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49 lines
2.2 KiB
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49 lines
2.2 KiB
HTML
<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>
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<ul>
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<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>
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</ul>
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<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>
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<p>Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/08/12/bb.png" style="width: 121px; height: 101px;" />
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<pre>
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<strong>Input:</strong> nums = [2,1,3]
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<strong>Output:</strong> 1
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<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.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/08/12/ex1.png" style="width: 241px; height: 161px;" />
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<pre>
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<strong>Input:</strong> nums = [3,4,5,1,2]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The following 5 arrays will yield the same BST:
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[3,1,2,4,5]
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[3,1,4,2,5]
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[3,1,4,5,2]
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[3,4,1,2,5]
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[3,4,1,5,2]
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</pre>
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<p><strong>Example 3:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/08/12/ex4.png" style="width: 121px; height: 161px;" />
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<pre>
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<strong>Input:</strong> nums = [1,2,3]
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> There are no other orderings of nums that will yield the same BST.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 1000</code></li>
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<li><code>1 <= nums[i] <= nums.length</code></li>
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<li>All integers in <code>nums</code> are <strong>distinct</strong>.</li>
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</ul>
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