leetcode-problemset/leetcode-cn/originData/number-of-ways-to-reorder-array-to-get-same-bst.json

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            "title": "Number of Ways to Reorder Array to Get Same BST",
            "titleSlug": "number-of-ways-to-reorder-array-to-get-same-bst",
            "content": "<p>Given an array <code>nums</code> that represents a permutation of integers from <code>1</code> to <code>n</code>. We are going to construct a binary search tree (BST) by inserting the elements of <code>nums</code> in order into an initially empty BST. Find the number of different ways to reorder <code>nums</code> so that the constructed BST is identical to that formed from the original array <code>nums</code>.</p>\n\n<ul>\n\t<li>For example, given <code>nums = [2,1,3]</code>, we will have 2 as the root, 1 as a left child, and 3 as a right child. The array <code>[2,3,1]</code> also yields the same BST but <code>[3,2,1]</code> yields a different BST.</li>\n</ul>\n\n<p>Return <em>the number of ways to reorder</em> <code>nums</code> <em>such that the BST formed is identical to the original BST formed from</em> <code>nums</code>.</p>\n\n<p>Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/bb.png\" style=\"width: 121px; height: 101px;\" />\n<pre>\n<strong>Input:</strong> nums = [2,1,3]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can reorder nums to be [2,3,1] which will yield the same BST. There are no other ways to reorder nums which will yield the same BST.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/ex1.png\" style=\"width: 241px; height: 161px;\" />\n<pre>\n<strong>Input:</strong> nums = [3,4,5,1,2]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The following 5 arrays will yield the same BST: \n[3,1,2,4,5]\n[3,1,4,2,5]\n[3,1,4,5,2]\n[3,4,1,2,5]\n[3,4,1,5,2]\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/12/ex4.png\" style=\"width: 121px; height: 161px;\" />\n<pre>\n<strong>Input:</strong> nums = [1,2,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no other orderings of nums that will yield the same BST.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= nums.length</code></li>\n\t<li>All integers in <code>nums</code> are <strong>distinct</strong>.</li>\n</ul>\n",
            "translatedTitle": "将子数组重新排序得到同一个二叉查找树的方案数",
            "translatedContent": "<p>给你一个数组 <code>nums</code>&nbsp;表示 <code>1</code>&nbsp;到 <code>n</code>&nbsp;的一个排列。我们按照元素在 <code>nums</code>&nbsp;中的顺序依次插入一个初始为空的二叉查找树（BST）。请你统计将 <code>nums</code>&nbsp;重新排序后，统计满足如下条件的方案数：重排后得到的二叉查找树与 <code>nums</code>&nbsp;原本数字顺序得到的二叉查找树相同。</p>\n\n<p>比方说，给你&nbsp;<code>nums = [2,1,3]</code>，我们得到一棵 2 为根，1 为左孩子，3 为右孩子的树。数组&nbsp;<code>[2,3,1]</code>&nbsp;也能得到相同的 BST，但&nbsp;<code>[3,2,1]</code>&nbsp;会得到一棵不同的&nbsp;BST 。</p>\n\n<p>请你返回重排 <code>nums</code>&nbsp;后，与原数组 <code>nums</code>&nbsp;得到相同二叉查找树的方案数。</p>\n\n<p>由于答案可能会很大，请将结果对<strong>&nbsp;</strong><code>10^9 + 7</code>&nbsp;取余数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/30/bb.png\" style=\"height: 101px; width: 121px;\"></p>\n\n<pre><strong>输入：</strong>nums = [2,1,3]\n<strong>输出：</strong>1\n<strong>解释：</strong>我们将 nums 重排， [2,3,1] 能得到相同的 BST 。没有其他得到相同 BST 的方案了。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/30/ex1.png\" style=\"height: 161px; width: 241px;\"></strong></p>\n\n<pre><strong>输入：</strong>nums = [3,4,5,1,2]\n<strong>输出：</strong>5\n<strong>解释：</strong>下面 5 个数组会得到相同的 BST：\n[3,1,2,4,5]\n[3,1,4,2,5]\n[3,1,4,5,2]\n[3,4,1,2,5]\n[3,4,1,5,2]\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/30/ex4.png\" style=\"height: 161px; width: 121px;\"></strong></p>\n\n<pre><strong>输入：</strong>nums = [1,2,3]\n<strong>输出：</strong>0\n<strong>解释：</strong>没有别的排列顺序能得到相同的 BST 。\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/30/abc.png\" style=\"height: 161px; width: 241px;\"></strong></p>\n\n<pre><strong>输入：</strong>nums = [3,1,2,5,4,6]\n<strong>输出：</strong>19\n</pre>\n\n<p><strong>示例&nbsp; 5：</strong></p>\n\n<pre><strong>输入：</strong>nums = [9,4,2,1,3,6,5,7,8,14,11,10,12,13,16,15,17,18]\n<strong>输出：</strong>216212978\n<strong>解释：</strong>得到相同 BST 的方案数是 3216212999。将它对 10^9 + 7 取余后得到 216212978。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= nums.length</code></li>\n\t<li><code>nums</code>&nbsp;中所有数 <strong>互不相同</strong>&nbsp;。</li>\n</ul>\n",
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