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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 class=\"example\">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 class=\"example\">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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                    "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": "/**\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": "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": "# @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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            "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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