October 6, 2020 – My Programming Notes

Daily Archives: October 6, 2020

JavaScript || How To Find All Combinations Of Well-Formed Brackets Using Vanilla JavaScript

October 06, 2020 admin No comments

The following is a module with functions which demonstrates how to find all combinations of well-formed brackets.

The task is to write a function Brackets(int n) that prints all combinations of well-formed brackets from 1…n. For example, Brackets(3), the output would be:

() (()) ()() ((())) (()()) (())() ()(()) ()()()

The number of possible combinations is the Catalan number of N pairs C(n).

1. Find All Well-Formed Brackets

The example below demonstrates the use of ‘Utils.brackets‘ to find all the well-formed bracket combinations.





		
		
			1. Find All Well-Formed Brackets
			
JavaScript
			
			// Find All Well-Formed Brackets

<script>
(() => {
    let results = Utils.brackets(4);    
    results.forEach((result) => {
        console.log(`Pair: ${result.pair}, Combination: ${result.combination}`);
    });
})();
</script>

// expected output:
/*
    Pair: 1, Combination: () 
    Pair: 2, Combination: (()), ()() 
    Pair: 3, Combination: ((())), (()()), (())(), ()(()), ()()() 
    Pair: 4, Combination: (((()))), ((()())), ((())()), ((()))(), (()(())), (()()()), (()())(), (())(()), (())()(), ()((())), ()(()()), ()(())(), ()()(()), ()()()()  
*/
			
				
					
				
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						// Find All Well-Formed Brackets
 
<script>
(() => {
    let results = Utils.brackets(4);    
    results.forEach((result) => {
        console.log(`Pair: ${result.pair}, Combination: ${result.combination}`);
    });
})();
</script>
 
// expected output:
/*
    Pair: 1, Combination: () 
    Pair: 2, Combination: (()), ()() 
    Pair: 3, Combination: ((())), (()()), (())(), ()(()), ()()() 
    Pair: 4, Combination: (((()))), ((()())), ((())()), ((()))(), (()(())), (()()()), (()())(), (())(()), (())()(), ()((())), ()(()()), ()(())(), ()()(()), ()()()()  
*/

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: brackets
    * USE: Returns all combinations of well-formed brackets from 1...n
    * @param pairs: The number of bracket combinations to generate.
    * @param open: Optional. The 'open bracket' symbol.
    * @param close: Optional. The 'close bracket' symbol.
    * @return: An array of bracket combination info.
    */
    exposed.brackets = (pairs, open = '(', close = ')') => {
        let results = [];
        let symbols = {
            open: open,
            close: close,
        };
        for (let pair = 1; pair <= pairs; ++pair) {
            results.push({
                pair: pair,
                combination: buildBrackets('', 0, 0, pair, symbols),
            });
        }
        return results;
    }

    let buildBrackets = (output, open, close, pair, symbols) => {
        if ((open === pair) && (close === pair)) {
            return output;
        }
        let result = '';
        if (open < pair) {
            let openCombo = buildBrackets(output + symbols.open, open + 1, close, pair, symbols);
            if (openCombo.length > 0) {
                result += (result.length > 0 ? ', ' : '') + openCombo;
            }
        }
        if (close < open) {
            let closeCombo = buildBrackets(output + symbols.close, open, close + 1, pair, symbols);
            if (closeCombo.length > 0) {
                result += (result.length > 0 ? ', ' : '') + closeCombo;
            }
        }
        return result;
    }

    (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: brackets
    * USE: Returns all combinations of well-formed brackets from 1...n
    * @param pairs: The number of bracket combinations to generate.
    * @param open: Optional. The 'open bracket' symbol.
    * @param close: Optional. The 'close bracket' symbol.
    * @return: An array of bracket combination info.
    */
    exposed.brackets = (pairs, open = '(', close = ')') => {
        let results = [];
        let symbols = {
            open: open,
            close: close,
        };
        for (let pair = 1; pair <= pairs; ++pair) {
            results.push({
                pair: pair,
                combination: buildBrackets('', 0, 0, pair, symbols),
            });
        }
        return results;
    }
 
    let buildBrackets = (output, open, close, pair, symbols) => {
        if ((open === pair) && (close === pair)) {
            return output;
        }
        let result = '';
        if (open < pair) {
            let openCombo = buildBrackets(output + symbols.open, open + 1, close, pair, symbols);
            if (openCombo.length > 0) {
                result += (result.length > 0 ? ', ' : '') + openCombo;
            }
        }
        if (close < open) {
            let closeCombo = buildBrackets(output + symbols.close, open, close + 1, pair, symbols);
            if (closeCombo.length > 0) {
                result += (result.length > 0 ? ', ' : '') + closeCombo;
            }
        }
        return result;
    }
 
    (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.

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.

Daily Archives: October 6, 2020

JavaScript || How To Find All Combinations Of Well-Formed Brackets Using Vanilla JavaScript

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

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