Given a BST and its root, print all sequences of nodes which give rise to the same bst

Question

Given a BST, find all sequences of nodes starting from root that will essentially give the same binary search tree.

Given a bst, say

  3
 /  \\
1             


        

Answer 1

well here is my python code which does producing all sequences of elements/numbers for same BST. for the logic i referred to the book cracking the coding interview by Gayle Laakmann Mcdowell

from binarytree import  Node, bst, pprint

def wavelist_list(first, second, wave, prefix):
    if first:
       fl = len(first)
    else:
       fl = 0

    if second:       
        sl = len(second)
    else:
       sl = 0   
    if fl == 0 or sl == 0:
       tmp = list()
       tmp.extend(prefix)
       if first:
          tmp.extend(first)
       if second:   
          tmp.extend(second)
       wave.append(tmp)
       return

    if fl:
        fitem = first.pop(0)
        prefix.append(fitem)
        wavelist_list(first, second, wave, prefix)
        prefix.pop()
        first.insert(0, fitem)

    if sl:
        fitem = second.pop(0)
        prefix.append(fitem)
        wavelist_list(first, second, wave, prefix)
        prefix.pop()
        second.insert(0, fitem)        


def allsequences(root):
    result = list()
    if root == None:
       return result

    prefix = list()
    prefix.append(root.value)

    leftseq = allsequences(root.left)
    rightseq = allsequences(root.right)
    lseq = len(leftseq)
    rseq = len(rightseq)

    if lseq and rseq:
       for i in range(lseq):
          for j in range(rseq):
            wave = list()
            wavelist_list(leftseq[i], rightseq[j], wave, prefix)
            for k in range(len(wave)):
                result.append(wave[k])

    elif lseq:
      for i in range(lseq):
        wave = list()
        wavelist_list(leftseq[i], None, wave, prefix)
        for k in range(len(wave)):
            result.append(wave[k])

    elif rseq:
      for j in range(rseq):
        wave = list()
        wavelist_list(None, rightseq[j], wave, prefix)
        for k in range(len(wave)):
            result.append(wave[k])
   else:
       result.append(prefix) 

   return result



if __name__=="__main__":
    n = int(input("what is height of tree?"))
    my_bst = bst(n)
    pprint(my_bst)

    seq = allsequences(my_bst)
    print("All sequences")
    for i in range(len(seq)):
        print("set %d = " %(i+1), end="")
        print(seq[i])

 example output:
 what is height of tree?3

       ___12      
      /     \     
  __ 6       13   
 /   \        \  
 0     11       14
  \               
   2              


  All sequences
  set 1 = [12, 6, 0, 2, 11, 13, 14]
  set 2 = [12, 6, 0, 2, 13, 11, 14]
  set 3 = [12, 6, 0, 2, 13, 14, 11]
  set 4 = [12, 6, 0, 13, 2, 11, 14]
  set 5 = [12, 6, 0, 13, 2, 14, 11]
  set 6 = [12, 6, 0, 13, 14, 2, 11]
  set 7 = [12, 6, 13, 0, 2, 11, 14]
  set 8 = [12, 6, 13, 0, 2, 14, 11]
  set 9 = [12, 6, 13, 0, 14, 2, 11]
  set 10 = [12, 6, 13, 14, 0, 2, 11]
  set 11 = [12, 13, 6, 0, 2, 11, 14]
  set 12 = [12, 13, 6, 0, 2, 14, 11]
  set 13 = [12, 13, 6, 0, 14, 2, 11]
  set 14 = [12, 13, 6, 14, 0, 2, 11]
  set 15 = [12, 13, 14, 6, 0, 2, 11]
  set 16 = [12, 6, 0, 11, 2, 13, 14]
  set 17 = [12, 6, 0, 11, 13, 2, 14]
  set 18 = [12, 6, 0, 11, 13, 14, 2]
  set 19 = [12, 6, 0, 13, 11, 2, 14]
  set 20 = [12, 6, 0, 13, 11, 14, 2]
  set 21 = [12, 6, 0, 13, 14, 11, 2]
  set 22 = [12, 6, 13, 0, 11, 2, 14]
  set 23 = [12, 6, 13, 0, 11, 14, 2]
  set 24 = [12, 6, 13, 0, 14, 11, 2]
  set 25 = [12, 6, 13, 14, 0, 11, 2]
  set 26 = [12, 13, 6, 0, 11, 2, 14]
  set 27 = [12, 13, 6, 0, 11, 14, 2]
  set 28 = [12, 13, 6, 0, 14, 11, 2]
  set 29 = [12, 13, 6, 14, 0, 11, 2]
  set 30 = [12, 13, 14, 6, 0, 11, 2]
  set 31 = [12, 6, 11, 0, 2, 13, 14]
  set 32 = [12, 6, 11, 0, 13, 2, 14]
  set 33 = [12, 6, 11, 0, 13, 14, 2]
  set 34 = [12, 6, 11, 13, 0, 2, 14]
  set 35 = [12, 6, 11, 13, 0, 14, 2]
  set 36 = [12, 6, 11, 13, 14, 0, 2]
  set 37 = [12, 6, 13, 11, 0, 2, 14]
  set 38 = [12, 6, 13, 11, 0, 14, 2]
  set 39 = [12, 6, 13, 11, 14, 0, 2]
  set 40 = [12, 6, 13, 14, 11, 0, 2]
  set 41 = [12, 13, 6, 11, 0, 2, 14]
  set 42 = [12, 13, 6, 11, 0, 14, 2]
  set 43 = [12, 13, 6, 11, 14, 0, 2]
  set 44 = [12, 13, 6, 14, 11, 0, 2]
  set 45 = [12, 13, 14, 6, 11, 0, 2]