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leetcode-cn/problem (Chinese)/硬币面值还原 [inverse-coin-change].html
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leetcode-cn/problem (Chinese)/硬币面值还原 [inverse-coin-change].html
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<p>给你一个 <strong>从 1 开始计数 </strong>的整数数组 <code>numWays</code>，其中 <code>numWays[i]</code> 表示使用某些 <strong>固定 </strong>面值的硬币（每种面值可以使用无限次）凑出总金额 <code>i</code> 的方法数。每种面值都是一个 <strong>正整数 </strong>，并且其值 <strong>最多 </strong>为 <code>numWays.length</code>。</p>
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<p>然而，具体的硬币面值已经 <strong>丢失 </strong>。你的任务是还原出可能生成这个 <code>numWays</code> 数组的面值集合。</p>
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<p>返回一个按从小到大顺序排列的数组，其中包含所有可能的 <strong>唯一 </strong>整数面值。</p>
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<p>如果不存在这样的集合，返回一个 <strong>空 </strong>数组。</p>
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<p> </p>
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<p><strong class="example">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">numWays = [0,1,0,2,0,3,0,4,0,5]</span></p>
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<p><strong>输出：</strong> <span class="example-io">[2,4,6]</span></p>
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<p><strong>解释：</strong></p>
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<table style="border: 1px solid black;">
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<tbody>
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<tr>
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<th style="border: 1px solid black;">金额</th>
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<th style="border: 1px solid black;">方法数</th>
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<th style="border: 1px solid black;">解释</th>
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</tr>
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<tr>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">0</td>
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<td style="border: 1px solid black;">无法用硬币凑出总金额 1。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">1</td>
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<td style="border: 1px solid black;">唯一的方法是 <code>[2]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">0</td>
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<td style="border: 1px solid black;">无法用硬币凑出总金额 3。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">4</td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">可以用 <code>[2, 2]</code> 或 <code>[4]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">5</td>
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<td style="border: 1px solid black;">0</td>
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<td style="border: 1px solid black;">无法用硬币凑出总金额 5。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">6</td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">可以用 <code>[2, 2, 2]</code>、<code>[2, 4]</code> 或 <code>[6]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">7</td>
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<td style="border: 1px solid black;">0</td>
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<td style="border: 1px solid black;">无法用硬币凑出总金额 7。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">8</td>
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<td style="border: 1px solid black;">4</td>
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<td style="border: 1px solid black;">可以用 <code>[2, 2, 2, 2]</code>、<code>[2, 2, 4]</code>、<code>[2, 6]</code> 或 <code>[4, 4]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">9</td>
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<td style="border: 1px solid black;">0</td>
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<td style="border: 1px solid black;">无法用硬币凑出总金额 9。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">10</td>
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<td style="border: 1px solid black;">5</td>
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<td style="border: 1px solid black;">可以用 <code>[2, 2, 2, 2, 2]</code>、<code>[2, 2, 2, 4]</code>、<code>[2, 4, 4]</code>、<code>[2, 2, 6]</code> 或 <code>[4, 6]</code>。</td>
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</tr>
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</tbody>
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</table>
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</div>
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<p><strong class="example">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">numWays = [1,2,2,3,4]</span></p>
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<p><strong>输出：</strong> <span class="example-io">[1,2,5]</span></p>
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<p><strong>解释：</strong></p>
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<table style="border: 1px solid black;">
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<tbody>
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<tr>
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<th style="border: 1px solid black;">金额</th>
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<th style="border: 1px solid black;">方法数</th>
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<th style="border: 1px solid black;">解释</th>
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</tr>
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<tr>
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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;">唯一的方法是 <code>[1]</code>。</td>
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</tr>
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<tr>
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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;">可以用 <code>[1, 1]</code> 或 <code>[2]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">2</td>
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<td style="border: 1px solid black;">可以用 <code>[1, 1, 1]</code> 或 <code>[1, 2]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">4</td>
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<td style="border: 1px solid black;">3</td>
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<td style="border: 1px solid black;">可以用 <code>[1, 1, 1, 1]</code>、<code>[1, 1, 2]</code> 或 <code>[2, 2]</code>。</td>
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</tr>
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<tr>
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<td style="border: 1px solid black;">5</td>
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<td style="border: 1px solid black;">4</td>
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<td style="border: 1px solid black;">可以用 <code>[1, 1, 1, 1, 1]</code>、<code>[1, 1, 1, 2]</code>、<code>[1, 2, 2]</code> 或 <code>[5]</code>。</td>
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</tr>
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</tbody>
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</table>
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</div>
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<p><strong class="example">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">numWays = [1,2,3,4,15]</span></p>
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<p><strong>输出：</strong> <span class="example-io">[]</span></p>
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<p><strong>解释：</strong></p>
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<p>没有任何面值集合可以生成该数组。</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 <= numWays.length <= 100</code></li>
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<li><code>0 <= numWays[i] <= 2 * 10<sup>8</sup></code></li>
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</ul>
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