algorithm: add UniquePaths2 algorithm

This algorithm allows to count ways to reach
right-bottom corner on the grid with obtacles

Author: Saimon398

Dynamic-Programming/UniquePaths2.js

@@ -0,0 +1,80 @@
+/*
+ * 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 }