Add same tree

Author: onixlas

binary-tree/100_Same_Tree/README.md

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+# Same Tree
+
+## Problem Description
+
+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:**  
+Input: `p = [1,2,3], q = [1,2,3]`
+Output: `true`
+
+**Example 2:**  
+Input: `p = [1,2], q = [1,null,2]`
+Output: `false`
+
+**Example 3:**  
+Input: `p = [1,2,1], q = [1,1,2]`
+Output: `false`
+
+## Solution
+
+```python
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+
+def is_same_tree(p: Optional[TreeNode], q: Optional[TreeNode]) -> bool:
+    """
+    Check if two binary trees are identical in structure and node values.
+
+    :param p: Root node of the first binary tree
+    :param q: Root node of the second binary tree
+    :return: True if trees are identical, False otherwise
+    """
+    if p is None and q is None:
+        return True
+    elif isinstance(p, int) and isinstance(q, int):
+        return p == q
+    elif isinstance(p, TreeNode) and isinstance(q, TreeNode):
+        if p.val != q.val:
+            return False
+        return self.is_same_tree(p.left, q.left) and self.is_same_tree(p.right, q.right)
+    return False
+```
+
+* **Time Complexity:** O(n)
+* **Space Complexity:** O(1)
+
+### Explanation of the Solution
+
+This algorithm checks if two binary trees are identical by performing a depth-first comparison:
+
+1. Base Cases:
+    * If both nodes are `None` (reached leaf nodes), return `True`
+    * If both nodes are integers, compare their values
+    * If one is `None` and the other isn't, trees aren't identical (returns `False`)
+2. Tree Comparison:
+    * First compares current node values
+    * Then recursively compares left subtrees and right subtrees
+    * Only returns `True` if all corresponding nodes match in both structure and value
+3. Termination:
+    * If any comparison fails at any level, immediately returns `False`
+    * Only returns `True` if entire trees are traversed successfully with all nodes matching
+
+The algorithm effectively performs a simultaneous traversal of both trees, comparing nodes at each step. The worst-case scenario occurs when the trees are identical, requiring a full traversal of all nodes.

binary-tree/100_Same_Tree/solution.py

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+from typing import Optional
+
+# 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
+
+
+def is_same_tree(p: Optional[TreeNode], q: Optional[TreeNode]) -> bool:
+    """
+    Check if two binary trees are identical in structure and node values.
+
+    :param p: Root node of the first binary tree
+    :param q: Root node of the second binary tree
+    :return: True if trees are identical, False otherwise
+    """
+    if p is None and q is None:
+        return True
+    elif isinstance(p, int) and isinstance(q, int):
+        return p == q
+    elif isinstance(p, TreeNode) and isinstance(q, TreeNode):
+        if p.val != q.val:
+            return False
+        return self.is_same_tree(p.left, q.left) and self.is_same_tree(p.right, q.right)
+    return False
+
+
+
+assert is_same_tree(p=TreeNode(1, 2, 3), q=TreeNode(1, 2, 3)) == True, 'Test 1 Failed'
+assert is_same_tree(p=TreeNode(1, 2), q=TreeNode(1, None, 2)) == False, 'Test 2 Failed'
+assert is_same_tree(p=TreeNode(1, 2, 1), q=TreeNode(1, 1, 2)) == False, 'Test 3 Failed'