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111 lines
3.7 KiB
HTML
111 lines
3.7 KiB
HTML
<p>给你一个整数数组 <code>nums</code> 和一个正整数 <code>k</code>，返回所有长度最多为 <code>k</code> 的 <strong>子序列</strong> 中 <strong>最大值 </strong>与 <strong>最小值 </strong>之和的总和。</p>
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<p><strong>非空子序列</strong> 是指从另一个数组中删除一些或不删除任何元素（且不改变剩余元素的顺序）得到的数组。</p>
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<p>由于答案可能非常大，请返回对 <code>10<sup>9</sup> + 7</code> 取余数的结果。</p>
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<p> </p>
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<p><strong>示例 1：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">nums = [1,2,3], k = 2</span></p>
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<p><strong>输出：</strong> 24</p>
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<p><strong>解释：</strong></p>
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<p>数组 <code>nums</code> 中所有长度最多为 2 的子序列如下：</p>
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<table style="border: 1px solid black; border-collapse: collapse;">
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<thead>
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<tr>
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<th style="border: 1px solid black;">子序列</th>
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<th style="border: 1px solid black;">最小值</th>
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<th style="border: 1px solid black;">最大值</th>
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<th style="border: 1px solid black;">和</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td style="border: 1px solid black;"><code>[1]</code></td>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">2</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><code>[2]</code></td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">4</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><code>[3]</code></td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">6</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><code>[1, 2]</code></td>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">3</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><code>[1, 3]</code></td>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">4</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><code>[2, 3]</code></td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">5</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;"><strong>总和</strong></td>
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<td style="border: 1px solid black;"> </td>
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<td style="border: 1px solid black;"> </td>
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<td style="border: 1px solid black;">24</td>
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</tr>
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</tbody>
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</table>
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<p>因此，输出为 24。</p>
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</div>
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<p><strong>示例 2：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">nums = [5,0,6], k = 1</span></p>
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<p><strong>输出：</strong> 22</p>
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<p><strong>解释：</strong></p>
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<p>对于长度恰好为 1 的子序列，最小值和最大值均为元素本身。因此，总和为 <code>5 + 5 + 0 + 0 + 6 + 6 = 22</code>。</p>
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</div>
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<p><strong>示例 3：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">nums = [1,1,1], k = 2</span></p>
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<p><strong>输出：</strong> 12</p>
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<p><strong>解释：</strong></p>
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<p>子序列 <code>[1, 1]</code> 和 <code>[1]</code> 各出现 3 次。对于所有这些子序列，最小值和最大值均为 1。因此，总和为 12。</p>
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</div>
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<p> </p>
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<p><strong>提示：</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>0 <= nums[i] <= 10<sup>9</sup></code></li>
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<li><code>1 <= k <= min(100, nums.length)</code></li>
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</ul>
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