LeetCode-M-Unique Binary Search Trees

題意

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.

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

解法

動態規劃＋記錄中間結果，不記錄會超時

實現

class Solution {
public:
    int numTrees(int n) {
        if(n == 0) return 1;
        if(n == 2 || n == 1) return n;
        int sum = 0;
        vector<int> result(n+1,0);
        result[0] = 1;
        result[1] = 1;
        result[2] = 2;
        for(int i = 3; i <= n; ++i){
            for(int j = 1; j <= i; ++j){
                result[i] = result[i] + result[j-1] * result[i-j];
            }
        }
        return result[n];
    }
};