{
    "data": {
        "question": {
            "questionId": "1692",
            "questionFrontendId": "1569",
            "boundTopicId": null,
            "title": "Number of Ways to Reorder Array to Get Same BST",
            "titleSlug": "number-of-ways-to-reorder-array-to-get-same-bst",
            "content": "<p>Given an array <code>nums</code> that represents a permutation of integers from <code>1</code> to <code>n</code>. We are going to construct a binary search tree (BST) by inserting the elements of <code>nums</code> in order into an initially empty BST. Find the number of different ways to reorder <code>nums</code> so that the constructed BST is identical to that formed from the original array <code>nums</code>.</p>\n\n<ul>\n\t<li>For example, given <code>nums = [2,1,3]</code>, we will have 2 as the root, 1 as a left child, and 3 as a right child. The array <code>[2,3,1]</code> also yields the same BST but <code>[3,2,1]</code> yields a different BST.</li>\n</ul>\n\n<p>Return <em>the number of ways to reorder</em> <code>nums</code> <em>such that the BST formed is identical to the original BST formed from</em> <code>nums</code>.</p>\n\n<p>Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/bb.png\" style=\"width: 121px; height: 101px;\" />\n<pre>\n<strong>Input:</strong> nums = [2,1,3]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can reorder nums to be [2,3,1] which will yield the same BST. There are no other ways to reorder nums which will yield the same BST.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/ex1.png\" style=\"width: 241px; height: 161px;\" />\n<pre>\n<strong>Input:</strong> nums = [3,4,5,1,2]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The following 5 arrays will yield the same BST: \n[3,1,2,4,5]\n[3,1,4,2,5]\n[3,1,4,5,2]\n[3,4,1,2,5]\n[3,4,1,5,2]\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/ex4.png\" style=\"width: 121px; height: 161px;\" />\n<pre>\n<strong>Input:</strong> nums = [1,2,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no other orderings of nums that will yield the same BST.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= nums.length</code></li>\n\t<li>All integers in <code>nums</code> are <strong>distinct</strong>.</li>\n</ul>\n",
            "translatedTitle": null,
            "translatedContent": null,
            "isPaidOnly": false,
            "difficulty": "Hard",
            "likes": 389,
            "dislikes": 42,
            "isLiked": null,
            "similarQuestions": "[]",
            "exampleTestcases": "[2,1,3]\n[3,4,5,1,2]\n[1,2,3]",
            "categoryTitle": "Algorithms",
            "contributors": [],
            "topicTags": [
                {
                    "name": "Array",
                    "slug": "array",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Math",
                    "slug": "math",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Divide and Conquer",
                    "slug": "divide-and-conquer",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Dynamic Programming",
                    "slug": "dynamic-programming",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Tree",
                    "slug": "tree",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Union Find",
                    "slug": "union-find",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Binary Search Tree",
                    "slug": "binary-search-tree",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Memoization",
                    "slug": "memoization",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Combinatorics",
                    "slug": "combinatorics",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Binary Tree",
                    "slug": "binary-tree",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                }
            ],
            "companyTagStats": null,
            "codeSnippets": [
                {
                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\npublic:\n    int numOfWays(vector<int>& nums) {\n        \n    }\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Java",
                    "langSlug": "java",
                    "code": "class Solution {\n    public int numOfWays(int[] nums) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def numOfWays(self, nums):\n        \"\"\"\n        :type nums: List[int]\n        :rtype: int\n        \"\"\"\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\n    def numOfWays(self, nums: List[int]) -> int:\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "\n\nint numOfWays(int* nums, int numsSize){\n\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int NumOfWays(int[] nums) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number[]} nums\n * @return {number}\n */\nvar numOfWays = function(nums) {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {Integer[]} nums\n# @return {Integer}\ndef num_of_ways(nums)\n    \nend",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func numOfWays(_ nums: [Int]) -> Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func numOfWays(nums []int) int {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def numOfWays(nums: Array[Int]): Int = {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun numOfWays(nums: IntArray): Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn num_of_ways(nums: Vec<i32>) -> i32 {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $nums\n     * @return Integer\n     */\n    function numOfWays($nums) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function numOfWays(nums: number[]): number {\n\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (num-of-ways nums)\n  (-> (listof exact-integer?) exact-integer?)\n\n  )",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec num_of_ways(Nums :: [integer()]) -> integer().\nnum_of_ways(Nums) ->\n  .",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec num_of_ways(nums :: [integer]) :: integer\n  def num_of_ways(nums) do\n\n  end\nend",
                    "__typename": "CodeSnippetNode"
                }
            ],
            "stats": "{\"totalAccepted\": \"9.2K\", \"totalSubmission\": \"18.8K\", \"totalAcceptedRaw\": 9223, \"totalSubmissionRaw\": 18771, \"acRate\": \"49.1%\"}",
            "hints": [
                "Use a divide and conquer strategy.",
                "The first number will always be the root. Consider the numbers smaller and larger than the root separately. When merging the results together, how many ways can you order x elements in x+y positions?"
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "[2,1,3]",
            "metaData": "{\n  \"name\": \"numOfWays\",\n  \"params\": [\n    {\n      \"name\": \"nums\",\n      \"type\": \"integer[]\"\n    }\n  ],\n  \"return\": {\n    \"type\": \"integer\"\n  }\n}",
            "judgerAvailable": true,
            "judgeType": "large",
            "mysqlSchemas": [],
            "enableRunCode": true,
            "enableTestMode": false,
            "enableDebugger": true,
            "envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code> OpenJDK 17 </code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu99 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n    int id;            /* we'll use this field as the key */\\r\\n    char name[10];\\r\\n    UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n    HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n    struct hash_entry *s;\\r\\n    HASH_FIND_INT(users, &user_id, s);\\r\\n    return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https://github.com/datastructures-js/queue\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</code></p>\\r\\n\\r\\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>\"], \"swift\": [\"Swift\", \"<p><code>Swift 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.17.6</code>.</p>\\r\\n\\r\\n<p>Support <a href=\\\"https://godoc.org/github.com/emirpasic/gods\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/3/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/3/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/3/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\"], \"scala\": [\"Scala\", \"<p><code>Scala 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.3.10</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 4.5.4, Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES2020 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 24.2\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.0 with Erlang/OTP 24.2\"]}",
            "libraryUrl": null,
            "adminUrl": null,
            "challengeQuestion": null,
            "__typename": "QuestionNode"
        }
    }
}