mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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194 lines
18 KiB
JSON
194 lines
18 KiB
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"title": "Maximum Strong Pair XOR II",
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"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p>\n\n<ul>\n\t<li><code>|x - y| <= min(x, y)</code></li>\n</ul>\n\n<p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p>\n\n<p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p>\n\n<p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4,5]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5).\nThe maximum XOR possible from these pairs is 3 XOR 4 = 7.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [10,100]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100).\nThe maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [500,520,2500,3000]\n<strong>Output:</strong> 1020\n<strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000).\nThe maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 <= nums[i] <= 2<sup>20</sup> - 1</code></li>\n</ul>\n",
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"Sort the array, now let <code>x <= y</code> which means <code>|x - y| <= min(x, y)</code> can now be written as <code>y - x <= x</code> or in other words, <code>y <= 2 * x</code>.",
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"If <code>x</code> and <code>y</code> have the same number of bits, try making<code>y</code>’s bits different from x if possible for each bit starting from the second most significant bit.",
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"If <code>y</code> has 1 more bit than <code>x</code> and <code>y <= 2 * x</code> use the idea about Digit DP to make <code>y</code>’s prefix smaller than <code>2 * x + 1</code> as well as trying to make each bit different from <code>x</code> using a Hashmap.",
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"Alternatively, use Trie data structure to find the pair with maximum <code>XOR</code>."
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