mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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195 lines
22 KiB
JSON
195 lines
22 KiB
JSON
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"categoryTitle": "Algorithms",
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"boundTopicId": 237823,
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"title": "Count Triplets That Can Form Two Arrays of Equal XOR",
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"content": "<p>Given an array of integers <code>arr</code>.</p>\n\n<p>We want to select three indices <code>i</code>, <code>j</code> and <code>k</code> where <code>(0 <= i < j <= k < arr.length)</code>.</p>\n\n<p>Let's define <code>a</code> and <code>b</code> as follows:</p>\n\n<ul>\n\t<li><code>a = arr[i] ^ arr[i + 1] ^ ... ^ arr[j - 1]</code></li>\n\t<li><code>b = arr[j] ^ arr[j + 1] ^ ... ^ arr[k]</code></li>\n</ul>\n\n<p>Note that <strong>^</strong> denotes the <strong>bitwise-xor</strong> operation.</p>\n\n<p>Return <em>the number of triplets</em> (<code>i</code>, <code>j</code> and <code>k</code>) Where <code>a == b</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [2,3,1,6,7]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The triplets are (0,1,2), (0,2,2), (2,3,4) and (2,4,4)\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> arr = [1,1,1,1,1]\n<strong>Output:</strong> 10\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= arr.length <= 300</code></li>\n\t<li><code>1 <= arr[i] <= 10<sup>8</sup></code></li>\n</ul>\n",
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"translatedTitle": "形成两个异或相等数组的三元组数目",
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"translatedContent": "<p>给你一个整数数组 <code>arr</code> 。</p>\n\n<p>现需要从数组中取三个下标 <code>i</code>、<code>j</code> 和 <code>k</code> ，其中 <code>(0 <= i < j <= k < arr.length)</code> 。</p>\n\n<p><code>a</code> 和 <code>b</code> 定义如下：</p>\n\n<ul>\n\t<li><code>a = arr[i] ^ arr[i + 1] ^ ... ^ arr[j - 1]</code></li>\n\t<li><code>b = arr[j] ^ arr[j + 1] ^ ... ^ arr[k]</code></li>\n</ul>\n\n<p>注意：<strong>^</strong> 表示 <strong>按位异或</strong> 操作。</p>\n\n<p>请返回能够令 <code>a == b</code> 成立的三元组 (<code>i</code>, <code>j</code> , <code>k</code>) 的数目。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>arr = [2,3,1,6,7]\n<strong>输出：</strong>4\n<strong>解释：</strong>满足题意的三元组分别是 (0,1,2), (0,2,2), (2,3,4) 以及 (2,4,4)\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>arr = [1,1,1,1,1]\n<strong>输出：</strong>10\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>arr = [2,3]\n<strong>输出：</strong>0\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<pre><strong>输入：</strong>arr = [1,3,5,7,9]\n<strong>输出：</strong>3\n</pre>\n\n<p><strong>示例 5：</strong></p>\n\n<pre><strong>输入：</strong>arr = [7,11,12,9,5,2,7,17,22]\n<strong>输出：</strong>8\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= arr.length <= 300</code></li>\n\t<li><code>1 <= arr[i] <= 10^8</code></li>\n</ul>\n",
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"We are searching for sub-array of length ≥ 2 and we need to split it to 2 non-empty arrays so that the xor of the first array is equal to the xor of the second array. This is equivalent to searching for sub-array with xor = 0.",
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"Keep the prefix xor of arr in another array, check the xor of all sub-arrays in O(n^2), if the xor of sub-array of length x is 0 add x-1 to the answer."
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