{ "data": { "question": { "questionId": "2249", "questionFrontendId": "2145", "categoryTitle": "Algorithms", "boundTopicId": 1223350, "title": "Count the Hidden Sequences", "titleSlug": "count-the-hidden-sequences", "content": "

You are given a 0-indexed array of n integers differences, which describes the differences between each pair of consecutive integers of a hidden sequence of length (n + 1). More formally, call the hidden sequence hidden, then we have that differences[i] = hidden[i + 1] - hidden[i].

\n\n

You are further given two integers lower and upper that describe the inclusive range of values [lower, upper] that the hidden sequence can contain.

\n\n\n\n

Return the number of possible hidden sequences there are. If there are no possible sequences, return 0.

\n\n

 

\n

Example 1:

\n\n
\nInput: differences = [1,-3,4], lower = 1, upper = 6\nOutput: 2\nExplanation: The possible hidden sequences are:\n- [3, 4, 1, 5]\n- [4, 5, 2, 6]\nThus, we return 2.\n
\n\n

Example 2:

\n\n
\nInput: differences = [3,-4,5,1,-2], lower = -4, upper = 5\nOutput: 4\nExplanation: 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
\n\n

Example 3:

\n\n
\nInput: differences = [4,-7,2], lower = 3, upper = 6\nOutput: 0\nExplanation: There are no possible hidden sequences. Thus, we return 0.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "统计隐藏数组数目", "translatedContent": "

给你一个下标从 0 开始且长度为 n 的整数数组 differences ，它表示一个长度为 n + 1 的 隐藏 数组 相邻 元素之间的 差值 。更正式的表述为：我们将隐藏数组记作 hidden ，那么 differences[i] = hidden[i + 1] - hidden[i] 。

\n\n

同时给你两个整数 lower 和 upper ，它们表示隐藏数组中所有数字的值都在 闭 区间 [lower, upper] 之间。

\n\n\n\n

请你返回 符合 要求的隐藏数组的数目。如果没有符合要求的隐藏数组，请返回 0 。

\n\n

 

\n\n

示例 1：

\n\n
输入：differences = [1,-3,4], lower = 1, upper = 6\n输出：2\n解释：符合要求的隐藏数组为：\n- [3, 4, 1, 5]\n- [4, 5, 2, 6]\n所以返回 2 。\n
\n\n

示例 2：

\n\n
输入：differences = [3,-4,5,1,-2], lower = -4, upper = 5\n输出：4\n解释：符合要求的隐藏数组为：\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]\n所以返回 4 。\n
\n\n

示例 3：

\n\n
输入：differences = [4,-7,2], lower = 3, upper = 6\n输出：0\n解释：没有符合要求的隐藏数组，所以返回 0 。\n
\n\n

 

\n\n

提示：

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exact-integer? exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec number_of_arrays(Differences :: [integer()], Lower :: integer(), Upper :: integer()) -> integer().\nnumber_of_arrays(Differences, Lower, Upper) ->\n .", "__typename": "CodeSnippetNode" }, { "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", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"5.9K\", \"totalSubmission\": \"16.2K\", \"totalAcceptedRaw\": 5896, \"totalSubmissionRaw\": 16250, \"acRate\": \"36.3%\"}", "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, "status": null, "sampleTestCase": "[1,-3,4]\n1\n6", "metaData": "{\n \"name\": \"numberOfArrays\",\n \"params\": [\n {\n \"name\": \"differences\",\n \"type\": \"integer[]\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"lower\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"upper\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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