Question 96 Different Binary Search Trees

1. Title

2. My initial thoughts and problems

Slightly, look directly at the solution

3. Problem solving method one: dynamic programming

Ideas:

class Solution {
    
    
    public int numTrees(int n) {
    
    
        int[] G = new int[n + 1];
        G[0] = 1;
        G[1] = 1;

        for (int i = 2; i <= n; ++i) {
    
    
            for (int j = 1; j <= i; ++j) {
    
    
                G[i] += G[j - 1] * G[i - j];
            }
        }
        return G[n];
    }
}

time complexity:

4. Problem solving method 2: Mathematics

class Solution {
    
    
    public int numTrees(int n) {
    
    
        // 提示：我们在这里需要用 long 类型防止计算过程中的溢出
        long C = 1;
        for (int i = 0; i < n; ++i) {
    
    
            C = C * 2 * (2 * i + 1) / (i + 2);
        }
        return (int) C;
    }
}