Contribute: Added algorithm and tests for Unique Paths DP problem

Dynamic-Programming/UniquePaths.js

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+/*
+ * A Dynamic Programming based solution for calculating the number ways to travel from Top-Left of the matrix to Bottom-Right of the matrix
+ * https://leetcode.com/problems/unique-paths/
+ * Problem Statement:
+ * There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.
+ * Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.
+ * Approach:
+ * As the given problem can be reduced to smaller and overlapping sub problems, we can use dynamic programming and memoization to solve this problem.
+ * Time complexity: O(M * N) (M->ROWS | N->COLS)
+ * Space complexity: O(M * N) (M->ROWS | N->COLS)
+ */
+
+/**
+ * @param {number} rows
+ * @param {number} cols
+ * @return {number}
+ */
+
+// Return the number of unique paths, given the dimensions of rows and columns
+
+const uniquePaths = (rows, cols) => {
+  let dp = new Array(cols).fill(1)
+
+  for (let i = 1; i < rows; i++) {
+    const tmp = []
+
+    for (let j = 0; j < cols; j++) {
+      if (j === 0) {
+        tmp[j] = dp[j]
+      } else {
+        tmp[j] = tmp[j - 1] + dp[j]
+      }
+    }
+    dp = tmp
+  }
+  return dp.pop()
+}
+
+export { uniquePaths }

Dynamic-Programming/tests/UniquePaths.test.js

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+import { uniquePaths } from '../UniquePaths'
+
+test('Test case for UniquePaths', () => {
+  expect(uniquePaths(3, 7)).toBe(28)
+  expect(uniquePaths(3, 2)).toBe(3)
+  expect(uniquePaths(8, 14)).toBe(77520)
+})