Unique-Binary-Search-Trees

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题目地址

LeetCode#96 Unique Binary Search Trees

题目描述

  Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?

Example:

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Input: 3
Output: 5
Explanation:
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

解题思路

  卡特兰数 + DP 求解。

解题代码

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class Solution {
public:
    int numTrees(int n) {
        if (n <= 0)
            return 0;
        vector<int> res(n + 1, 0);
        res[0] = 1;
        res[1] = 1;
        for (int i = 2; i <= n; i++) {
            for (int j = 0; j < i; j++) {
                res[i] += res[j] * res[i - j - 1];
            }
        }
        return res[n];
    }
};
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