b tree properties code example

Example 1: b tree in c

// Searching a key on a B-tree in C

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

#define MAX 3
#define MIN 2

struct btreeNode
{
  int val[MAX + 1], count;
  struct btreeNode *link[MAX + 1];
};

struct btreeNode *root;

struct btreeNode *createNode(int val, struct btreeNode *child)
{
  struct btreeNode *newNode;
  newNode = (struct btreeNode *)malloc(sizeof(struct btreeNode));
  newNode->val[1] = val;
  newNode->count = 1;
  newNode->link[0] = root;
  newNode->link[1] = child;
  return newNode;
}

void addValToNode(int val, int pos, struct btreeNode *node,
          struct btreeNode *child)
{
  int j = node->count;
  while (j > pos)
  {
    node->val[j + 1] = node->val[j];
    node->link[j + 1] = node->link[j];
    j--;
  }
  node->val[j + 1] = val;
  node->link[j + 1] = child;
  node->count++;
}

void splitNode(int val, int *pval, int pos, struct btreeNode *node,
         struct btreeNode *child, struct btreeNode **newNode)
{
  int median, j;

  if (pos > MIN)
    median = MIN + 1;
  else
    median = MIN;

  *newNode = (struct btreeNode *)malloc(sizeof(struct btreeNode));
  j = median + 1;
  while (j <= MAX)
  {
    (*newNode)->val[j - median] = node->val[j];
    (*newNode)->link[j - median] = node->link[j];
    j++;
  }
  node->count = median;
  (*newNode)->count = MAX - median;

  if (pos <= MIN)
  {
    addValToNode(val, pos, node, child);
  }
  else
  {
    addValToNode(val, pos - median, *newNode, child);
  }
  *pval = node->val[node->count];
  (*newNode)->link[0] = node->link[node->count];
  node->count--;
}

int setValueInNode(int val, int *pval,
           struct btreeNode *node, struct btreeNode **child)
{

  int pos;
  if (!node)
  {
    *pval = val;
    *child = NULL;
    return 1;
  }

  if (val < node->val[1])
  {
    pos = 0;
  }
  else
  {
    for (pos = node->count;
       (val < node->val[pos] && pos > 1); pos--)
      ;
    if (val == node->val[pos])
    {
      printf("Duplicates not allowed\n");
      return 0;
    }
  }
  if (setValueInNode(val, pval, node->link[pos], child))
  {
    if (node->count < MAX)
    {
      addValToNode(*pval, pos, node, *child);
    }
    else
    {
      splitNode(*pval, pval, pos, node, *child, child);
      return 1;
    }
  }
  return 0;
}

void insert(int val)
{
  int flag, i;
  struct btreeNode *child;

  flag = setValueInNode(val, &i, root, &child);
  if (flag)
    root = createNode(i, child);
}

void search(int val, int *pos, struct btreeNode *myNode)
{
  if (!myNode)
  {
    return;
  }

  if (val < myNode->val[1])
  {
    *pos = 0;
  }
  else
  {
    for (*pos = myNode->count;
       (val < myNode->val[*pos] && *pos > 1); (*pos)--)
      ;
    if (val == myNode->val[*pos])
    {
      printf("%d is found", val);
      return;
    }
  }
  search(val, pos, myNode->link[*pos]);

  return;
}

void traversal(struct btreeNode *myNode)
{
  int i;
  if (myNode)
  {
    for (i = 0; i < myNode->count; i++)
    {
      traversal(myNode->link[i]);
      printf("%d ", myNode->val[i + 1]);
    }
    traversal(myNode->link[i]);
  }
}

int main()
{
  int val, ch;

  insert(8);
  insert(9);
  insert(10);
  insert(11);
  insert(15);
  insert(16);
  insert(17);
  insert(18);
  insert(20);
  insert(23);

  traversal(root);

  printf("\n");
  search(11, &ch, root);
}

Example 2: b tree

In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time