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https://gitee.com/coder-xiaomo/leetcode-problemset
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189 lines
19 KiB
JSON
189 lines
19 KiB
JSON
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"title": "Minimize Length of Array Using Operations",
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"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> containing <strong>positive</strong> integers.</p>\n\n<p>Your task is to <strong>minimize</strong> the length of <code>nums</code> by performing the following operations <strong>any</strong> number of times (including zero):</p>\n\n<ul>\n\t<li>Select <strong>two</strong> <strong>distinct</strong> indices <code>i</code> and <code>j</code> from <code>nums</code>, such that <code>nums[i] > 0</code> and <code>nums[j] > 0</code>.</li>\n\t<li>Insert the result of <code>nums[i] % nums[j]</code> at the end of <code>nums</code>.</li>\n\t<li>Delete the elements at indices <code>i</code> and <code>j</code> from <code>nums</code>.</li>\n</ul>\n\n<p>Return <em>an integer denoting the <strong>minimum</strong> <strong>length</strong> of </em><code>nums</code><em> after performing the operation any number of times.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,4,3,1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows:\nOperation 1: Select indices 2 and 1, insert nums[2] % nums[1] at the end and it becomes [1,4,3,1,3], then delete elements at indices 2 and 1.\nnums becomes [1,1,3].\nOperation 2: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [1,1,3,1], then delete elements at indices 1 and 2.\nnums becomes [1,1].\nOperation 3: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [1,1,0], then delete elements at indices 1 and 0.\nnums becomes [0].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length. </pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,5,5,10,5]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows:\nOperation 1: Select indices 0 and 3, insert nums[0] % nums[3] at the end and it becomes [5,5,5,10,5,5], then delete elements at indices 0 and 3.\nnums becomes [5,5,5,5]. \nOperation 2: Select indices 2 and 3, insert nums[2] % nums[3] at the end and it becomes [5,5,5,5,0], then delete elements at indices 2 and 3. \nnums becomes [5,5,0]. \nOperation 3: Select indices 0 and 1, insert nums[0] % nums[1] at the end and it becomes [5,5,0,0], then delete elements at indices 0 and 1.\nnums becomes [0,0].\nThe length of nums cannot be reduced further. Hence, the answer is 2.\nIt can be shown that 2 is the minimum achievable length. </pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,4]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows: \nOperation 1: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [2,3,4,3], then delete elements at indices 1 and 2.\nnums becomes [2,3].\nOperation 2: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [2,3,1], then delete elements at indices 1 and 0.\nnums becomes [1].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length.</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"The problem can be solved by considering different cases.",
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"Let the minimum value in <code>nums</code> be <code>x</code>; we can consider the following cases:",
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"If <code>x</code> occurs once: The minimum length of <code>nums</code> achievable in this case is <code>1</code>, since every other value, <code>y</code>, can be paired with <code>x</code>, resulting in deleting <code>x</code> and <code>y</code>, and inserting <code>x % y == x</code>, since <code>x < y</code>. So, only <code>x</code> remains after the operations.",
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"If there is a value <code>y</code> in <code>nums</code> such that <code>y % x</code> is not equal to <code>0</code>: The minimum achievable length in this case is <code>1</code> as well, because inserting <code>y % x</code> creates a new minimum, since <code>y % x < x</code>, returning to the first case.",
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"If neither of the previous cases holds, and <code>x</code> occurs <code>cnt</code> times: The minimum length of <code>nums</code> achievable in this case is <code>ceil(cnt / 2)</code>."
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