README.md

96. Unique Binary Search Trees

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

Solutions (Ruby)

1. Dynamic Programming

# @param {Integer} n
# @return {Integer}
def num_trees(n)
    dp = [0] * (n + 1)
    dp[0] = 1

    for i in 1..n
        for j in 1..i
            dp[i] += dp[j - 1] * dp[i - j]
        end
    end

    return dp[n]
end

Solutions (Rust)

1. Dynamic Programming

impl Solution {
    pub fn num_trees(n: i32) -> i32 {
        let n = n as usize;
        let mut dp = vec![0; n + 1];
        dp[0] = 1;

        for i in 1..=n {
            for j in 1..=i {
                dp[i] += dp[j - 1] * dp[i - j];
            }
        }

        dp[n]
    }
}