Unique Binary Search Trees

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Unique Binary Search Trees

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.

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1         3     3      2      1
 \       /     /      / \      \
  3     2     1      1   3      2
 /     /       \                 \
2     1         2                 3

比较像矩阵链乘：取不同的分界点作为根，求两边的子树数量的乘积。

递归形式的AC代码，对迭代递推还是不够熟练：

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class Solution {
public:

    vector<vector<int>> DP;

    int solve(int begin, int end)
    {
        if (begin >= end) return 1;
        if (DP[begin][end]) return DP[begin][end];
        int f = 0;
        for (int i = begin; i <= end; ++i)
        {
            int r = solve(begin,i-1);
            int l = solve(i+1,end);
            f += r * l;
        }
        DP[begin][end] = f;
        return f;
    }

    int numTrees(int n) {
        if (1 >= n) return 1;
        DP = vector<vector<int>>(n+1,vector<int>(n+1,0));
        solve(1,n);
        int result = 0;
        return DP[1][n];
    }
};