### Problem Statement#

Given the roots of two binary trees `p` and `q`, write a function to check if they are the same or not.

Two binary trees are considered the same if they are structurally identical, and the nodes have the same value.

#### Example 1:#

``````    2               2
1       3       1       3

Input: p = [1,2,3], q = [1,2,3]
Output: true
``````

#### Example 2:#

``````    1       1
2               2

Input: p = [1,2], q = [1,null,2]
Output: false
``````

#### Example 3:#

``````    2               1
1       1       1       2

Input: p = [1,2,1], q = [1,1,2]
Output: false
``````

### Recursive Implementation#

``````# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

class Solution:
def isSameTree(self, p: Optional[TreeNode], q: Optional[TreeNode]) -> bool:
"""
* While the values of p and q are equal,
drill down recursively
* If p and q are null, we have a leaf, return True
* Return False for all other cases
* p.val != q.val
* structure differs
"""
# T: O(N) ~ visit each node once
# S: O(N) ~ recursive call stack
if p and q and p.val == q.val:
return  self.isSameTree(p.left, q.left) and \
self.isSameTree(p.right, q.right)
elif not p and not q:
return True
else:
return  False
``````

### Iterative Implementation#

``````# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

from collections import deque
class Solution:
def isSameTree(self, p: Optional[TreeNode], q: Optional[TreeNode]) -> bool:
"""
* Same as above
"""
queue = deque([(p, q)])

while queue:
p, q = queue.popleft()

if p and q and p.val == q.val:
# Traverse tree while values and
# strcture are equal
queue.append((p.left, q.left))
queue.append((p.right, q.right))
elif not p and not q:
# We have found a leaf.
# No new information here.
pass
else:
# Either the values of p and q
# turned out to be different or
# the structure differed
return False

return True
``````

Leetcode 100 Same Tree