{ "data": { "question": { "questionId": "939", "questionFrontendId": "903", "boundTopicId": null, "title": "Valid Permutations for DI Sequence", "titleSlug": "valid-permutations-for-di-sequence", "content": "<p>You are given a string <code>s</code> of length <code>n</code> where <code>s[i]</code> is either:</p>\n\n<ul>\n\t<li><code>'D'</code> means decreasing, or</li>\n\t<li><code>'I'</code> means increasing.</li>\n</ul>\n\n<p>A permutation <code>perm</code> of <code>n + 1</code> integers of all the integers in the range <code>[0, n]</code> is called a <strong>valid permutation</strong> if for all valid <code>i</code>:</p>\n\n<ul>\n\t<li>If <code>s[i] == 'D'</code>, then <code>perm[i] > perm[i + 1]</code>, and</li>\n\t<li>If <code>s[i] == 'I'</code>, then <code>perm[i] < perm[i + 1]</code>.</li>\n</ul>\n\n<p>Return <em>the number of <strong>valid permutations</strong> </em><code>perm</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = "DID"\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The 5 valid permutations of (0, 1, 2, 3) are:\n(1, 0, 3, 2)\n(2, 0, 3, 1)\n(2, 1, 3, 0)\n(3, 0, 2, 1)\n(3, 1, 2, 0)\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = "D"\n<strong>Output:</strong> 1\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == s.length</code></li>\n\t<li><code>1 <= n <= 200</code></li>\n\t<li><code>s[i]</code> is either <code>'I'</code> or <code>'D'</code>.</li>\n</ul>\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 442, "dislikes": 35, "isLiked": null, "similarQuestions": "[]", "exampleTestcases": "\"DID\"\n\"D\"", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int numPermsDISequence(string s) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int numPermsDISequence(String s) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def numPermsDISequence(self, s):\n \"\"\"\n :type s: str\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def numPermsDISequence(self, s: str) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\nint numPermsDISequence(char * s){\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int NumPermsDISequence(string s) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {string} s\n * @return {number}\n */\nvar numPermsDISequence = function(s) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {String} s\n# @return {Integer}\ndef num_perms_di_sequence(s)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func numPermsDISequence(_ s: String) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func numPermsDISequence(s string) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def numPermsDISequence(s: String): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun numPermsDISequence(s: String): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn num_perms_di_sequence(s: String) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param String $s\n * @return Integer\n */\n function numPermsDISequence($s) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function numPermsDISequence(s: string): number {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (num-perms-di-sequence s)\n (-> string? exact-integer?)\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec num_perms_di_sequence(S :: unicode:unicode_binary()) -> integer().\nnum_perms_di_sequence(S) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec num_perms_di_sequence(s :: String.t) :: integer\n def num_perms_di_sequence(s) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"10.5K\", \"totalSubmission\": \"18.5K\", \"totalAcceptedRaw\": 10534, \"totalSubmissionRaw\": 18483, \"acRate\": \"57.0%\"}", "hints": [], "solution": null, "status": null, "sampleTestCase": "\"DID\"", "metaData": "{\n \"name\": \"numPermsDISequence\",\n \"params\": [\n {\n \"name\": \"s\",\n \"type\": \"string\"\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" } } }