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        "question": {
            "questionId": "2249",
            "questionFrontendId": "2145",
            "boundTopicId": null,
            "title": "Count the Hidden Sequences",
            "titleSlug": "count-the-hidden-sequences",
            "content": "<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>differences</code>, which describes the <strong>differences </strong>between each pair of <strong>consecutive </strong>integers of a <strong>hidden</strong> sequence of length <code>(n + 1)</code>. More formally, call the hidden sequence <code>hidden</code>, then we have that <code>differences[i] = hidden[i + 1] - hidden[i]</code>.</p>\n\n<p>You are further given two integers <code>lower</code> and <code>upper</code> that describe the <strong>inclusive</strong> range of values <code>[lower, upper]</code> that the hidden sequence can contain.</p>\n\n<ul>\n\t<li>For example, given <code>differences = [1, -3, 4]</code>, <code>lower = 1</code>, <code>upper = 6</code>, the hidden sequence is a sequence of length <code>4</code> whose elements are in between <code>1</code> and <code>6</code> (<strong>inclusive</strong>).\n\n\t<ul>\n\t\t<li><code>[3, 4, 1, 5]</code> and <code>[4, 5, 2, 6]</code> are possible hidden sequences.</li>\n\t\t<li><code>[5, 6, 3, 7]</code> is not possible since it contains an element greater than <code>6</code>.</li>\n\t\t<li><code>[1, 2, 3, 4]</code> is not possible since the differences are not correct.</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>Return <em>the number of <strong>possible</strong> hidden sequences there are.</em> If there are no possible sequences, return <code>0</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [1,-3,4], lower = 1, upper = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The possible hidden sequences are:\n- [3, 4, 1, 5]\n- [4, 5, 2, 6]\nThus, we return 2.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [3,-4,5,1,-2], lower = -4, upper = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The possible hidden sequences are:\n- [-3, 0, -4, 1, 2, 0]\n- [-2, 1, -3, 2, 3, 1]\n- [-1, 2, -2, 3, 4, 2]\n- [0, 3, -1, 4, 5, 3]\nThus, we return 4.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [4,-7,2], lower = 3, upper = 6\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no possible hidden sequences. Thus, we return 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == differences.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= differences[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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            "exampleTestcases": "[1,-3,4]\n1\n6\n[3,-4,5,1,-2]\n-4\n5\n[4,-7,2]\n3\n6",
            "categoryTitle": "Algorithms",
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                {
                    "name": "Array",
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                {
                    "name": "Prefix Sum",
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                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\npublic:\n    int numberOfArrays(vector<int>& differences, int lower, int upper) {\n        \n    }\n};",
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                    "lang": "Java",
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                    "code": "class Solution {\n    public int numberOfArrays(int[] differences, int lower, int upper) {\n        \n    }\n}",
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                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def numberOfArrays(self, differences, lower, upper):\n        \"\"\"\n        :type differences: List[int]\n        :type lower: int\n        :type upper: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "lang": "Python3",
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                    "code": "class Solution:\n    def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:\n        ",
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                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "\n\nint numberOfArrays(int* differences, int differencesSize, int lower, int upper){\n\n}",
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                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int NumberOfArrays(int[] differences, int lower, int upper) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
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                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number[]} differences\n * @param {number} lower\n * @param {number} upper\n * @return {number}\n */\nvar numberOfArrays = function(differences, lower, upper) {\n    \n};",
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                    "lang": "Ruby",
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                    "code": "# @param {Integer[]} differences\n# @param {Integer} lower\n# @param {Integer} upper\n# @return {Integer}\ndef number_of_arrays(differences, lower, upper)\n    \nend",
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                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func numberOfArrays(_ differences: [Int], _ lower: Int, _ upper: Int) -> Int {\n        \n    }\n}",
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                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func numberOfArrays(differences []int, lower int, upper int) int {\n    \n}",
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                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def numberOfArrays(differences: Array[Int], lower: Int, upper: Int): Int = {\n        \n    }\n}",
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                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun numberOfArrays(differences: IntArray, lower: Int, upper: Int): Int {\n        \n    }\n}",
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                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn number_of_arrays(differences: Vec<i32>, lower: i32, upper: i32) -> i32 {\n        \n    }\n}",
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                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $differences\n     * @param Integer $lower\n     * @param Integer $upper\n     * @return Integer\n     */\n    function numberOfArrays($differences, $lower, $upper) {\n        \n    }\n}",
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                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function numberOfArrays(differences: number[], lower: number, upper: number): number {\n\n};",
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                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (number-of-arrays differences lower upper)\n  (-> (listof exact-integer?) exact-integer? exact-integer? exact-integer?)\n\n  )",
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                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec number_of_arrays(Differences :: [integer()], Lower :: integer(), Upper :: integer()) -> integer().\nnumber_of_arrays(Differences, Lower, Upper) ->\n  .",
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                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec number_of_arrays(differences :: [integer], lower :: integer, upper :: integer) :: integer\n  def number_of_arrays(differences, lower, upper) do\n\n  end\nend",
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            "hints": [
                "Fix the first element of the hidden sequence to any value x and ignore the given bounds. Notice that we can then determine all the other elements of the sequence by using the differences array.",
                "We will also be able to determine the difference between the minimum and maximum elements of the sequence. Notice that the value of x does not affect this.",
                "We now have the ‘range’ of the sequence (difference between min and max element), we can then calculate how many ways there are to fit this range into the given range of lower to upper.",
                "Answer is (upper - lower + 1) - (range of sequence)"
            ],
            "solution": null,
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            "sampleTestCase": "[1,-3,4]\n1\n6",
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