leetcode-problemset/leetcode/originData/find-all-possible-stable-binary-arrays-ii.json

{
    "data": {
        "question": {
            "questionId": "3407",
            "questionFrontendId": "3130",
            "boundTopicId": null,
            "title": "Find All Possible Stable Binary Arrays II",
            "titleSlug": "find-all-possible-stable-binary-arrays-ii",
            "content": "<p>You are given 3 positive integers <code>zero</code>, <code>one</code>, and <code>limit</code>.</p>\n\n<p>A <span data-keyword=\"binary-array\">binary array</span> <code>arr</code> is called <strong>stable</strong> if:</p>\n\n<ul>\n\t<li>The number of occurrences of 0 in <code>arr</code> is <strong>exactly </strong><code>zero</code>.</li>\n\t<li>The number of occurrences of 1 in <code>arr</code> is <strong>exactly</strong> <code>one</code>.</li>\n\t<li>Each <span data-keyword=\"subarray-nonempty\">subarray</span> of <code>arr</code> with a size greater than <code>limit</code> must contain <strong>both </strong>0 and 1.</li>\n</ul>\n\n<p>Return the <em>total</em> number of <strong>stable</strong> binary arrays.</p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">zero = 1, one = 1, limit = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The two possible stable binary arrays are <code>[1,0]</code> and <code>[0,1]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">zero = 1, one = 2, limit = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only possible stable binary array is <code>[1,0,1]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">zero = 3, one = 3, limit = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">14</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>All the possible stable binary arrays are <code>[0,0,1,0,1,1]</code>, <code>[0,0,1,1,0,1]</code>, <code>[0,1,0,0,1,1]</code>, <code>[0,1,0,1,0,1]</code>, <code>[0,1,0,1,1,0]</code>, <code>[0,1,1,0,0,1]</code>, <code>[0,1,1,0,1,0]</code>, <code>[1,0,0,1,0,1]</code>, <code>[1,0,0,1,1,0]</code>, <code>[1,0,1,0,0,1]</code>, <code>[1,0,1,0,1,0]</code>, <code>[1,0,1,1,0,0]</code>, <code>[1,1,0,0,1,0]</code>, and <code>[1,1,0,1,0,0]</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= zero, one, limit &lt;= 1000</code></li>\n</ul>\n",
            "translatedTitle": null,
            "translatedContent": null,
            "isPaidOnly": false,
            "difficulty": "Hard",
            "likes": 31,
            "dislikes": 6,
            "isLiked": null,
            "similarQuestions": "[{\"title\": \"Contiguous Array\", \"titleSlug\": \"contiguous-array\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Binary Subarrays With Sum\", \"titleSlug\": \"binary-subarrays-with-sum\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]",
            "exampleTestcases": "1\n1\n2\n1\n2\n1\n3\n3\n2",
            "categoryTitle": "Algorithms",
            "contributors": [],
            "topicTags": [],
            "companyTagStats": null,
            "codeSnippets": [
                {
                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\npublic:\n    int numberOfStableArrays(int zero, int one, int limit) {\n        \n    }\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Java",
                    "langSlug": "java",
                    "code": "class Solution {\n    public int numberOfStableArrays(int zero, int one, int limit) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def numberOfStableArrays(self, zero, one, limit):\n        \"\"\"\n        :type zero: int\n        :type one: int\n        :type limit: int\n        :rtype: int\n        \"\"\"\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\n    def numberOfStableArrays(self, zero: int, one: int, limit: int) -> int:\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "int numberOfStableArrays(int zero, int one, int limit) {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int NumberOfStableArrays(int zero, int one, int limit) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number} zero\n * @param {number} one\n * @param {number} limit\n * @return {number}\n */\nvar numberOfStableArrays = function(zero, one, limit) {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function numberOfStableArrays(zero: number, one: number, limit: number): number {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer $zero\n     * @param Integer $one\n     * @param Integer $limit\n     * @return Integer\n     */\n    function numberOfStableArrays($zero, $one, $limit) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func numberOfStableArrays(_ zero: Int, _ one: Int, _ limit: Int) -> Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun numberOfStableArrays(zero: Int, one: Int, limit: Int): Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Dart",
                    "langSlug": "dart",
                    "code": "class Solution {\n  int numberOfStableArrays(int zero, int one, int limit) {\n    \n  }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func numberOfStableArrays(zero int, one int, limit int) int {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {Integer} zero\n# @param {Integer} one\n# @param {Integer} limit\n# @return {Integer}\ndef number_of_stable_arrays(zero, one, limit)\n    \nend",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def numberOfStableArrays(zero: Int, one: Int, limit: Int): Int = {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn number_of_stable_arrays(zero: i32, one: i32, limit: i32) -> i32 {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (number-of-stable-arrays zero one limit)\n  (-> exact-integer? exact-integer? exact-integer? exact-integer?)\n  )",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec number_of_stable_arrays(Zero :: integer(), One :: integer(), Limit :: integer()) -> integer().\nnumber_of_stable_arrays(Zero, One, Limit) ->\n  .",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec number_of_stable_arrays(zero :: integer, one :: integer, limit :: integer) :: integer\n  def number_of_stable_arrays(zero, one, limit) do\n    \n  end\nend",
                    "__typename": "CodeSnippetNode"
                }
            ],
            "stats": "{\"totalAccepted\": \"1.3K\", \"totalSubmission\": \"5.6K\", \"totalAcceptedRaw\": 1335, \"totalSubmissionRaw\": 5648, \"acRate\": \"23.6%\"}",
            "hints": [
                "Let <code>dp[x][y][z = 0/1]</code> be the number of stable arrays with exactly <code>x</code> zeros, <code>y</code> ones, and the last element is <code>z</code>. (0 or 1).\r\n<code>dp[x][y][0] + dp[x][y][1]</code> is the answer for given <code>(x, y)</code>.",
                "If we have already placed <code>x</code> 1 and <code>y</code> 0, if we place a group of <code>k</code> 0, the number of ways is <code>dp[x-k][y][1]</code>. We can place a group with size <code>i</code>, where <code>i</code> varies from 1 to <code>min(limit, zero - x)</code>.\r\nSimilarly, we can solve by placing a group of ones.",
                "Speed up the calculation using prefix arrays to store the sum of <code>dp</code> states."
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "1\n1\n2",
            "metaData": "{\n  \"name\": \"numberOfStableArrays\",\n  \"params\": [\n    {\n      \"name\": \"zero\",\n      \"type\": \"integer\"\n    },\n    {\n      \"type\": \"integer\",\n      \"name\": \"one\"\n    },\n    {\n      \"type\": \"integer\",\n      \"name\": \"limit\"\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 17 </code> using the latest C++ 20 standard, and <code>libstdc++</code> provided by GCC 11.</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 21</code>. Using compile arguments: <code>--enable-preview --release 21</code></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 11</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one 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>\\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://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-12\\\" target=\\\"_blank\\\">C# 12</a> with .NET 8 runtime</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 20.10.0</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 5.4.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/blob/v5/README.md\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\\\"https://github.com/datastructures-js/queue/tree/v4.2.3\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.2</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 5.9</code>.</p>\\r\\n\\r\\n<p>You may use <a href=\\\"https://github.com/apple/swift-algorithms/tree/1.2.0\\\" target=\\\"_blank\\\">swift-algorithms 1.2.0</a> and <a href=\\\"https://github.com/apple/swift-collections/tree/1.1.0\\\" target=\\\"_blank\\\">swift-collections 1.1.0</a>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.21</code></p>\\r\\n<p>Support <a href=\\\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\\\" target=\\\"_blank\\\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\\\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\\\" target=\\\"_blank\\\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.11</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 3.3.1</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.9.0</code>.</p>\\r\\n\\r\\n<p>We are using an experimental compiler provided by JetBrains.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.74.1</code>. Your code will be compiled with <code>opt-level</code> 2.</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 8.2</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 5.1.6, Node.js 20.10.0</code>.</p>\\r\\n\\r\\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022</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 ES2022 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><a href=\\\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS</a> v8.11</p>\\r\\n\\r\\n<p>Using <code>#lang racket</code></p>\\r\\n\\r\\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 26\"], \"elixir\": [\"Elixir\", \"Elixir 1.15 with Erlang/OTP 26\"], \"dart\": [\"Dart\", \"<p>Dart 3.2</p>\\r\\n\\r\\n<p>Your code will be run directly without compiling</p>\"]}",
            "libraryUrl": null,
            "adminUrl": null,
            "challengeQuestion": null,
            "__typename": "QuestionNode"
        }
    }
}