Question: You are given 2 number streams. You need to find whether they will create the same BST or not.

Array1:10 5 20 15 30
Array2:10 20 15 30 5
Result: True

Array1:10 5 20 15 30
Array2:10 15 30 20 5
Result: False (see corresponding trees below)


Method of building a BST from an incoming stream is like below:

  1. Make first element as root.
  2. If current element is smaller then root -> insert in left subtree.
  3. If current element is greater then root -> insert in right subtree.
  4. If current element is equal to root -> skip (or as pre-decided)
  5. While inserting in left and right subtree, follow above steps recursively.

So in above question, we have to check top-down if all the subtrees are identical or not. For that, we should follow below steps:

  1. Check if stream is finished if yes -> return false
  2. Check if both the stream has same number of elements, if not -> return false
  3. Check if root is same, if not -> return false
  4. leftsubtree arrays = constructed from smaller elements than root
  5. rightsubtree arrays = constructed from greater elements than root
  6. if leftsubtree == rightsubtree -> return true
  7. For finding result in step 6, follow above steps recursively

Code: While writing code, I am skipping the element equal to root.

def checkidenticaltree(a, b)
return false if a.length != b.length
return false if a[0] != b[0]
return true if a.length <= 1

a_left = {|v| v < a[0]}
a_right = {|v| v > a[0]}
b_left = {|v| v < b[0]}
b_right = {|v| v > b[0]}

return checkidenticaltree(a_right, b_right) && checkidenticaltree(a_left, b_left)

def checkidenticaltree(a, b):
if len(a) != len(b):
return False
if a[0] != b[0]:
return False
if len(a) <= 1:
return True

a_left = []
a_right = []
for x in a:
if x < a[0]:
elif x > a[0]:

b_left = []
b_right = []
for x in b:
if x < b[0]:
elif x > b[0]:

return checkidenticaltree(a_right, b_right) and checkidenticaltree(a_left, b_left)

PS: This is not a very efficient approach as we have to segment stream on each recursion. It will be great, if we can find some bottom-up approach. Any suggestions?

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