mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
161 lines
21 KiB
JSON
161 lines
21 KiB
JSON
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"questionId": "1000570",
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"questionFrontendId": "LCP 82",
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"categoryTitle": "Algorithms",
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"boundTopicId": 2258739,
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"title": "万灵之树",
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"titleSlug": "cnHoX6",
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"content": "English description is not available for the problem. Please switch to Chinese.",
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"translatedTitle": "万灵之树",
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"translatedContent": "探险家小扣终于来到了万灵之树前，挑战最后的谜题。\n已知小扣拥有足够数量的链接节点和 `n` 颗幻境宝石，`gem[i]` 表示第 `i` 颗宝石的数值。现在小扣需要使用这些链接节点和宝石组合成一颗二叉树，其组装规则为：\n- 链接节点将作为二叉树中的非叶子节点，且每个链接节点必须拥有 `2` 个子节点；\n- 幻境宝石将作为二叉树中的叶子节点，所有的幻境宝石都必须被使用。\n\n能量首先进入根节点，而后将按如下规则进行移动和记录：\n- 若能量首次到达该节点时：\n - 记录数字 `1`；\n - 若该节点为叶节点，将额外记录该叶节点的数值；\n- 若存在未到达的子节点，则选取未到达的一个子节点（优先选取左子节点）进入；\n- 若无子节点或所有子节点均到达过，此时记录 `9`，并回到当前节点的父节点（若存在）。\n\n如果最终记下的数依序连接成一个整数 `num`，满足 $num \\mod~p=target$，则视为解开谜题。\n请问有多少种二叉树的组装方案，可以使得最终记录下的数字可以解开谜题\n\n**注意：**\n- 两棵结构不同的二叉树，作为不同的组装方案\n- 两棵结构相同的二叉树且存在某个相同位置处的宝石编号不同，也作为不同的组装方案\n- 可能存在数值相同的两颗宝石\n\n**示例 1：**\n> 输入：`gem = [2,3]`\n> `p = 100000007`\n> `target = 11391299`\n>\n> 输出：`1`\n>\n> 解释：\n> 包含 `2` 个叶节点的结构只有一种。\n> 假设 B、C 节点的值分别为 3、2，对应 target 为 11391299，如下图所示。\n> 11391299 % 100000007 = 11391299，满足条件;\n> 假设 B、C 节点的值分别为 2、3，对应 target 为 11291399;\n> 11291399 % 100000007 = 11291399，不满足条件；\n> 因此只存在 1 种方案，返回 1\n.gif){:height=300px}\n\n\n**示例 2：**\n> 输入：`gem = [3,21,3]`\n> `p = 7`\n> `target = 5`\n>\n> 输出：`4`\n>\n> 解释：\n包含 `3` 个叶节点树结构有两种，列举如下：\n满足条件的组合有四种情况：\n> 当结构为下图（1）时：叶子节点的值为 [3,3,21] 或 [3,3,21]，得到的整数为 `11139139912199`。\n> 当结构为下图（2）时：叶子节点的值为 [21,3,3] 或 [21,3,3]，得到的整数为 `11219113913999`。\n{:width=500px}\n\n\n**提示：**\n- `1 <= gem.length <= 9`\n- `0 <= gem[i] <= 10^9`\n- `1 <= p <= 10^9`，保证 $p$ 为素数。\n- `0 <= target < p`\n- 存在 2 组 `gem.length == 9` 的用例",
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