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{
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"title": "House Robber IV",
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"content": "<p>There are several consecutive houses along a street, each of which has some money inside. There is also a robber, who wants to steal money from the homes, but he <strong>refuses to steal from adjacent homes</strong>.</p>\n\n<p>The <strong>capability</strong> of the robber is the maximum amount of money he steals from one house of all the houses he robbed.</p>\n\n<p>You are given an integer array <code>nums</code> representing how much money is stashed in each house. More formally, the <code>i<sup>th</sup></code> house from the left has <code>nums[i]</code> dollars.</p>\n\n<p>You are also given an integer <code>k</code>, representing the <strong>minimum</strong> number of houses the robber will steal from. It is always possible to steal at least <code>k</code> houses.</p>\n\n<p>Return <em>the <strong>minimum</strong> capability of the robber out of all the possible ways to steal at least </em><code>k</code><em> houses</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,5,9], k = 2\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> \nThere are three ways to rob at least 2 houses:\n- Rob the houses at indices 0 and 2. Capability is max(nums[0], nums[2]) = 5.\n- Rob the houses at indices 0 and 3. Capability is max(nums[0], nums[3]) = 9.\n- Rob the houses at indices 1 and 3. Capability is max(nums[1], nums[3]) = 9.\nTherefore, we return min(5, 9, 9) = 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,7,9,3,1], k = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are 7 ways to rob the houses. The way which leads to minimum capability is to rob the house at index 0 and 4. Return max(nums[0], nums[4]) = 2.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= (nums.length + 1)/2</code></li>\n</ul>\n",
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"hints": [
"Can we use binary search to find the minimum value of a non-contiguous subsequence of a given size k?",
"Initialize the search range with the minimum and maximum elements of the input array.",
"Use a check function to determine if it is possible to select k non-consecutive elements that are less than or equal to the current \"guess\" value.",
"Adjust the search range based on the outcome of the check function, until the range converges and the minimum value is found."
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