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_build/html/.buildinfo

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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 8b102b6ce68f3bc9f65a9c18adf2ae17
+tags: 645f666f9bcd5a90fca523b33c5a78b7

_build/html/_sources/01. Array Hashing/1. Two Sum.ipynb

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+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "id": "d6161252-e815-48d5-a2a3-5444c12e3b49",
+      "metadata": {},
+      "source": [
+        "# 100: Same Tree\n",
+        "\n",
+        "**Difficulty:** Easy\n",
+        "\n",
+        "**Link to Problem:** [To see the Same Tree problem on LeetCode, click here!](https://leetcode.com/problems/same-tree/)\n",
+        "\n",
+        "---\n",
+        "Given the roots of two binary trees `p` and `q`, write a function to check if they are the same or not.\n",
+        "\n",
+        "Two binary trees are considered the same if they are structurally identical, and the nodes have the same value.\n",
+        "\n",
+        "**Constraints**\n",
+        "\n",
+        "1. The number of nodes in both trees is in the range `[0, 100]`.\n",
+        "2. $-10^4$ <= `Node.val` <= $10^4$"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 5,
+      "id": "aabf7095-07dc-4ab7-876c-ec7213ed0de5",
+      "metadata": {
+        "trusted": true
+      },
+      "outputs": [],
+      "source": [
+        "# Definition for a binary tree node.\n",
+        "class TreeNode:\n",
+        "    def __init__(self, val=0, left=None, right=None):\n",
+        "        # Initialize a TreeNode with a value (val), left child, and right child.\n",
+        "        self.val = val\n",
+        "        self.left = left\n",
+        "        self.right = right\n",
+        "\n",
+        "def isSameTree(p, q):\n",
+        "    # Base case: If both p and q are None, the trees are the same.\n",
+        "    if not p and not q:\n",
+        "        return True\n",
+        "    \n",
+        "    # Base case: If either p or q is None (but not both), the trees are different.\n",
+        "    if not p or not q:\n",
+        "        return False\n",
+        "    \n",
+        "    # Check if the values of the current nodes (p.val and q.val) are equal.\n",
+        "    if p.val != q.val:\n",
+        "        return False\n",
+        "    \n",
+        "    # Recursively check the left and right subtrees of p and q.\n",
+        "    # If both subtrees are the same, the entire trees are the same.\n",
+        "    return isSameTree(p.left, q.left) and isSameTree(p.right, q.right)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "id": "ece39324-cd9e-47d7-8677-a001878494d9",
+      "metadata": {},
+      "source": [
+        "In this code, we define a `TreeNode` class to represent binary tree nodes and a `isSameTree` function to check if two binary trees are the same. The function uses recursive traversal to compare the trees' structures and values.\n",
+        "\n",
+        "1. We start by defining a `TreeNode` class, which represents a node in a binary tree. Each node has a `val` (the node's value), a `left` child, and a right child. This class will help us create and work with binary trees.\n",
+        "2. Next, we define the `isSameTree` function, which checks if two binary trees (`p` and `q`) are the same.\n",
+        "      + The base case for the recursion is when both `p` and `q` are `None`. In this case, they are considered the same, so we return `True`.\n",
+        "      + If either `p` or `q` is `None` (but not both), they cannot be the same, so we return `False`.\n",
+        "      + If the values of the current nodes `p.val` and `q.val` are not equal, we return `False` because the trees cannot be the same.\n",
+        "      + Finally, we recursively check the left and right subtrees of `p` and `q` to see if they are the same."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "id": "a54ea5b7-c53f-46c0-a44f-ef769ac68244",
+      "metadata": {},
+      "source": [
+        "## Test cases"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "id": "355f5bfd-94e1-4c5b-9914-cc20775f4160",
+      "metadata": {
+        "trusted": true
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "True\n"
+          ]
+        }
+      ],
+      "source": [
+        "### Example 1\n",
+        "\n",
+        "#Input: `p = [1,2,3]`, `q = [1,2,3]`\n",
+        "\n",
+        "p1 = TreeNode(1, TreeNode(2), TreeNode(3))\n",
+        "q1 = TreeNode(1, TreeNode(2), TreeNode(3))\n",
+        "print(isSameTree(p1, q1)) "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 3,
+      "id": "192912fb-9d12-4911-9a4f-bfd37043e11d",
+      "metadata": {
+        "trusted": true
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "False\n"
+          ]
+        }
+      ],
+      "source": [
+        "### Example 2\n",
+        "\n",
+        "#Input: `p = [1,2]`, `q = [1,null,2]`\n",
+        "\n",
+        "p2 = TreeNode(1, TreeNode(2), None)\n",
+        "q2 = TreeNode(1, None, TreeNode(2))\n",
+        "print(isSameTree(p2, q2))"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "id": "5897c29d-26f8-486a-878c-43c09ff25ce4",
+      "metadata": {
+        "trusted": true
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "False\n"
+          ]
+        }
+      ],
+      "source": [
+        "### Example 3\n",
+        "\n",
+        "#Input: p = [1,2,1], q = [1,1,2]\n",
+        "\n",
+        "p3 = TreeNode(1, TreeNode(2), TreeNode(1))\n",
+        "q3 = TreeNode(1, TreeNode(1), TreeNode(2))\n",
+        "print(isSameTree(p3, q3))"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "id": "7d9dd448-c5f5-4192-8aa5-7c70ec7f42e2",
+      "metadata": {},
+      "source": [
+        "## Time and Space Complexity Analysis\n",
+        "\n",
+        "**Time Complexity**\n",
+        "\n",
+        "The time complexity of the `isSameTree` function can be analyzed as follows:\n",
+        "\n",
+        "In the worst case, the function needs to visit every node in both trees once to determine if they are the same.\n",
+        "Since each node is visited exactly once, the time complexity is $O(n)$, where $n$ is the total number of nodes in the input trees.\n",
+        "\n",
+        "**Space Complexity**\n",
+        "The space complexity of the `isSameTree` function can be analyzed as follows:\n",
+        "\n",
+        "The space used by the function's call stack during recursion is proportional to the maximum depth of the binary trees.\n",
+        "In the worst case, when the trees are completely unbalanced (all nodes form a single branch), the maximum depth will be $n$, where $n$ is the total number of nodes in the input trees.\n",
+        "Therefore, the space complexity is $O(n)$ due to the recursive call stack.\n",
+        "In addition to the call stack, there is a small constant amount of space used for variables and comparisons within each recursive call, but this space is not significant in terms of the overall space complexity.\n",
+        "\n",
+        "**In summary:**\n",
+        "\n",
+        "+ Time Complexity: $O(n)$ where $n$ is the total number of nodes in the input trees.\n",
+        "+ Space Complexity: $O(n)$ due to the recursive call stack."
+      ]
+    }
+  ],
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