Count Unique Binary Search Trees - The Coding Shala

Last Updated: 19-Jan-2021
Home >> Interview Questions >> Count Unique Binary Search Trees

 In this post, we will learn how to Count Unique Binary Search Trees and will implement its solution in Java.

Count Unique Binary Search Trees Problem

Given N, Find the total number of unique (Binary Search Trees)BSTs that can be made using values from 1 to N.

Example:
Input: 3
Output: 5
Explanation:
Given n = 3, there are a total of 5 unique BST's:
Unique Binary Search Trees - The Coding Shala

Count Unique Binary Search Trees Java Program

Approach 1

Using Dynamic Programming.

One way to solve this problem is we can generate a list of all possible unique binary search trees and return the size of the list.

We can use dynamic programming to solve this problem. For every value of i here i is the root, then 1 to i-1 numbers will come in the left subtree and i+1 to n numbers come in the right subtree so the answer will be a total of (i-1)*(n-i).

Time complexity: O(n^2).

Java Program: 

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


Other Posts You May Like
Please leave a comment below if you like this post or found some errors, it will help me to improve my content.
By

Comments

Post a Comment

Popular Posts from this Blog

Java Program to Convert Binary to Decimal - The Coding Shala

Home >> Java Programs >> Convert Binary to Decimal  Hey there, welcome back to another post. In this post, we will learn how to convert Binary to Decimal in Java. Java Program to Convert Binary to Decimal You have given a binary number, convert it to a decimal number. Example:  Input: 101 Output: 5 Input: 111 Output: 7 Binary to Decimal Conversion in Java Approach We will the below formula to convert binary to decimal: decimal number = (2^0) * (rightmost digit) + (2^1) * (second rightmost digit) + ...  for example:  binary number = 110 decimal number = 2^0 * 0 + 2^1 * 1 + 2^2 * 1 = 1 * 0 + 2 * 1 + 4 * 1 = 0 + 2 + 4 = 6 Java Program:  import java.util.Scanner; /** * https://www.thecodingshala.com/ */ public class Main { public static void printDecimal( int num) { int decimal = 0; int twos = 1; // 2^0 = 1 initial value while (num > 0) { ...
Read more

N-th Tribonacci Number Solution - The Coding Shala

Home >> Programming >> N-th Tribonacci Number  Hey there, welcome back to another post. In this post, we will learn how to solve the N-th Tribonacci Number problem and will implement its solution in Java. N-th Tribonacci Number Problem Statement The Tribonacci sequence Tn is defined as follows: T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0. Given n, return the value of Tn.  Example 1:  Input: n = 4 Output: 4 Explanation: T_3 = 0 + 1 + 1 = 2 T_4 = 1 + 1 + 2 = 4 N-th Tribonacci Number Java Solution using Bottom-Up DP This problem is similar to the Fibonacci series. We can solve it using the Bottom-Up approach of dynamic programming. Time Complexity: O(n) Space Complexity: O(n) The space complexity can be reduced to O(1) by using variables to store the previous three values instead of using an array. Java Program:  class Solution { public int tribonacci( int n) { if (n == 0) return 0; ...
Read more

Shell Script to Create a Simple Calculator - The Coding Shala

Home >> Scripting >> simple calculator Shell Script to Create a Simple Calculator Write a shell script to create a simple calculator using a switch-case statement? Code:  #! / bin / bash echo "simple calculator" sum = 0 i = "y" echo "enter first number" read n1 echo "enter second number" read n2 while [ $ i = "y" ] do echo "1.Addition" echo "2.Subtraction" echo "3.Multiplication" echo "4.Division" echo "Enter choice" read ch case $ch in 1 ) sum =$(echo " $n1 + $n2" | bc - l) echo "Addition is =" $ sum ;; 2 ) sum =$(echo "$n1 - $n2" | bc - l) echo "Sub is =" $ sum ;; 3 ) sum =$(echo "$n1 * $n2" | bc - l) echo "Mul is =" $ sum ;; 4 ) sum =$(echo "$n1 / $n2" | bc - l) echo "div is =" $ sum ;; * )echo "invalid choice" esac echo "Do y...
Read more

LeetCode - Shuffle the Array Solution - The Coding Shala

Home >> LeetCode >> Shuffle the Array  In this post, we will learn how to solve LeetCode's Shuffle the Array problem and will implement its solution in Java. Shuffle the Array Given the array nums consisting of 2n elements in the form [x1,x2,...,xn,y1,y2,...,yn]. Return the array in the form [x1,y1,x2,y2,...,xn,yn]. Example 1: Input: nums = [2,5,1,3,4,7], n = 3 Output: [2,3,5,4,1,7]  Explanation: Since x1=2, x2=5, x3=1, y1=3, y2=4, y3=7 then the answer is [2,3,5,4,1,7]. Example 2: Input: nums = [1,2,3,4,4,3,2,1], n = 4 Output: [1,4,2,3,3,2,4,1] Practice this problem on LeetCode: Click Here. Shuffle the Array Java Solution Approach 1: Using a new Array. Space complexity: O(n). Java Program:  class Solution { public int [] shuffle ( int [] nums , int n ) { int [] ans = new int [ 2 * n ]; int j = 0 ; for ( int i = 0 ; i < 2 * n ; i = i + 2 ){ ans [ i ] = nums [ j ]; ans...
Read more

Introduction to Kotlin Programming Language for Backend Development - The Coding Shala

Home >> Learn Kotlin >> Kotlin Introduction Are you looking for a powerful and reliable programming language for backend development? Look no further than Kotlin. Kotlin is a modern, statically typed programming language that has gained a lot of popularity in recent years. In this blog post, we'll take a look at what Kotlin is and why it's a great choice for backend development. What is Kotlin? Kotlin is a statically typed, cross-platform, general-purpose programming language that was developed by JetBrains in 2011. It is designed to be more concise, expressive, and safe than Java, the most widely used programming language for Android development. Kotlin can be compiled to run on the Java Virtual Machine (JVM), JavaScript, and native platforms, making it a versatile language for different types of applications. Why use Kotlin for backend development? Kotlin has several features that make it a suitable language for backend development, such as: Concisenes...
Read more