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54 lines
2.4 KiB
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54 lines
2.4 KiB
HTML
<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>
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<p>You are to split <code>ranges</code> into <strong>two</strong> (possibly empty) groups such that:</p>
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<ul>
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<li>Each range belongs to exactly one group.</li>
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<li>Any two <strong>overlapping</strong> ranges must belong to the <strong>same</strong> group.</li>
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</ul>
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<p>Two ranges are said to be <strong>overlapping</strong> if there exists at least <strong>one</strong> integer that is present in both ranges.</p>
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<ul>
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<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>
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</ul>
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<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>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> ranges = [[6,10],[5,15]]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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The two ranges are overlapping, so they must be in the same group.
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Thus, there are two possible ways:
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- Put both the ranges together in group 1.
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- Put both the ranges together in group 2.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> ranges = [[1,3],[10,20],[2,5],[4,8]]
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<strong>Output:</strong> 4
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<strong>Explanation:</strong>
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Ranges [1,3], and [2,5] are overlapping. So, they must be in the same group.
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Again, ranges [2,5] and [4,8] are also overlapping. So, they must also be in the same group.
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Thus, there are four possible ways to group them:
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- All the ranges in group 1.
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- All the ranges in group 2.
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- Ranges [1,3], [2,5], and [4,8] in group 1 and [10,20] in group 2.
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- Ranges [1,3], [2,5], and [4,8] in group 2 and [10,20] in group 1.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= ranges.length <= 10<sup>5</sup></code></li>
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<li><code>ranges[i].length == 2</code></li>
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<li><code>0 <= start<sub>i</sub> <= end<sub>i</sub> <= 10<sup>9</sup></code></li>
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</ul>
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