96. Unique Binary Search Trees

96. Unique Binary Search Trees

Medium

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

Example:

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

not difficult, it is easy

first you should decide the root num, then the litter num is left of it, the bigger nums are right of it;
we can get that
f(n) = f(n-1) + f(1) * f(n-2) + f(2) * f(n-3) +... + f(n-2) * f(1) + f(n-1)
we can makesure that f(0) = 1
and then
f(n) = ∑f(k) * f(n-1-k)
so we use db solution

class Solution {
public:
    vector<int> kinds_num(int n){
        vector<int> result;
        result.push_back(1);
        for (int i=1;i<=n;i++){
            int tmp = 0;
            for (int j=0;j<=i-1;j++){
                tmp += result[j] * result[i-1-j];
            }
            result.push_back(tmp);
        }
        return result;
    }
    int numTrees(int n) {
        vector<int> result;
        result = kinds_num(n);
        return result[n];
    }
};