mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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236 lines
18 KiB
JSON
236 lines
18 KiB
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"title": "Number of Ways to Reorder Array to Get Same BST",
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"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> </p>\n<p><strong class=\"example\">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 class=\"example\">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 class=\"example\">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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 1000</code></li>\n\t<li><code>1 <= nums[i] <= nums.length</code></li>\n\t<li>All integers in <code>nums</code> are <strong>distinct</strong>.</li>\n</ul>\n",
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"Use a divide and conquer strategy.",
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"The first number will always be the root. Consider the numbers smaller and larger than the root separately. When merging the results together, how many ways can you order x elements in x+y positions?"
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