Add Pascal's Triangle based solution for Unique Paths problem.

Author: trekhleb

README.md

@@ -118,7 +118,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples 
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking and dynamic programming examples 
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples 
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 

src/algorithms/uncategorized/unique-paths/README.md

@@ -94,6 +94,13 @@ the bottom right one with number `3`.
 
 **Auxiliary Space Complexity**: `O(m * n)` - since we need to have DP matrix.
 
+### Pascal's Triangle Based
+
+This question is actually another form of Pascal Triangle.
+
+The corner of this rectangle is at `m + n - 2` line, and 
+at `min(m, n) - 1` position of the Pascal's Triangle.
+
 ## References
 
 - [LeetCode](https://leetcode.com/problems/unique-paths/description/)

src/algorithms/uncategorized/unique-paths/__test__/uniquePaths.test.js

@@ -0,0 +1,12 @@
+import uniquePaths from '../uniquePaths';
+
+describe('uniquePaths', () => {
+  it('should find the number of unique paths on board', () => {
+    expect(uniquePaths(3, 2)).toBe(3);
+    expect(uniquePaths(7, 3)).toBe(28);
+    expect(uniquePaths(3, 7)).toBe(28);
+    expect(uniquePaths(10, 10)).toBe(48620);
+    expect(uniquePaths(100, 1)).toBe(1);
+    expect(uniquePaths(1, 100)).toBe(1);
+  });
+});

src/algorithms/uncategorized/unique-paths/uniquePaths.js

@@ -0,0 +1,13 @@
+import pascalTriangle from '../../math/pascal-triangle/pascalTriangle';
+
+/**
+ * @param {number} width
+ * @param {number} height
+ * @return {number}
+ */
+export default function uniquePaths(width, height) {
+  const pascalLine = width + height - 2;
+  const pascalLinePosition = Math.min(width, height) - 1;
+
+  return pascalTriangle(pascalLine)[pascalLinePosition];
+}