96. Unique Binary Search Trees

Posted 2020-09-18 蓝色地中海

Problem statement:

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

For example,
Given n = 3, there are total of 5 unique BST‘s.

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

Solution:

This problem wants the number of unique BST tree. The DP will solve it.

dp[i] means how many bst trees it can build if there n == i.

If there are i tree nodes, there are i - 1 nodes in left and right tree. we enumerate all possible solutions.

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