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 @@
+importuniquePathsfrom'../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 @@
+importpascalTrianglefrom'../../math/pascal-triangle/pascalTriangle';
+
+/**
+ * @param{number} width
+ * @param{number} height
+ * @return{number}
+ */
+exportdefaultfunctionuniquePaths(width,height){
+constpascalLine=width+height-2;
+constpascalLinePosition=Math.min(width,height)-1;
+
+returnpascalTriangle(pascalLine)[pascalLinePosition];
+}