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leetcode-problemset/leetcode/originData/number-of-excellent-pairs.json
2023-12-09 19:57:46 +08:00

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{
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"title": "Number of Excellent Pairs",
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"content": "<p>You are given a <strong>0-indexed</strong> positive integer array <code>nums</code> and a positive integer <code>k</code>.</p>\n\n<p>A pair of numbers <code>(num1, num2)</code> is called <strong>excellent</strong> if the following conditions are satisfied:</p>\n\n<ul>\n\t<li><strong>Both</strong> the numbers <code>num1</code> and <code>num2</code> exist in the array <code>nums</code>.</li>\n\t<li>The sum of the number of set bits in <code>num1 OR num2</code> and <code>num1 AND num2</code> is greater than or equal to <code>k</code>, where <code>OR</code> is the bitwise <strong>OR</strong> operation and <code>AND</code> is the bitwise <strong>AND</strong> operation.</li>\n</ul>\n\n<p>Return <em>the number of <strong>distinct</strong> excellent pairs</em>.</p>\n\n<p>Two pairs <code>(a, b)</code> and <code>(c, d)</code> are considered distinct if either <code>a != c</code> or <code>b != d</code>. For example, <code>(1, 2)</code> and <code>(2, 1)</code> are distinct.</p>\n\n<p><strong>Note</strong> that a pair <code>(num1, num2)</code> such that <code>num1 == num2</code> can also be excellent if you have at least <strong>one</strong> occurrence of <code>num1</code> in the array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,1], k = 3\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The excellent pairs are the following:\n- (3, 3). (3 AND 3) and (3 OR 3) are both equal to (11) in binary. The total number of set bits is 2 + 2 = 4, which is greater than or equal to k = 3.\n- (2, 3) and (3, 2). (2 AND 3) is equal to (10) in binary, and (2 OR 3) is equal to (11) in binary. The total number of set bits is 1 + 2 = 3.\n- (1, 3) and (3, 1). (1 AND 3) is equal to (01) in binary, and (1 OR 3) is equal to (11) in binary. The total number of set bits is 1 + 2 = 3.\nSo the number of excellent pairs is 5.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,1,1], k = 10\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no excellent pairs for this array.\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;= 60</code></li>\n</ul>\n",
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"hints": [
"Can you find a different way to describe the second condition?",
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