{ "data": { "question": { "questionId": "1692", "questionFrontendId": "1569", "categoryTitle": "Algorithms", "boundTopicId": 390487, "title": "Number of Ways to Reorder Array to Get Same BST", "titleSlug": "number-of-ways-to-reorder-array-to-get-same-bst", "content": "

Given an array nums that represents a permutation of integers from 1 to n. We are going to construct a binary search tree (BST) by inserting the elements of nums in order into an initially empty BST. Find the number of different ways to reorder nums so that the constructed BST is identical to that formed from the original array nums.

\n\n\n\n

Return the number of ways to reorder nums such that the BST formed is identical to the original BST formed from nums.

\n\n

Since the answer may be very large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: nums = [2,1,3]\nOutput: 1\nExplanation: 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
\n\n

Example 2:

\n\"\"\n
\nInput: nums = [3,4,5,1,2]\nOutput: 5\nExplanation: 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
\n\n

Example 3:

\n\"\"\n
\nInput: nums = [1,2,3]\nOutput: 0\nExplanation: There are no other orderings of nums that will yield the same BST.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "将子数组重新排序得到同一个二叉查找树的方案数", "translatedContent": "

给你一个数组 nums 表示 1 到 n 的一个排列。我们按照元素在 nums 中的顺序依次插入一个初始为空的二叉查找树（BST）。请你统计将 nums 重新排序后，统计满足如下条件的方案数：重排后得到的二叉查找树与 nums 原本数字顺序得到的二叉查找树相同。

\n\n

比方说，给你 nums = [2,1,3]，我们得到一棵 2 为根，1 为左孩子，3 为右孩子的树。数组 [2,3,1] 也能得到相同的 BST，但 [3,2,1] 会得到一棵不同的 BST 。

\n\n

请你返回重排 nums 后，与原数组 nums 得到相同二叉查找树的方案数。

\n\n

由于答案可能会很大，请将结果对 10^9 + 7 取余数。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
输入：nums = [2,1,3]\n输出：1\n解释：我们将 nums 重排， [2,3,1] 能得到相同的 BST 。没有其他得到相同 BST 的方案了。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
输入：nums = [3,4,5,1,2]\n输出：5\n解释：下面 5 个数组会得到相同的 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
\n\n

示例 3：

\n\n

\"\"

\n\n
输入：nums = [1,2,3]\n输出：0\n解释：没有别的排列顺序能得到相同的 BST 。\n
\n\n

示例 4：

\n\n

\"\"

\n\n
输入：nums = [3,1,2,5,4,6]\n输出：19\n
\n\n

示例  5：

\n\n
输入：nums = [9,4,2,1,3,6,5,7,8,14,11,10,12,13,16,15,17,18]\n输出：216212978\n解释：得到相同 BST 的方案数是 3216212999。将它对 10^9 + 7 取余后得到 216212978。\n
\n\n

 

\n\n

提示：

\n\n\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 40, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [], "langToValidPlayground": "{\"cpp\": true, \"java\": true, \"python\": true, \"python3\": true, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"ruby\": false, \"bash\": false, \"swift\": false, \"golang\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"kotlin\": false, \"rust\": false, \"php\": false, \"typescript\": false, \"racket\": false, \"erlang\": false, \"elixir\": false}", "topicTags": [ { "name": "Tree", "slug": "tree", "translatedName": "树", "__typename": "TopicTagNode" }, { "name": "Union Find", "slug": "union-find", "translatedName": "并查集", "__typename": "TopicTagNode" }, { "name": "Binary Search Tree", "slug": "binary-search-tree", "translatedName": "二叉搜索树", "__typename": "TopicTagNode" }, { "name": "Memoization", "slug": "memoization", "translatedName": "记忆化搜索", "__typename": "TopicTagNode" }, { "name": "Array", "slug": "array", "translatedName": "数组", "__typename": "TopicTagNode" }, { "name": "Math", "slug": "math", "translatedName": "数学", "__typename": "TopicTagNode" }, { "name": "Divide and Conquer", "slug": "divide-and-conquer", "translatedName": "分治", "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": "动态规划", "__typename": "TopicTagNode" }, { "name": "Binary Tree", "slug": "binary-tree", "translatedName": "二叉树", "__typename": "TopicTagNode" }, { "name": "Combinatorics", "slug": "combinatorics", "translatedName": "组合数学", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int numOfWays(vector& 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 \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def numOfWays(self, nums: List[int]) -> int:", "__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 {\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\": \"2.3K\", \"totalSubmission\": \"4.9K\", \"totalAcceptedRaw\": 2343, \"totalSubmissionRaw\": 4943, \"acRate\": \"47.4%\"}", "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, "envInfo": "{\"cpp\":[\"C++\",\"

\\u7248\\u672c\\uff1aclang 11<\\/code> \\u91c7\\u7528\\u6700\\u65b0C++ 17\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O2<\\/code>\\u7ea7\\u4f18\\u5316\\u3002AddressSanitizer<\\/a> \\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\"

\\u7248\\u672c\\uff1aOpenJDK 17<\\/code>\\u3002\\u53ef\\u4ee5\\u4f7f\\u7528Java 8\\u7684\\u7279\\u6027\\u4f8b\\u5982\\uff0clambda expressions \\u548c stream API\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\"

\\u7248\\u672c\\uff1a Python 2.7.12<\\/code><\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\"

\\u7248\\u672c\\uff1aGCC 8.2<\\/code>\\uff0c\\u91c7\\u7528GNU99\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O1<\\/code>\\u7ea7\\u4f18\\u5316\\u3002 AddressSanitizer<\\/a>\\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n

1. \\u5f80\\u54c8\\u5e0c\\u8868\\u4e2d\\u6dfb\\u52a0\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\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
2. \\u5728\\u54c8\\u5e0c\\u8868\\u4e2d\\u67e5\\u627e\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\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
3. \\u4ece\\u54c8\\u5e0c\\u8868\\u4e2d\\u5220\\u9664\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\"],\"csharp\":[\"C#\",\"
C# 10<\\/a> \\u8fd0\\u884c\\u5728 .NET 6 \\u4e0a<\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u7f16\\u8bd1\\u65f6\\u9ed8\\u8ba4\\u5f00\\u542f\\u4e86debug\\u6807\\u8bb0(\\/debug:pdbonly<\\/code>)\\u3002<\\/p>\"],\"javascript\":[\"JavaScript\",\"
\\u7248\\u672c\\uff1aNode.js 16.13.2<\\/code><\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u6267\\u884c\\u65f6\\u5c06\\u5e26\\u4e0a --harmony<\\/code> \\u6807\\u8bb0\\u6765\\u5f00\\u542f \\u65b0\\u7248ES6\\u7279\\u6027<\\/a>\\u3002<\\/p>\\r\\n\\r\\n
lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n
 \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528  datastructures-js\\/priority-queue<\\/a> \\u548c  datastructures-js\\/queue<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"
\\u4f7f\\u7528Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n
\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"
\\u7248\\u672c\\uff1aSwift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n
\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"
\\u7248\\u672c\\uff1aGo 1.17<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"
\\u7248\\u672c\\uff1aPython 3.10<\\/code><\\/p>\\r\\n\\r\\n
\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n
\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"
\\u7248\\u672c\\uff1aScala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"
\\u7248\\u672c\\uff1aKotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"
\\u7248\\u672c\\uff1arust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 crates.io \\u7684 rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"
PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n
With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"
TypeScript 4.5.4<\\/p>\\r\\n\\r\\n
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\"],\"racket\":[\"Racket\",\"
Racket CS<\\/a> v8.3<\\/p>\\r\\n\\r\\n
\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n
\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"]}",
            "book": null,
            "isSubscribed": false,
            "isDailyQuestion": false,
            "dailyRecordStatus": null,
            "editorType": "CKEDITOR",
            "ugcQuestionId": null,
            "style": "LEETCODE",
            "exampleTestcases": "[2,1,3]\n[3,4,5,1,2]\n[1,2,3]",
            "__typename": "QuestionNode"
        }
    }
}