UniquePaths2 and HornerScheme

Dynamic-Programming/UniquePaths2.js

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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/
+ */
+
+/**
+ * @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
+}
+
+/**
+ * @description Return number of unique paths
+ * @param {Object []} obstacles Obstacles grid
+ * @returns {Number}
+ */
+const uniquePaths2 = (obstacles) => {
+  if (!(obstacles instanceof Object)) {
+    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
+    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]) {
+        grid[i][j] = 0
+      } else {
+        grid[i][j] = grid[i - 1][j] + grid[i][j - 1]
+      }
+    }
+  }
+  return grid[rows - 1][columns - 1]
+}
+
+export { uniquePaths2 }

Dynamic-Programming/tests/UniquePaths2.test.js

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+import { uniquePaths2 } from '../UniquePaths2'
+
+describe('Unique Paths2', () => {
+  // Should return number of ways, taken into account the obstacles
+  test('Case 1: there are obstacles in the way', () => {
+    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()
+  })
+})

Maths/HornerScheme.js

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+/**
+ * @function hornerScheme
+ * @description Convert a number from decimal system to another (till decimal)
+ * @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 `${number}`
+  }
+  let absoluteValue = Math.abs(number)
+  let convertedNumber = ''
+  while (absoluteValue > 0) {
+    // Every iteration last digit is taken away
+    // and added to the previois one
+    const lastDigit = absoluteValue % base
+    convertedNumber = lastDigit + convertedNumber
+    absoluteValue = Math.trunc(absoluteValue / base)
+  }
+  // Result is whether negative or positive,
+  // depending on the original value
+  const result = number < 0 ? `-${convertedNumber}` : convertedNumber
+  return result
+}
+
+export { hornerScheme }

Maths/test/HornerScheme.test.js

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+import { hornerScheme } from '../HornerScheme'
+
+describe('Horner Scheme', () => {
+  test('Case 1: testing conversion to the binary system', () => {
+    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()
+  })
+})