[leetcode]96. Unique Binary Search Trees

Analysis

intern intern intern—— [每天刷題並不難0.0]

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

動態規劃解決，狀態轉移方程：
DP[n] = DP[0]DP[n-1]+DP[1]DP[n-2]+…+DP[i-1]DP[n-i]+…DP[n-1]DP[0];

Implement

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