leetcode-problemset/leetcode/originData/maximum-value-at-a-given-index-in-a-bounded-array.json

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            "title": "Maximum Value at a Given Index in a Bounded Array",
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            "content": "<p>You are given three positive integers:&nbsp;<code>n</code>, <code>index</code>, and <code>maxSum</code>. You want to construct an array <code>nums</code> (<strong>0-indexed</strong>)<strong> </strong>that satisfies the following conditions:</p>\n\n<ul>\n\t<li><code>nums.length == n</code></li>\n\t<li><code>nums[i]</code> is a <strong>positive</strong> integer where <code>0 &lt;= i &lt; n</code>.</li>\n\t<li><code>abs(nums[i] - nums[i+1]) &lt;= 1</code> where <code>0 &lt;= i &lt; n-1</code>.</li>\n\t<li>The sum of all the elements of <code>nums</code> does not exceed <code>maxSum</code>.</li>\n\t<li><code>nums[index]</code> is <strong>maximized</strong>.</li>\n</ul>\n\n<p>Return <code>nums[index]</code><em> of the constructed array</em>.</p>\n\n<p>Note that <code>abs(x)</code> equals <code>x</code> if <code>x &gt;= 0</code>, and <code>-x</code> otherwise.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, index = 2,  maxSum = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> nums = [1,2,<u><strong>2</strong></u>,1] is one array that satisfies all the conditions.\nThere are no arrays that satisfy all the conditions and have nums[2] == 3, so 2 is the maximum nums[2].\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 6, index = 1,  maxSum = 10\n<strong>Output:</strong> 3\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= maxSum &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= index &lt; n</code></li>\n</ul>\n",
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                    "name": "Binary Search",
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                    "code": "class Solution {\npublic:\n    int maxValue(int n, int index, int maxSum) {\n        \n    }\n};",
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                    "code": "class Solution(object):\n    def maxValue(self, n, index, maxSum):\n        \"\"\"\n        :type n: int\n        :type index: int\n        :type maxSum: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "class Solution:\n    def maxValue(self, n: int, index: int, maxSum: int) -> int:\n        ",
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                    "code": "\n\nint maxValue(int n, int index, int maxSum){\n\n}",
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                    "lang": "C#",
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                    "code": "public class Solution {\n    public int MaxValue(int n, int index, int maxSum) {\n        \n    }\n}",
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                    "code": "/**\n * @param {number} n\n * @param {number} index\n * @param {number} maxSum\n * @return {number}\n */\nvar maxValue = function(n, index, maxSum) {\n    \n};",
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                    "code": "# @param {Integer} n\n# @param {Integer} index\n# @param {Integer} max_sum\n# @return {Integer}\ndef max_value(n, index, max_sum)\n    \nend",
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                    "code": "class Solution {\n    func maxValue(_ n: Int, _ index: Int, _ maxSum: Int) -> Int {\n        \n    }\n}",
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                    "lang": "Go",
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                    "code": "func maxValue(n int, index int, maxSum int) int {\n    \n}",
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                    "lang": "Scala",
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                    "code": "object Solution {\n    def maxValue(n: Int, index: Int, maxSum: Int): Int = {\n        \n    }\n}",
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                    "lang": "Kotlin",
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                    "code": "class Solution {\n    fun maxValue(n: Int, index: Int, maxSum: Int): Int {\n        \n    }\n}",
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                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn max_value(n: i32, index: i32, max_sum: i32) -> i32 {\n        \n    }\n}",
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                    "lang": "PHP",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer $n\n     * @param Integer $index\n     * @param Integer $maxSum\n     * @return Integer\n     */\n    function maxValue($n, $index, $maxSum) {\n        \n    }\n}",
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                    "code": "function maxValue(n: number, index: number, maxSum: number): number {\n\n};",
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                    "lang": "Racket",
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                    "code": "(define/contract (max-value n index maxSum)\n  (-> exact-integer? exact-integer? exact-integer? exact-integer?)\n\n  )",
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                    "lang": "Erlang",
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                    "code": "-spec max_value(N :: integer(), Index :: integer(), MaxSum :: integer()) -> integer().\nmax_value(N, Index, MaxSum) ->\n  .",
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                    "lang": "Elixir",
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                    "code": "defmodule Solution do\n  @spec max_value(n :: integer, index :: integer, max_sum :: integer) :: integer\n  def max_value(n, index, max_sum) do\n\n  end\nend",
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            "hints": [
                "What if the problem was instead determining if you could generate a valid array with nums[index] == target?",
                "To generate the array, set nums[index] to target, nums[index-i] to target-i, and nums[index+i] to target-i. Then, this will give the minimum possible sum, so check if the sum is less than or equal to maxSum.",
                "n is too large to actually generate the array, so you can use the formula 1 + 2 + ... + n = n * (n+1) / 2 to quickly find the sum of nums[0...index] and nums[index...n-1].",
                "Binary search for the target. If it is possible, then move the lower bound up. Otherwise, move the upper bound down."
            ],
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