96. Unique Binary Search Trees

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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.

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

>

题意：给一个数字n，计算把[1,n]组成一颗二叉树有多少种方式。

Code:

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//
// Created by cpz on 2017/11/23.
//

#include "head.h"

class Solution {
public:
    int numTrees(int n)
    {
        vector<vector<int>> dp(n + 2, vector<int>(n + 2, 1));
        for (int len = 1; len < n; ++len)
        {
            for (int start = 1; start + len<= n ; ++start)
            {
                int end = start + len ;
                int sum = 0;
                for (int k = start; k <= end ; ++k)
                {
                    sum+=dp[start][k-1]*dp[k+1][end];
                }
                dp[start][end] = sum;
            }
        }
        return dp[1][n];
    }
};