leetcode-problemset/leetcode-cn/originData/count-ways-to-group-overlapping-ranges.json

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            "questionId": "2651",
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            "categoryTitle": "Algorithms",
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            "title": "Count Ways to Group Overlapping Ranges",
            "titleSlug": "count-ways-to-group-overlapping-ranges",
            "content": "<p>You are given a 2D integer array <code>ranges</code> where <code>ranges[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> denotes that all integers between <code>start<sub>i</sub></code> and <code>end<sub>i</sub></code> (both <strong>inclusive</strong>) are contained in the <code>i<sup>th</sup></code> range.</p>\n\n<p>You are to split <code>ranges</code> into <strong>two</strong> (possibly empty) groups such that:</p>\n\n<ul>\n\t<li>Each range belongs to exactly one group.</li>\n\t<li>Any two <strong>overlapping</strong> ranges must belong to the <strong>same</strong> group.</li>\n</ul>\n\n<p>Two ranges are said to be <strong>overlapping</strong>&nbsp;if there exists at least <strong>one</strong> integer that is present in both ranges.</p>\n\n<ul>\n\t<li>For example, <code>[1, 3]</code> and <code>[2, 5]</code> are overlapping because <code>2</code> and <code>3</code> occur in both ranges.</li>\n</ul>\n\n<p>Return <em>the <strong>total number</strong> of ways to split</em> <code>ranges</code> <em>into two groups</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> ranges = [[6,10],[5,15]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> \nThe two ranges are overlapping, so they must be in the same group.\nThus, there are two possible ways:\n- Put both the ranges together in group 1.\n- Put both the ranges together in group 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> ranges = [[1,3],[10,20],[2,5],[4,8]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> \nRanges [1,3], and [2,5] are overlapping. So, they must be in the same group.\nAgain, ranges [2,5] and [4,8] are also overlapping. So, they must also be in the same group. \nThus, there are four possible ways to group them:\n- All the ranges in group 1.\n- All the ranges in group 2.\n- Ranges [1,3], [2,5], and [4,8] in group 1 and [10,20] in group 2.\n- Ranges [1,3], [2,5], and [4,8] in group 2 and [10,20] in group 1.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= ranges.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>ranges[i].length == 2</code></li>\n\t<li><code>0 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "统计将重叠区间合并成组的方案数",
            "translatedContent": "<p>给你一个二维整数数组&nbsp;<code>ranges</code>&nbsp;，其中&nbsp;<code>ranges[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>&nbsp;表示&nbsp;<code>start<sub>i</sub></code>&nbsp;到&nbsp;<code>end<sub>i</sub></code>&nbsp;之间（包括二者）的所有整数都包含在第&nbsp;<code>i</code>&nbsp;个区间中。</p>\n\n<p>你需要将&nbsp;<code>ranges</code>&nbsp;分成 <strong>两个</strong>&nbsp;组（可以为空），满足：</p>\n\n<ul>\n\t<li>每个区间只属于一个组。</li>\n\t<li>两个有 <strong>交集</strong>&nbsp;的区间必须在 <strong>同一个&nbsp;</strong>组内。</li>\n</ul>\n\n<p>如果两个区间有至少 <strong>一个</strong>&nbsp;公共整数，那么这两个区间是 <b>有交集</b>&nbsp;的。</p>\n\n<ul>\n\t<li>比方说，区间&nbsp;<code>[1, 3]</code> 和&nbsp;<code>[2, 5]</code>&nbsp;有交集，因为&nbsp;<code>2</code>&nbsp;和&nbsp;<code>3</code>&nbsp;在两个区间中都被包含。</li>\n</ul>\n\n<p>请你返回将 <code>ranges</code>&nbsp;划分成两个组的 <strong>总方案数</strong>&nbsp;。由于答案可能很大，将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>ranges = [[6,10],[5,15]]\n<b>输出：</b>2\n<b>解释：</b>\n两个区间有交集，所以它们必须在同一个组内。\n所以有两种方案：\n- 将两个区间都放在第 1 个组中。\n- 将两个区间都放在第 2 个组中。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>ranges = [[1,3],[10,20],[2,5],[4,8]]\n<b>输出：</b>4\n<b>解释：</b>\n区间 [1,3] 和 [2,5] 有交集，所以它们必须在同一个组中。\n同理，区间 [2,5] 和 [4,8] 也有交集，所以它们也必须在同一个组中。\n所以总共有 4 种分组方案：\n- 所有区间都在第 1 组。\n- 所有区间都在第 2 组。\n- 区间 [1,3] ，[2,5] 和 [4,8] 在第 1 个组中，[10,20] 在第 2 个组中。\n- 区间 [1,3] ，[2,5] 和 [4,8] 在第 2 个组中，[10,20] 在第 1 个组中。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= ranges.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>ranges[i].length == 2</code></li>\n\t<li><code>0 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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            "hints": [
                "Can we use sorting here?",
                "Sort the ranges and merge the overlapping ranges. Then count number of non-overlapping ranges.",
                "How many ways can we group these non-overlapping ranges?"
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