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C Program To Implement Red Black Tree Operations.

A red–black tree is a self-balancing binary search tree which supports the operation search, find predecessor, find successor, find minimum, find maximum, insertion and deletion in O(log n)-time. In addition to the requirements imposed on a binary search tree, the following must be satisfied to be a red–black tree:

1)   A node is either red or black.
2)   The root is black.
3)   All leaves (NIL) are black.
4)   If a node is red, then both its children are black.
5)   Every path from a given node to any of its descendant NIL nodes contains the same number of black nodes. 

If there is a modification in RB tree due to insertion or deletion of any element, the new tree is then rearranged and repainted to restore the properties.

coloring and rotation properties

Suppose insert a node z in any RB tree; at first set the color of z to red. Now there are several cases we have to consider to keep the tree balanced:

ü  Case 1: y is red and z is a left child

y is red and z is a left child

ü  Case 2: y is red and z is a right child

y is red and z is a right child

ü  Case 3: y is black and z is a left child

y is black and z is a left child

ü  Case 4: y is black and z is a right child

y is black and z is a right child

Suppose we need to delete node z from the RB tree. If z is red, it doesn’t violate any property. If z is a leaf, it also doesn’t violate any property. Otherwise z is black and has a child; it violates property 2, 4, and 5. For property 2, set the color of root to black after deletion.

To fix property 4 and 5:
ü  If z's child x (which is the replacing node) is red, set x to black. Done!
ü  If x is black, add another black to x, so that x will be a doubly black node, and property 4 and 5 are fixed. But property 1 is violated.

To fix property 1, we must consider whether
ü  x is a left child or right child.
ü  The color of x's sibling w is red or black.
ü  The colors of w's children.  

Let x is a left child; the other case can be done by symmetric operation. Now there are several cases we need to consider to keep the tree balanced:

ü  Case 1: w is red

w is red

ü  Case 2: w is black; both w’s children are black

w is black; both w’s children are black

ü  Case 3: w is black, w’s left child is red, w’s right child is black

w is black, w’s left child is red, w’s right child is black

ü  Case 4: w is black; w’s right child is red

w is black; w’s right child is red

Source Code of RB Tree:
#include <stdio.h>
#include <stdlib.h>

enum nodeColor { RED, BLACK };

struct rbNode {
int data, color;
struct rbNode *link[2];
};

struct rbNode *root = NULL;

struct rbNode * createNode(int data) {
struct rbNode *newnode;
newnode = (struct rbNode *)malloc(sizeof(struct rbNode));

newnode->data = data;
newnode->color = RED;
newnode->link[0] = newnode->link[1] = NULL;

return newnode;
}

void insertion (int data) {
struct rbNode *stack[98], *ptr, *newnode, *xPtr, *yPtr;
int dir[98], ht = 0, index;
ptr = root;

if (!root) {
root = createNode(data);
return;
}

stack[ht] = root;
dir[ht++] = 0;

// find the place to insert the new node
while (ptr != NULL) {

if (ptr->data == data) {
printf("\nDUPLICATES NOT ALLOWED.\n");
return;
}

index = (data - ptr->data) > 0 ? 1 : 0;
stack[ht] = ptr;

ptr = ptr->link[index];
dir[ht++] = index;
}

// insert the new node
stack[ht - 1]->link[index] = newnode = createNode(data);

while ((ht >= 3) && (stack[ht - 1]->color == RED)) {

if (dir[ht - 2] == 0) {
yPtr = stack[ht - 2]->link[1];

if (yPtr != NULL && yPtr->color == RED) {
stack[ht - 2]->color = RED;

stack[ht - 1]->color = yPtr->color = BLACK;
ht = ht -2;
}

else {
if (dir[ht - 1] == 0) {
yPtr = stack[ht - 1];
}

else {
xPtr = stack[ht - 1];
yPtr = xPtr->link[1];

xPtr->link[1] = yPtr->link[0];
yPtr->link[0] = xPtr;
stack[ht - 2]->link[0] = yPtr;
}

xPtr = stack[ht - 2];
xPtr->color = RED;
yPtr->color = BLACK;

xPtr->link[0] = yPtr->link[1];
yPtr->link[1] = xPtr;

if (xPtr == root) {
root = yPtr;
}

else {
stack[ht - 3]->link[dir[ht - 3]] = yPtr;
}
break;
}}

else {
yPtr = stack[ht - 2]->link[0];

if ((yPtr != NULL) && (yPtr->color == RED)) {
stack[ht - 2]->color = RED;

stack[ht - 1]->color = yPtr->color = BLACK;
ht = ht - 2;
}

else {
if (dir[ht - 1] == 1) {
yPtr = stack[ht - 1];
}

else {
xPtr = stack[ht - 1];
yPtr = xPtr->link[0];

xPtr->link[0] = yPtr->link[1];
yPtr->link[1] = xPtr;
stack[ht - 2]->link[1] = yPtr;
}

xPtr = stack[ht - 2];
yPtr->color = BLACK;
xPtr->color = RED;

xPtr->link[1] = yPtr->link[0];
yPtr->link[0] = xPtr;

if (xPtr == root) {
root = yPtr;
}

else {
stack[ht - 3]->link[dir[ht - 3]] = yPtr;
}
break;
}}}
root->color = BLACK;
}

void deletion(int data) {
struct rbNode *stack[98], *ptr, *xPtr, *yPtr;
struct rbNode *pPtr, *qPtr, *rPtr;

int dir[98], ht = 0, diff, i;
enum nodeColor color;

if (!root) {
printf("\nGIVEN DATA NOT FOUND.\n"); 
return;
}
ptr = root;

// search the node to delete
while (ptr != NULL) {

if ((data - ptr->data) == 0)
break;

diff = (data - ptr->data) > 0 ? 1 : 0;
stack[ht] = ptr;
dir[ht++] = diff;
ptr = ptr->link[diff];
}

if (ptr->link[1] == NULL) {

// node with no children
if ((ptr == root) && (ptr->link[0] == NULL)) {
free(ptr);
root = NULL;
}

// deleting root with one child
else if (ptr == root) {
root = ptr->link[0];
free(ptr);
}

else {
// node with one child
stack[ht - 1]->link[dir[ht - 1]] = ptr->link[0];
}}

else {
xPtr = ptr->link[1];
if (xPtr->link[0] == NULL) {

xPtr->link[0] = ptr->link[0];
color = xPtr->color;
xPtr->color = ptr->color;
ptr->color = color;

if (ptr == root) {
root = xPtr;
}

else {
stack[ht - 1]->link[dir[ht - 1]] = xPtr;
}

dir[ht] = 1;
stack[ht++] = xPtr;
}

// deleting node with 2 children
else {
i = ht++;

while (1) {
dir[ht] = 0;
stack[ht++] = xPtr;

yPtr = xPtr->link[0];
if (!yPtr->link[0])
break;
xPtr = yPtr;
}

dir[i] = 1;
stack[i] = yPtr;

if (i > 0)
stack[i - 1]->link[dir[i - 1]] = yPtr;

yPtr->link[0] = ptr->link[0];
xPtr->link[0] = yPtr->link[1];
yPtr->link[1] = ptr->link[1];

if (ptr == root) {
root = yPtr;
}

color = yPtr->color;
yPtr->color = ptr->color;
ptr->color = color;
}}

if (ht < 1)
return;

if (ptr->color == BLACK) {
while (1) {
pPtr = stack[ht - 1]->link[dir[ht - 1]];

if (pPtr && pPtr->color == RED) {
pPtr->color = BLACK;
break;
}

if (ht < 2)
break;

if (dir[ht - 2] == 0) {
rPtr = stack[ht - 1]->link[1];

if (!rPtr)
break;

if (rPtr->color == RED) {

stack[ht - 1]->color = RED;
rPtr->color = BLACK;
stack[ht - 1]->link[1] = rPtr->link[0];
rPtr->link[0] = stack[ht - 1];

if (stack[ht - 1] == root) {
root = rPtr;
}

else {
stack[ht - 2]->link[dir[ht - 2]] = rPtr;
}

dir[ht] = 0;
stack[ht] = stack[ht - 1];
stack[ht - 1] = rPtr;
ht++;

rPtr = stack[ht - 1]->link[1];
}

if ( (!rPtr->link[0] || rPtr->link[0]->color == BLACK) &&
(!rPtr->link[1] || rPtr->link[1]->color == BLACK)) {

rPtr->color = RED;
}

else {
if (!rPtr->link[1] || rPtr->link[1]->color == BLACK) {

qPtr = rPtr->link[0];
rPtr->color = RED;
qPtr->color = BLACK;

rPtr->link[0] = qPtr->link[1];
qPtr->link[1] = rPtr;
rPtr = stack[ht - 1]->link[1] = qPtr;
}

rPtr->color = stack[ht - 1]->color;
stack[ht - 1]->color = BLACK;
rPtr->link[1]->color = BLACK;

stack[ht - 1]->link[1] = rPtr->link[0];
rPtr->link[0] = stack[ht - 1];

if (stack[ht - 1] == root) {
root = rPtr;
}

else {
stack[ht - 2]->link[dir[ht - 2]] = rPtr;
}
break;
}}

else {
rPtr = stack[ht - 1]->link[0];

if (!rPtr)
break;

if (rPtr->color == RED) {
stack[ht - 1]->color = RED;
rPtr->color = BLACK;

stack[ht - 1]->link[0] = rPtr->link[1];
rPtr->link[1] = stack[ht - 1];

if (stack[ht - 1] == root) {
root = rPtr;
}

else {
stack[ht - 2]->link[dir[ht - 2]] = rPtr;
}

dir[ht] = 1;
stack[ht] = stack[ht - 1];
stack[ht - 1] = rPtr;
ht++;

rPtr = stack[ht - 1]->link[0];
}

if ( (!rPtr->link[0] || rPtr->link[0]->color == BLACK) &&
(!rPtr->link[1] || rPtr->link[1]->color == BLACK)) {
rPtr->color = RED;
}

else {
if (!rPtr->link[0] || rPtr->link[0]->color == BLACK) {
qPtr = rPtr->link[1];
rPtr->color = RED;
qPtr->color = BLACK;

rPtr->link[1] = qPtr->link[0];
qPtr->link[0] = rPtr;
rPtr = stack[ht - 1]->link[0] = qPtr;
}

rPtr->color = stack[ht - 1]->color;
stack[ht - 1]->color = BLACK;
rPtr->link[0]->color = BLACK;

stack[ht - 1]->link[0] = rPtr->link[1];
rPtr->link[1] = stack[ht - 1];

if (stack[ht - 1] == root) {
root = rPtr;
}

else {
stack[ht - 2]->link[dir[ht - 2]] = rPtr;
}
break;
}}

ht--;
return; 
}}} 

void searchElement(int data) {
struct rbNode *temp = root;
int diff;

while (temp != NULL) {
diff = data - temp->data;

if (diff > 0) {
temp = temp->link[1];
}

else if (diff < 0) {
temp = temp->link[0];
}

else {
printf("\nGIVEN DATA WAS FOUND IN RB TREE.\n");
return;
}}
printf("\nGIVEN DATA WAS NOT FOUND IN RB TREE.\n");
return;
}

void inorderTraversal(struct rbNode *node) {
if (node) {
inorderTraversal(node->link[0]);
printf("%d ", node->data);

inorderTraversal(node->link[1]);
return;
}}

int main() {
int ch, data;

while (1) {
printf("\t(1) INSERTION\t(2) DELETION\n");
printf("\t(3) SEARCH\t(4) DISPLAY\n");

printf("\t(5) EXIT \n\nENTER YOUR CHOICE: ");
scanf("%d", &ch);

switch (ch) {
case 1:
printf("\nENTER THE DATA TO INSERT: ");
scanf("%d", &data);
insertion(data);
break;

case 2:
printf("\nENTER THE DATA TO DELETE: ");
scanf("%d", &data);
deletion(data);
break;

case 3:
printf("\nENTER THE SEARCH ELEMENT: ");
scanf("%d", &data);
searchElement(data);
break;

case 4:
printf("\nINORDER TRAVERSAL OF RB TREE: "); 
inorderTraversal(root);
printf("\n"); 
break;

case 5:
exit(0);

default:
printf("\nYOU HAVE ENTERED WRONG OPTION.\n");
break;
}
printf("\n");
}
return 0;
}
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