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UniquePaths2 and HornerScheme #1240
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d648030
algorithm: add UniquePaths2 algorithm
Saimon398 1005207
test: add test for UniquePaths2.js
Saimon398 b888548
algorithm: add HornerScheme algorithm
Saimon398 d4e1ec9
test: add test for Maths/HornerScheme.js
Saimon398 be56ea7
fix: fixed spelling errors in Horner Scheme tests
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/* | ||
* Unique Paths 2 | ||
* | ||
* There is a robot on an `m x n` grid. | ||
* The robot is initially located at the top-left corner | ||
* The robot tries to move to the bottom-right corner. | ||
* The robot can only move either down or right at any point in time. | ||
* | ||
* Given grid with obstacles | ||
* An obstacle and space are marked as 1 or 0 respectively in grid. | ||
* A path that the robot takes cannot include any square that is an obstacle. | ||
* Return the number of possible unique paths that the robot can take to reach the bottom-right corner. | ||
* | ||
* More info: https://leetcode.com/problems/unique-paths-ii/ | ||
*/ | ||
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/** | ||
* @description Return 'rows x columns' grid with cells filled by 'filler' | ||
* @param {Number} rows Number of rows in the grid | ||
* @param {Number} columns Number of columns in the grid | ||
* @param {String | Number | Boolean} filler The value to fill cells | ||
* @returns {Object []} | ||
*/ | ||
const generateMatrix = (rows, columns, filler = 0) => { | ||
const matrix = [] | ||
for (let i = 0; i < rows; i += 1) { | ||
const submatrix = [] | ||
for (let k = 0; k < columns; k += 1) { | ||
submatrix[k] = filler | ||
} | ||
matrix[i] = submatrix | ||
} | ||
return matrix | ||
} | ||
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/** | ||
* @description Return number of unique paths | ||
* @param {Object []} obstacles Obstacles grid | ||
* @returns {Number} | ||
*/ | ||
const uniquePaths2 = (obstacles) => { | ||
if (!(obstacles instanceof Object)) { | ||
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throw new Error('Input data must be type of Array') | ||
} | ||
// Create grid for calculating number of unique ways | ||
const rows = obstacles.length | ||
const columns = obstacles[0].length | ||
const grid = generateMatrix(rows, columns) | ||
// Fill the outermost cell with 1 b/c it has | ||
// the only way to reach neighbor | ||
for (let i = 0; i < rows; i += 1) { | ||
// If robot encounters an obstacle in these cells, | ||
// he cannot continue movind in that direction | ||
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if (obstacles[i][0]) { | ||
break | ||
} | ||
grid[i][0] = 1 | ||
} | ||
for (let j = 0; j < columns; j += 1) { | ||
if (obstacles[0][j]) { | ||
break | ||
} | ||
grid[0][j] = 1 | ||
} | ||
// Fill the rest of grid by dynamic programming | ||
// using following reccurent formula: | ||
// K[i][j] = K[i - 1][j] + K[i][j - 1] | ||
for (let i = 1; i < rows; i += 1) { | ||
for (let j = 1; j < columns; j += 1) { | ||
if (obstacles[i][j]) { | ||
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grid[i][j] = 0 | ||
} else { | ||
grid[i][j] = grid[i - 1][j] + grid[i][j - 1] | ||
} | ||
} | ||
} | ||
return grid[rows - 1][columns - 1] | ||
} | ||
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export { uniquePaths2 } |
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import { uniquePaths2 } from '../UniquePaths2' | ||
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describe('Unique Paths2', () => { | ||
// Should return number of ways, taken into account the obstacles | ||
test('Case 1: there are obstacles in the way', () => { | ||
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expect(uniquePaths2([[0, 0, 0], [0, 1, 0], [0, 0, 0]])).toEqual(2) | ||
expect(uniquePaths2([[0, 0, 0], [0, 1, 0], [0, 0, 0], [1, 0, 0]])).toEqual(3) | ||
}) | ||
// Should return number of all possible ways to reach right-bottom corner | ||
test('Case 2: there are no obstacles in the way', () => { | ||
expect(uniquePaths2([[0, 0, 0], [0, 0, 0], [0, 0, 0]])).toEqual(6) | ||
expect(uniquePaths2([[0, 0, 0], [0, 0, 0]])).toEqual(3) | ||
}) | ||
// Should throw an exception b/c input data has wrong type | ||
test('Case 3: there are wrong type of input data', () => { | ||
expect(() => uniquePaths2('wrong input')).toThrow() | ||
expect(() => uniquePaths2(100)).toThrow() | ||
}) | ||
}) |
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/** | ||
* @function hornerScheme | ||
* @description Convert a number from decimal system to another (till decimal) | ||
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* @param {Number} number Number to be converted | ||
* @param {Number} base Base of new number system | ||
* @returns {String} Converted Number | ||
* @see [HornerMethod](https://en.wikipedia.org/wiki/Horner%27s_method) | ||
* @example | ||
* const num1 = 125 // Needs to be converted to the binary number system | ||
* gornerScheme(num, 2); // ===> 1111101 | ||
* @example | ||
* const num2 = 125 // Needs to be converted to the octal number system | ||
* gornerScheme(num, 8); // ===> 175 | ||
*/ | ||
const hornerScheme = (number, base) => { | ||
if (typeof number !== 'number' || typeof base !== 'number') { | ||
throw new Error('Input data must be numbers') | ||
} | ||
// Zero in any number system is zero | ||
if (number === 0) { | ||
return `${number}` | ||
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} | ||
let absoluteValue = Math.abs(number) | ||
let convertedNumber = '' | ||
while (absoluteValue > 0) { | ||
// Every iteration last digit is taken away | ||
// and added to the previois one | ||
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const lastDigit = absoluteValue % base | ||
convertedNumber = lastDigit + convertedNumber | ||
absoluteValue = Math.trunc(absoluteValue / base) | ||
} | ||
// Result is whether negative or positive, | ||
// depending on the original value | ||
const result = number < 0 ? `-${convertedNumber}` : convertedNumber | ||
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return result | ||
} | ||
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export { hornerScheme } |
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import { hornerScheme } from '../HornerScheme' | ||
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describe('Horner Scheme', () => { | ||
test('Case 1: testing conversion to the binary system', () => { | ||
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expect(hornerScheme(210, 2)).toEqual('11010010') | ||
expect(hornerScheme(-210, 2)).toEqual('-11010010') | ||
}) | ||
test('Case 2: testing conversion to the system with base 5', () => { | ||
expect(hornerScheme(210, 5)).toEqual('1320') | ||
expect(hornerScheme(-210, 5)).toEqual('-1320') | ||
}) | ||
test('Case 3: testing conversion to the octal system', () => { | ||
expect(hornerScheme(210, 8)).toEqual('322') | ||
expect(hornerScheme(-210, 8)).toEqual('-322') | ||
}) | ||
test('Case 4: testing 0', () => { | ||
expect(hornerScheme(0, 8)).toEqual('0') | ||
expect(hornerScheme(0, 8)).toEqual('0') | ||
}) | ||
test('Case 5: testing throwing an exception', () => { | ||
expect(() => hornerScheme('string', 2)).toThrow() | ||
expect(() => hornerScheme(10, 'base')).toThrow() | ||
expect(() => hornerScheme(true, false)).toThrow() | ||
}) | ||
}) |
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