mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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183 lines
25 KiB
JSON
183 lines
25 KiB
JSON
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"title": "Minimum Index of a Valid Split",
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"content": "<p>An element <code>x</code> of an integer array <code>arr</code> of length <code>m</code> is <strong>dominant</strong> if <code>freq(x) * 2 > m</code>, where <code>freq(x)</code> is the number of occurrences of <code>x</code> in <code>arr</code>. Note that this definition implies that <code>arr</code> can have <strong>at most one</strong> dominant element.</p>\n\n<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code> with one dominant element.</p>\n\n<p>You can split <code>nums</code> at an index <code>i</code> into two arrays <code>nums[0, ..., i]</code> and <code>nums[i + 1, ..., n - 1]</code>, but the split is only <strong>valid</strong> if:</p>\n\n<ul>\n\t<li><code>0 <= i < n - 1</code></li>\n\t<li><code>nums[0, ..., i]</code>, and <code>nums[i + 1, ..., n - 1]</code> have the same dominant element.</li>\n</ul>\n\n<p>Here, <code>nums[i, ..., j]</code> denotes the subarray of <code>nums</code> starting at index <code>i</code> and ending at index <code>j</code>, both ends being inclusive. Particularly, if <code>j < i</code> then <code>nums[i, ..., j]</code> denotes an empty subarray.</p>\n\n<p>Return <em>the <strong>minimum</strong> index of a <strong>valid split</strong></em>. If no valid split exists, return <code>-1</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,2,2]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can split the array at index 2 to obtain arrays [1,2,2] and [2]. \nIn array [1,2,2], element 2 is dominant since it occurs twice in the array and 2 * 2 > 3. \nIn array [2], element 2 is dominant since it occurs once in the array and 1 * 2 > 1.\nBoth [1,2,2] and [2] have the same dominant element as nums, so this is a valid split. \nIt can be shown that index 2 is the minimum index of a valid split. </pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,1,3,1,1,1,7,1,2,1]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> We can split the array at index 4 to obtain arrays [2,1,3,1,1] and [1,7,1,2,1].\nIn array [2,1,3,1,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.\nIn array [1,7,1,2,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.\nBoth [2,1,3,1,1] and [1,7,1,2,1] have the same dominant element as nums, so this is a valid split.\nIt can be shown that index 4 is the minimum index of a valid split.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,3,3,3,7,2,2]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It can be shown that there is no valid split.\n</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\t<li><code>nums</code> has exactly one dominant element.</li>\n</ul>\n",
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"translatedTitle": "合法分割的最小下标",
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"translatedContent": "<p>如果元素 <code>x</code> 在长度为 <code>m</code> 的整数数组 <code>arr</code> 中满足 <code>freq(x) * 2 > m</code> ，那么我们称 <code>x</code> 是 <strong>支配元素</strong> 。其中 <code>freq(x)</code> 是 <code>x</code> 在数组 <code>arr</code> 中出现的次数。注意，根据这个定义，数组 <code>arr</code> <strong>最多</strong> 只会有 <strong>一个</strong> 支配元素。</p>\n\n<p>给你一个下标从 <strong>0</strong> 开始长度为 <code>n</code> 的整数数组 <code>nums</code> ，数据保证它含有一个支配元素。</p>\n\n<p>你需要在下标 <code>i</code> 处将 <code>nums</code> 分割成两个数组 <code>nums[0, ..., i]</code> 和 <code>nums[i + 1, ..., n - 1]</code> ，如果一个分割满足以下条件，我们称它是 <strong>合法</strong> 的：</p>\n\n<ul>\n\t<li><code>0 <= i < n - 1</code></li>\n\t<li><code>nums[0, ..., i]</code> 和 <code>nums[i + 1, ..., n - 1]</code> 的支配元素相同。</li>\n</ul>\n\n<p>这里， <code>nums[i, ..., j]</code> 表示 <code>nums</code> 的一个子数组，它开始于下标 <code>i</code> ，结束于下标 <code>j</code> ，两个端点都包含在子数组内。特别地，如果 <code>j < i</code> ，那么 <code>nums[i, ..., j]</code> 表示一个空数组。</p>\n\n<p>请你返回一个 <strong>合法分割</strong> 的 <strong>最小</strong> 下标。如果合法分割不存在，返回 <code>-1</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>nums = [1,2,2,2]\n<b>输出：</b>2\n<b>解释：</b>我们将数组在下标 2 处分割，得到 [1,2,2] 和 [2] 。\n数组 [1,2,2] 中，元素 2 是支配元素，因为它在数组中出现了 2 次，且 2 * 2 > 3 。\n数组 [2] 中，元素 2 是支配元素，因为它在数组中出现了 1 次，且 1 * 2 > 1 。\n两个数组 [1,2,2] 和 [2] 都有与 nums 一样的支配元素，所以这是一个合法分割。\n下标 2 是合法分割中的最小下标。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [2,1,3,1,1,1,7,1,2,1]\n<b>输出：</b>4\n<b>解释：</b>我们将数组在下标 4 处分割，得到 [2,1,3,1,1] 和 [1,7,1,2,1] 。\n数组 [2,1,3,1,1] 中，元素 1 是支配元素，因为它在数组中出现了 3 次，且 3 * 2 > 5 。\n数组 [1,7,1,2,1] 中，元素 1 是支配元素，因为它在数组中出现了 3 次，且 3 * 2 > 5 。\n两个数组 [2,1,3,1,1] 和 [1,7,1,2,1] 都有与 nums 一样的支配元素，所以这是一个合法分割。\n下标 4 是所有合法分割中的最小下标。</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><b>输入：</b>nums = [3,3,3,3,7,2,2]\n<b>输出：</b>-1\n<b>解释：</b>没有合法分割。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</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\t<li><code>nums</code> 有且只有一个支配元素。</li>\n</ul>\n",
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"Find the dominant element of nums by using a hashmap to maintain element frequency, we denote the dominant element as x and its frequency as f.",
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"For each index in [0, n - 2], calculate f1, x’s frequency in the subarray [0, i] when looping the index. And f2, x’s frequency in the subarray [i + 1, n - 1] which is equal to f - f1. Then we can check whether x is dominant in both subarrays."
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