does not free the callers void *key
void TREE_Remove(TREE *d , void *k ){
if(node_Search(d->head , k , d->cmp)==NULL) return;
if(node_Size(d->head)==1){
node_Free(d->head , d->free_key , d->free_val);
d->head = NULL;
}
else{
void **to_fix = (void**) malloc( 1 * sizeof(void*) );
d->head = node_Remove(d->head, k, to_fix , d->cmp , d->free_key , d->free_val );
d->head = node_RebalanceDirectionAVL(d->head , *(to_fix) , d->cmp);
free(to_fix);
}
TREE_Valid(d);
return;
}
// returns the number of elements in the given TREE
unsigned TREE_Size(TREE *d){ return node_Size(d->head); }
// returns a sorted list of the keys in the given TREE
void** TREE_KeyList(TREE *d){
if(d->head==NULL) return NULL;
void **key_list = (void**) malloc(node_Size(d->head) * sizeof(void*) );
node_FillKeys(d->head , key_list);
return key_list;
}
// gives the average of the depths of all the nodes
// the root of a tree has a depth of 1, the roots child a depth of 2, the roots grandchild a depth of 3, etc etc
double TREE_AverageDepth(TREE *d){ return node_AverageDepth(d->head, node_Size(d->head), 1); }
// returns the hieght of the 'root/head' of the tree
unsigned TREE_Height(TREE *d){ return node_Height(d->head); }
// returns the key of the nth member in sorted order of the TREE, returns NULL if invalid n
// returns the actual key currently being used by the TREE
void *TREE_nth(TREE *d , unsigned n){
if( n >= node_Size(d->head) ) return NULL;
return node_nth(d->head , n, 0);
}
// the given key does not have to exist in the TREE and is not freed or mutated during runtime
// ie: if the inputted key is in the TREE, it is returning the index
// if the inputted key is NOT in the TREE, returns numbers of elements that come before
unsigned TREE_Position( TREE *d , void *k ){ return node_Position(d->head, k, d->cmp); }