bracketsproblem.js

function isPrime(n) {
	for ( let i = 2; i < n / 2; i++ ) {
		if ( n % i == 0 ) {
			return false;
		}
	}

	return true;
}

function createMatrix(size) {
	const array = []; // Array to store the matrix
	const tmp = []; // First row, containing numbers 1 .. size

	for ( let i = 1; i <= size; i++ ) {
		tmp.push(i);
	}

	array.push(tmp);

	// Initialize the rest of the rows as 0s
	for ( let i = 0; i < size - 1; i++ ) {
		const tmp = [];

		for ( let j = 0; j < size; j++ ) {
			tmp.push(0);
		}

		array.push(tmp);
	}

	// Fill in the array given the rules
	for ( let y = 1; y < size; y++ ) {
		array[y][0] = y + 1;

		for ( let x = 1; x < size; x++ ) {
			const find = array[y - 1].indexOf(array[y][x - 1]) + 1;

			if ( find == size ) {
				array[y][x] = 1;
			}
			else {
				array[y][x] = array[y - 1][find] + 1;
			}
		}
	}

	return array;
}

function verifyMatrix(matrix, debug=True) {
	// 3 rules:
	// 1. no chain has one person draw twice
	// 2. no person draws two chains on the same day
	// 3. no person receives a drawing from the same person more than once

	// Verify rule #1
	for ( let y = 0; y < matrix.length; y++ ) {
		let good = true;
		const check = {};

		for ( let x = 0; x < matrix[y].length; x++ ) {
			if ( check[matrix[y][x]] ) {
				good = false;
				break;
			}

			check[matrix[y][x]] = true;
		}

		if ( !good ) {
			if ( debug ) console.log("Rule #1 broken on line " + (y + 1).toString());
			return false;
		}
	}

	// Verify rule #2
	for ( let x = 0; x < matrix.length; x++ ) {
		let good = true;
		const check = {};

		for ( let y = 0; y < matrix[x].length; y++ ) {
			if ( check[matrix[y][x]] ) {
				good = false;
				break;
			}

			check[matrix[y][x]] = true;
		}

		if ( !good ) {
			if ( debug ) console.log("Rule #2 broken on vertical line " + (x + 1).toString());
			return false;
		}
	}

	//Verify rule #3
	const verf = {};

	for ( let i = 0; i < matrix.length; i++ ) {
		for ( let j = 0; j < matrix[i].length; j++ ) {
			if ( i != j ) {
				verf[i.toString() + "_" + j.toString()] = false; 
			}
		}
	}

	for ( let y = 0; y < matrix.length; y++ ) {
		for ( let x = 0; x < matrix[y].length - 1; x++ ) {
			const first = matrix[y][x];
			const second = matrix[y][x + 1];
			const check = first.toString() + "_" + second.toString();

			if ( verf[check] ) {
				if ( debug ) console.log("Rule #3 at location (" + x.toString() + ", " + y.toString() + ")");
				return false;
			}

			verf[check] = true;
		} 
 	}


	if ( debug ) console.log("All rules passing.");
	return true;
}

function debugMatrix(matrix) {
	for ( let y = 0; y < matrix.length; y++ ) {
		let row = "";

		for ( let x = 0; x < matrix[y].length; x++ ) {
			row = row + matrix[y][x].toString() + "\t";
		}

		console.log(row);
	}
}


for ( let i = 1; i < 100; i++ ) {
	const matrix = createMatrix(i);
	const worked = verifyMatrix(matrix, false);

	if ( worked ) {
		if ( isPrime(i + 1) ) {
			console.log("Brackets is the best");
		}
		else {
			console.log("BRB throwing self off cliff");
		}
	}
}