# Searching a key on a B-tree in Python

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# Create a node

class BTreeNode:

  def __init__(self, leaf=False):

    self.leaf = leaf

    self.keys = []

    self.child = []

​

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# Tree

class BTree:

  def __init__(self, t):

    self.root = BTreeNode(True)

    self.t = t

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    # Insert node

  def insert(self, k):

    root = self.root

    if len(root.keys) == (2 * self.t) - 1:

      temp = BTreeNode()

      self.root = temp

      temp.child.insert(0, root)

      self.split_child(temp, 0)

      self.insert_non_full(temp, k)

    else:

      self.insert_non_full(root, k)

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    # Insert nonfull

  def insert_non_full(self, x, k):

    i = len(x.keys) - 1

    if x.leaf:

      x.keys.append((None, None))

      while i >= 0 and k[0] < x.keys[i][0]:

        x.keys[i + 1] = x.keys[i]

        i -= 1

      x.keys[i + 1] = k

    else:

      while i >= 0 and k[0] < x.keys[i][0]:

        i -= 1

      i += 1

      if len(x.child[i].keys) == (2 * self.t) - 1:

        self.split_child(x, i)

        if k[0] > x.keys[i][0]:

          i += 1

      self.insert_non_full(x.child[i], k)

​

    # Split the child

  def split_child(self, x, i):

    t = self.t

    y = x.child[i]

    z = BTreeNode(y.leaf)

    x.child.insert(i + 1, z)

    x.keys.insert(i, y.keys[t - 1])

    z.keys = y.keys[t: (2 * t) - 1]

    y.keys = y.keys[0: t - 1]

    if not y.leaf:

      z.child = y.child[t: 2 * t]

      y.child = y.child[0: t - 1]

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  # Print the tree

  def print_tree(self, x, l=0):

    print("Level ", l, " ", len(x.keys), end=":")

    for i in x.keys:

      print(i, end=" ")

    print()

    l += 1

    if len(x.child) > 0:

      for i in x.child:

        self.print_tree(i, l)

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  # Search key in the tree

  def search_key(self, k, x=None):

    if x is not None:

      i = 0

      while i < len(x.keys) and k > x.keys[i][0]:

        i += 1

      if i < len(x.keys) and k == x.keys[i][0]:

        return (x, i)

      elif x.leaf:

        return None

      else:

        return self.search_key(k, x.child[i])

    else:

      return self.search_key(k, self.root)

​

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def main():

  B = BTree(3)

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  for i in range(10):

    B.insert((i, 2 * i))

​

  B.print_tree(B.root)

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  if B.search_key(8) is not None:

    print("\nFound")

  else:

    print("\nNot Found")

​

​

if __name__ == '__main__':

  main()