algorithm: unique paths 2 (#1257)

* algorithm: add UniquePaths2 algo and a test for it

* fix: fix inaccuracies and spelling errors

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 {Array [][]}
+ */
+const generateMatrix = (rows, columns, filler = 0) => {
+  const matrix = []
+  for (let i = 0; i < rows; i++) {
+    const submatrix = []
+    for (let k = 0; k < columns; k++) {
+      submatrix[k] = filler
+    }
+    matrix[i] = submatrix
+  }
+  return matrix
+}
+
+/**
+ * @description Return number of unique paths
+ * @param {Array [][]} obstacles Obstacles grid
+ * @returns {Number}
+ */
+const uniquePaths2 = (obstacles) => {
+  if (!Array.isArray(obstacles)) {
+    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++) {
+    // If robot encounters an obstacle in these cells,
+    // he cannot continue moving in that direction
+    if (obstacles[i][0]) {
+      break
+    }
+    grid[i][0] = 1
+  }
+  for (let j = 0; j < columns; j++) {
+    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++) {
+    for (let j = 1; j < columns; j++) {
+      grid[i][j] = obstacles[i][j] ? 0 : 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('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('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('There are wrong type of input data', () => {
+    expect(() => uniquePaths2('wrong input')).toThrow()
+    expect(() => uniquePaths2(100)).toThrow()
+  })
+})