mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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175 lines
16 KiB
JSON
175 lines
16 KiB
JSON
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"questionId": "1793",
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"title": "Minimum Moves to Make Array Complementary",
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"content": "<p>You are given an integer array <code>nums</code> of <strong>even</strong> length <code>n</code> and an integer <code>limit</code>. In one move, you can replace any integer from <code>nums</code> with another integer between <code>1</code> and <code>limit</code>, inclusive.</p>\n\n<p>The array <code>nums</code> is <strong>complementary</strong> if for all indices <code>i</code> (<strong>0-indexed</strong>), <code>nums[i] + nums[n - 1 - i]</code> equals the same number. For example, the array <code>[1,2,3,4]</code> is complementary because for all indices <code>i</code>, <code>nums[i] + nums[n - 1 - i] = 5</code>.</p>\n\n<p>Return the <em><strong>minimum</strong> number of moves required to make </em><code>nums</code><em> <strong>complementary</strong></em>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,4,3], limit = 4\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> In 1 move, you can change nums to [1,2,<u>2</u>,3] (underlined elements are changed).\nnums[0] + nums[3] = 1 + 3 = 4.\nnums[1] + nums[2] = 2 + 2 = 4.\nnums[2] + nums[1] = 2 + 2 = 4.\nnums[3] + nums[0] = 3 + 1 = 4.\nTherefore, nums[i] + nums[n-1-i] = 4 for every i, so nums is complementary.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,2,1], limit = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> In 2 moves, you can change nums to [<u>2</u>,2,2,<u>2</u>]. You cannot change any number to 3 since 3 > limit.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,1,2], limit = 2\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> nums is already complementary.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i] <= limit <= 10<sup>5</sup></code></li>\n\t<li><code>n</code> is even.</li>\n</ul>\n",
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"categoryTitle": "Algorithms",
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"hints": [
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"Given a target sum x, each pair of nums[i] and nums[n-1-i] would either need 0, 1, or 2 modifications.",
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"Can you find the optimal target sum x value such that the sum of modifications is minimized?",
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"Create a difference array to efficiently sum all the modifications."
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