p11_gridProduct.js

/* In the 20×20 grid below, four numbers along
 * diagonal line have been selected.
 * 
 * 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
 * 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
 * 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
 * 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
 * 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
 * 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
 * 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
 * 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
 * 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
 * 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
 * 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
 * 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
 * 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
 * 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
 * 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
 * 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
 * 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
 * 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
 * 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
 * 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
 * 
 * The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
 * 
 * What is the greatest product of four adjacent numbers in the same direction
 * (up, down, left, right, or diagonally) in the 20×20 grid?
 * ---------------------------------------------------------------------------*/

var GRIDSTRING, GRIDSIZE;	//global constants

//largest values of multiplications
var largestHorizontal, largestVertical, largestDiagUp, largestDiagDown;

GRIDSIZE = 20;

GRIDSTRING = 
	'08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 ' +
	'49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 ' +
	'81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 ' +
	'52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 ' +
	'22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 ' +
	'24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 ' +
	'32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 ' +
	'67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 ' +
	'24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 ' +
	'21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 ' +
	'78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 ' +
	'16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 ' +
	'86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 ' +
	'19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 ' +
	'04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 ' +
	'88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 ' +
	'04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 ' +
	'20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 ' +
	'20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 ' +
	'01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48';

/*
 * greatestHorizontal takes in a series of numbers in the form of a
 * continuous string, in which each number is separated by a space.
 * The function returns the greatest product of horizontally adjacent integers 
 * contained in the string, multiplying the
 * number of integers passed in as the 2nd argument at a time. Go to
 * 			https://projecteuler.net/problem=11
 * for further clarification.
 *
 * @param the string of integers
 * @param the number of adjacent integers to multiply in sequence
 *
 * @return the greatest product
 */
function greatestHorizontal(numString, numToMultiply) {
	var numArray, index, index2, productsArray, thisProduct;

	thisProduct = 1;
	if (numToMultiply === undefined) numToMultiply = 4;
	productsArray = [];

	//create array of numbers from the string
	numArray = numString.split(" ");

	//get an array of products
	for (index = 0; index < numArray.length - numToMultiply + 1; index++) {
		for (index2 = 0; index2 < numToMultiply; index2++) {
			thisProduct *= Number(numArray[index + index2]);
		}
	
		productsArray.push(thisProduct);
		thisProduct = 1;
	}

	return productsArray.reduce(function(n1, n2) {return Math.max(n1, n2)});
}

/*
 * greatestVertical takes in a series of numbers in the form of a
 * continuous string, in which each number is separated by a space.
 * The function returns the greatest product of vertically adjacent integers 
 * contained in the string, multiplying the
 * number of integers passed in as the 2nd argument at a time. Go to
 * 			https://projecteuler.net/problem=11
 * for further clarification.
 *
 * @param the string of integers
 * @param the number of adjacent integers to multiply in sequence
 *
 * @return the greatest product
 */
function greatestVertical(numString, numToMultiply) {	
	var numArray, index, index2, productsArray, thisProduct;

	thisProduct = 1;
	if (numToMultiply === undefined) numToMultiply = 4;
	productsArray = [];

	//create array of numbers from the string
	numArray = numString.split(" ");

	for (index = 0;
			index < numArray.length - GRIDSIZE * (numToMultiply - 1); index++) {
		for (index2 = 0; index2 < numToMultiply; index2++) {
			thisProduct *= numArray[index + GRIDSIZE * index2];
		}
		productsArray.push(thisProduct);
		thisProduct = 1;
	}
	
	return productsArray.reduce(function(n1, n2) {return Math.max(n1, n2)});
}

/*
 * greatestDiagDown takes in a series of numbers in the form of a
 * continuous string, in which each number is separated by a space.
 * The function returns the greatest product of integers cascading
 * down, multiplying the number of integers passed in
 * as the 2nd argument at a time. Go to
 * 			https://projecteuler.net/problem=11
 * for further clarification.
 *
 * @param the string of integers
 * @param the number of cascading integers to multiply in sequence
 *
 * @return the greatest product
 */
function greatestDiagDown(numString, numToMultiply) {
	
	var numArray, index, index2, productsArray, thisProduct, final3;

	thisProduct = 1;
	if (numToMultiply === undefined) numToMultiply = 4;
	productsArray = [];
	increment = numToMultiply - 2;
	
	//create array of numbers from the string
	numArray = numString.split(" ");

	for (index = 0;
			index < numArray.length - GRIDSIZE * (numToMultiply - 1); index++) {
	
		if (index % GRIDSIZE === GRIDSIZE - (numToMultiply - 1)) {
			index += increment;
			continue;
		}
		
		for (index2 = 0; index2 < numToMultiply; index2++) {
			thisProduct *=
				Number(numArray[index + (GRIDSIZE * index2) + index2]);
		}
		
		productsArray.push(thisProduct);
		thisProduct = 1;
	}
	
	return productsArray.reduce(function(n1, n2) {return Math.max(n1, n2)});

}

/*
 * greatestDiagUp takes in a series of numbers in the form of a
 * continuous string, in which each number is separated by a space.
 * The function returns the greatest product of integers cascading
 * down, multiplying the number of integers passed in
 * as the 2nd argument at a time. Go to
 * 			https://projecteuler.net/problem=11
 * for further clarification.
 *
 * @param the string of integers
 * @param the number of cascading integers to multiply in sequence
 *
 * @return the greatest product
 */
function greatestDiagUp(numString, numToMultiply) {
	/*
 	 * This function works by re-ordering the passed in string by simply
 	 * flipping the rows vertically. The bottom row goes to the top and
 	 * vice versa, for every row. This new string is then passed to
 	 * greatestDiagDown which will return what we want after it has acted
 	 * on the new string.
 	 */
	var index, strFlipped, stringArray, stringArrayFlipped, numArray;
	stringArray = [];
	
	//create array of numbers from the string
	numArray = numString.split(" ");
	
	//create array containing each row but going from bottom to top	
	for (index = Math.pow(GRIDSIZE, 2); index > 0; index -= GRIDSIZE) {
		stringArray.push(numArray.slice(index - GRIDSIZE, index));
	}
	
	//concatenate it to create a new array in the order wanted
	stringArrayFlipped = stringArray.reduce(function(n1, n2) {
		return n1.concat(n2);
	});

	//join the array into a string
	strFlipped = stringArrayFlipped.join(" ");
	
	//call greatestDiagDown
	return greatestDiagDown(strFlipped, numToMultiply);
}

largestHorizontal = greatestHorizontal(GRIDSTRING);
largestVertical = greatestVertical(GRIDSTRING);
largestDiagDown = greatestDiagDown(GRIDSTRING);
largestDiagUp = greatestDiagUp(GRIDSTRING);

//print out the largest of these 4 largest products
console.log(Math.max(largestHorizontal, largestVertical, largestDiagDown,
			largestDiagUp));