JavaScript || How To Calculate Nth Catalan Number Using Vanilla JavaScript

October 06, 2020 admin No comments

In combinatorial mathematics, a Catalan number forms a sequence of natural numbers that occur in various counting problems. It can be used to determine how many different ways to split something up.

The following is a module with functions which demonstrates how to calculate nth Catalan number.

1. Calculate Nth Catalan Number

The example below demonstrates the use of ‘Utils.catalan‘ to calculate nth Catalan number.





		
		
			1. Calculate Nth Catalan Number
			
JavaScript
			
			// Calculate Nth Catalan Number

<script>
(() => {    
    for (let number = 0; number <= 10; ++number) {
        console.log(`Number: ${number}, Catalan: ${Utils.catalan(number)}`);
    }
})();
</script>

// expected output:
/*
    Number: 0, Catalan: 1  
    Number: 1, Catalan: 1  
    Number: 2, Catalan: 2  
    Number: 3, Catalan: 5  
    Number: 4, Catalan: 14  
    Number: 5, Catalan: 42  
    Number: 6, Catalan: 132  
    Number: 7, Catalan: 429  
    Number: 8, Catalan: 1430  
    Number: 9, Catalan: 4862  
    Number: 10, Catalan: 16796  
*/
			
				
					
				
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						// Calculate Nth Catalan Number
 
<script>
(() => {    
    for (let number = 0; number <= 10; ++number) {
        console.log(`Number: ${number}, Catalan: ${Utils.catalan(number)}`);
    }
})();
</script>
 
// expected output:
/*
    Number: 0, Catalan: 1  
    Number: 1, Catalan: 1  
    Number: 2, Catalan: 2  
    Number: 3, Catalan: 5  
    Number: 4, Catalan: 14  
    Number: 5, Catalan: 42  
    Number: 6, Catalan: 132  
    Number: 7, Catalan: 429  
    Number: 8, Catalan: 1430  
    Number: 9, Catalan: 4862  
    Number: 10, Catalan: 16796  
*/

2. Utils Namespace

The following is the Utils.js Namespace. Include this in your project to start using!





		
		
			Utils.js Namespace
			
JavaScript
			
			// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Oct 6, 2020
//    Taken From: http://programmingnotes.org/
//    File:  Utils.js
//    Description: Javascript that handles general utility functions
// ============================================================================
/**
* NAMESPACE: Utils
* USE: Handles general utility functions.
*/
var Utils = Utils || {};
(function(namespace) {
    'use strict';

    // Property to hold public variables and functions
    let exposed = namespace;

    /**
    * FUNCTION: catalan
    * USE: Calculates the catalan number for the number in question
    * @param n: The number to calculate the catalan number.
    * @return: The catalan number for the number in question.
    */
    exposed.catalan = (n) => {
        n = Math.max(0, n);
        let result = Array(n + 1);
        result[0] = result[1] = 1;
        for (let x = 2; x <= n; ++x) {
            result[x] = 0;
            for (let y = 0; y < x; ++y) {
                result[x] += result[y] * result[x - y - 1];
            }
        }
        return result[n];
    }

    (function (factory) {
        if (typeof define === 'function' && define.amd) {
            define([], factory);
        } else if (typeof exports === 'object') {
            module.exports = factory();
        }
    }(function() { return namespace; })); 
}(Utils)); // http://programmingnotes.org/
			
				
					
				
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						// ============================================================================
//    Author: Kenneth Perkins
//    Date:   Oct 6, 2020
//    Taken From: http://programmingnotes.org/
//    File:  Utils.js
//    Description: Javascript that handles general utility functions
// ============================================================================
/**
* NAMESPACE: Utils
* USE: Handles general utility functions.
*/
var Utils = Utils || {};
(function(namespace) {
    'use strict';
 
    // Property to hold public variables and functions
    let exposed = namespace;
 
    /**
    * FUNCTION: catalan
    * USE: Calculates the catalan number for the number in question
    * @param n: The number to calculate the catalan number.
    * @return: The catalan number for the number in question.
    */
    exposed.catalan = (n) => {
        n = Math.max(0, n);
        let result = Array(n + 1);
        result[0] = result[1] = 1;
        for (let x = 2; x <= n; ++x) {
            result[x] = 0;
            for (let y = 0; y < x; ++y) {
                result[x] += result[y] * result[x - y - 1];
            }
        }
        return result[n];
    }
 
    (function (factory) {
        if (typeof define === 'function' && define.amd) {
            define([], factory);
        } else if (typeof exports === 'object') {
            module.exports = factory();
        }
    }(function() { return namespace; })); 
}(Utils)); // http://programmingnotes.org/

QUICK NOTES:
The highlighted lines are sections of interest to look out for.

The code is heavily commented, so no further insight is necessary. If you have any questions, feel free to leave a comment below.

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Posted in: JavaScript, Vanilla JavaScript Tags: javascript

JavaScript || How To Calculate Nth Catalan Number Using Vanilla JavaScript

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