Summary: in this tutorial, you will learn about the red-black tree data structure and how to implement the red-black tree in C.
Introduction to red-black tree data structure
A red-black tree is a special kind of the binary search tree where each tree’s node stores a color, which is either red or black. A red-black tree is a self-balancing binary search tree, in which the insert or remove operation is done intelligently to make sure that the tree is always balanced.
The complexity of any operation in the tree such as search, insert or delete is O(logN) where N is the number of nodes in the red-black tree.
The red-black tree data structure is used to implement associative arrays.
Red-black tree implementation in C
#include <stdlib.h>
#include "fatal.h"
typedef int ElementType;
#define NegInfinity (-10000)
#ifndef _RedBlack_H
#define _RedBlack_H
struct RedBlackNode;
typedef struct RedBlackNode *Position;
typedef struct RedBlackNode *RedBlackTree;
RedBlackTree MakeEmpty(RedBlackTree T);
Position Find(ElementType X, RedBlackTree T);
Position FindMin(RedBlackTree T);
Position FindMax(RedBlackTree T);
RedBlackTree Initialize(void);
RedBlackTree Insert(ElementType X, RedBlackTree T);
RedBlackTree Remove(ElementType X, RedBlackTree T);
ElementType Retrieve(Position P);
void PrintTree(RedBlackTree T);
#endif /* _RedBlack_H */Code language: C++ (cpp)#include "redblack.h"
#include <stdio.h>
#include "fatal.h"
typedef enum ColorType {
Red, Black
} ColorType;
struct RedBlackNode {
ElementType Element;
RedBlackTree Left;
RedBlackTree Right;
ColorType Color;
};
static Position NullNode = NULL; /* Needs initialization */
/* Initialization procedure */
RedBlackTree
Initialize(void) {
RedBlackTree T;
if (NullNode == NULL) {
NullNode = malloc(sizeof ( struct RedBlackNode));
if (NullNode == NULL)
FatalError("Out of space!!!");
NullNode->Left = NullNode->Right = NullNode;
NullNode->Color = Black;
NullNode->Element = 12345;
}
/* Create the header node */
T = malloc(sizeof ( struct RedBlackNode));
if (T == NULL)
FatalError("Out of space!!!");
T->Element = NegInfinity;
T->Left = T->Right = NullNode;
T->Color = Black;
return T;
}
/* END */
void
Output(ElementType Element) {
printf("%d\n", Element);
}
/* Print the tree, watch out for NullNode, */
/* and skip header */
static void
DoPrint(RedBlackTree T) {
if (T != NullNode) {
DoPrint(T->Left);
Output(T->Element);
DoPrint(T->Right);
}
}
void
PrintTree(RedBlackTree T) {
DoPrint(T->Right);
}
/* END */
static RedBlackTree
MakeEmptyRec(RedBlackTree T) {
if (T != NullNode) {
MakeEmptyRec(T->Left);
MakeEmptyRec(T->Right);
free(T);
}
return NullNode;
}
RedBlackTree
MakeEmpty(RedBlackTree T) {
T->Right = MakeEmptyRec(T->Right);
return T;
}
Position
Find(ElementType X, RedBlackTree T) {
if (T == NullNode)
return NullNode;
if (X < T->Element)
return Find(X, T->Left);
else
if (X > T->Element)
return Find(X, T->Right);
else
return T;
}
Position
FindMin(RedBlackTree T) {
T = T->Right;
while (T->Left != NullNode)
T = T->Left;
return T;
}
Position
FindMax(RedBlackTree T) {
while (T->Right != NullNode)
T = T->Right;
return T;
}
/* This function can be called only if K2 has a left child */
/* Perform a rotate between a node (K2) and its left child */
/* Update heights, then return new root */
static Position
SingleRotateWithLeft(Position K2) {
Position K1;
K1 = K2->Left;
K2->Left = K1->Right;
K1->Right = K2;
return K1; /* New root */
}
/* This function can be called only if K1 has a right child */
/* Perform a rotate between a node (K1) and its right child */
/* Update heights, then return new root */
static Position
SingleRotateWithRight(Position K1) {
Position K2;
K2 = K1->Right;
K1->Right = K2->Left;
K2->Left = K1;
return K2; /* New root */
}
/* Perform a rotation at node X */
/* (whose parent is passed as a parameter) */
/* The child is deduced by examining Item */
static Position
Rotate(ElementType Item, Position Parent) {
if (Item < Parent->Element)
return Parent->Left = Item < Parent->Left->Element ?
SingleRotateWithLeft(Parent->Left) :
SingleRotateWithRight(Parent->Left);
else
return Parent->Right = Item < Parent->Right->Element ?
SingleRotateWithLeft(Parent->Right) :
SingleRotateWithRight(Parent->Right);
}
static Position X, P, GP, GGP;
static
void HandleReorient(ElementType Item, RedBlackTree T) {
X->Color = Red; /* Do the color flip */
X->Left->Color = Black;
X->Right->Color = Black;
if (P->Color == Red) /* Have to rotate */ {
GP->Color = Red;
if ((Item < GP->Element) != (Item < P->Element))
P = Rotate(Item, GP); /* Start double rotate */
X = Rotate(Item, GGP);
X->Color = Black;
}
T->Right->Color = Black; /* Make root black */
}
RedBlackTree
Insert(ElementType Item, RedBlackTree T) {
X = P = GP = T;
NullNode->Element = Item;
while (X->Element != Item) /* Descend down the tree */ {
GGP = GP;
GP = P;
P = X;
if (Item < X->Element)
X = X->Left;
else
X = X->Right;
if (X->Left->Color == Red && X->Right->Color == Red)
HandleReorient(Item, T);
}
if (X != NullNode)
return NullNode; /* Duplicate */
X = malloc(sizeof ( struct RedBlackNode));
if (X == NULL)
FatalError("Out of space!!!");
X->Element = Item;
X->Left = X->Right = NullNode;
if (Item < P->Element) /* Attach to its parent */
P->Left = X;
else
P->Right = X;
HandleReorient(Item, T); /* Color it red; maybe rotate */
return T;
}
RedBlackTree
Remove(ElementType Item, RedBlackTree T) {
printf("Remove is unimplemented\n");
if (Item)
return T;
return T;
}
ElementType
Retrieve(Position P) {
return P->Element;
}Code language: C++ (cpp)#include "redblack.h"
#include <stdio.h>
#define N 800
main() {
RedBlackTree T;
Position P;
int i;
int j = 0;
T = Initialize();
T = MakeEmpty(T);
for (i = 0; i < N; i++, j = (j + 7) % N)
T = Insert(j, T);
printf("Inserts are complete\n");
for (i = 0; i < N; i++)
if ((P = Find(i, T)) == NULL || Retrieve(P) != i)
printf("Error at %d\n", i);
printf("Min is %d, Max is %d\n", Retrieve(FindMin(T)),
Retrieve(FindMax(T)));
return 0;
}Code language: C++ (cpp)In this tutorial, you have learned how to implement red-black tree data structure in C.
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