red_black_delete.c

/* C implementation of Red-Black Tree Deletion.
   A red-black tree is a specialized binary search
   tree data structure noted for fast storage and
   retrieval of ordered information, and guarantee
   that operations will complete within a known time.
   It is very important to understand the workings
   of red-black trees since it is used for the
   implementation of the Completely Fair Scheduler
   (CFS) in the Linx kernel and in other importamt
   applications in operating systems research.
   Compared to other self-balancing binary search
   tree, the nodes in a red-black tree hold an extra
   bit called "color" that represent "red" and "black"
   and which is used when reorganizing the tree to
   guarantee that is always approximately balanced.
   The key properties of red-black trees, in addition to
   those of any binary search tree, are five:
   1) Every node is either red or black.
   2) All leaf nodes (Nil nodes) are considerd black.
   3) A red node cannot have a red child
   4) Every path from a given node to any of its
   descendent NIL nodes goes through the same number of
   black nodes. This is called the "black height" of
   the tree.
   5) If a node N had exactly one child, it must be a
   red child because if it were black, its NIL
   descendents would sit at a different black depth than
   N's NIl childrem, violating requirement 4.
   The rebalancing is not perfect, but guarantees
   seaching on O(log n) time, where n is the numberà
   of nodes in the tree. Insertion and deletion, while
   they require complex adjustements to the tree, are
   carried out in the worst case O(log n) time as well.
   For more in-depth information and proofs, see
   https://en.wikipedia.org/wiki/Red%E2%80%93black_tree
 */




#include <stdio.h>
#include <stdlib.h>

enum nodeColor {
  RED,
  BLACK
};

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

struct rbNode *root = NULL;

// Create a red-black tree
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;
}

// Insert an node
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;
  while (ptr != NULL) {
    if (ptr->data == data) {
      printf("Duplicates Not Allowed!!\n");
      return;
    }
    index = (data - ptr->data) > 0 ? 1 : 0;
    stack[ht] = ptr;
    ptr = ptr->link[index];
    dir[ht++] = index;
  }
  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;
}

// Delete a node
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("Tree not available\n");
    return;
  }

  ptr = root;
  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) {
    if ((ptr == root) && (ptr->link[0] == NULL)) {
      free(ptr);
      root = NULL;
    } else if (ptr == root) {
      root = ptr->link[0];
      free(ptr);
    } else {
      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;
    } 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--;
    }
  }
}

// Print the inorder traversal of the tree
void inorderTraversal(struct rbNode *node) {
  if (node) {
    inorderTraversal(node->link[0]);
    printf("%d  ", node->data);
    inorderTraversal(node->link[1]);
  }
  return;
}

// Driver code
int main() {
  int ch, data;
  while (1) {
    printf("1. Insertion\t2. Deletion\n");
    printf("3. Traverse\t4. Exit");
    printf("\nEnter your choice:");
    scanf("%d", &ch);
    switch (ch) {
      case 1:
        printf("Enter the element to insert:");
        scanf("%d", &data);
        insertion(data);
        break;
      case 2:
        printf("Enter the element to delete:");
        scanf("%d", &data);
        deletion(data);
        break;
      case 3:
        inorderTraversal(root);
        printf("\n");
        break;
      case 4:
        exit(0);
      default:
        printf("Not available\n");
        break;
    }
    printf("\n");
  }
  return 0;
}