【LeetCode】Unique Binary Search Trees
2015-05-07 11:59
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Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
For example,
Given n = 3, there are a total of 5 unique BST's.
For example,
Given n = 3, there are a total of 5 unique BST's.
1 3 3 2 1 \ / / / \ \ 3 2 1 1 3 2 / / \ \ 2 1 2 3
Solution: 这题可以利用二叉搜索树的性质进行递推或者说DP。 二叉搜索树的根天然地就将问题分解为两个规模更小的等价子问题,所以一旦确定了根,由左子树和右子树所有的可能情况相乘便是当前根下的所有解的可能(乘法原理)。 于是递推式可以写成: s = Σ(k: 0..n) s[k]*s[n-k-1] n 从 0 递推 到 n 就行。 递推基: s[0] = 1,空树只有一种可能
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