Create 62. Unique Paths.md

TBXark · web-flow · commit 2b97e899b904 · 2020-07-31T15:12:22.000+08:00
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+# 62. Unique Paths
+
+### 2020-07-31
+
+A robot is located at the top-left corner of a *m* x *n* grid (marked 'Start' in the diagram below).
+
+The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
+
+How many possible unique paths are there?
+
+![img](https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png)
+
+Above is a 7 x 3 grid. How many possible unique paths are there?
+
+ 
+
+**Example 1:**
+
+```
+Input: m = 3, n = 2
+Output: 3
+Explanation:
+From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
+1. Right -> Right -> Down
+2. Right -> Down -> Right
+3. Down -> Right -> Right
+```
+
+**Example 2:**
+
+```
+Input: m = 7, n = 3
+Output: 28
+```
+
+ 
+
+**Constraints:**
+
+- `1 <= m, n <= 100`
+- It's guaranteed that the answer will be less than or equal to `2 * 10 ^ 9`.
+
+
+# Solution
+
+```swift
+class Solution {
+    func uniquePaths(_ m: Int, _ n: Int) -> Int {
+        var cache = [[Int]].init(repeating: [Int].init(repeating: 0, count: n), count: m)
+        for y in 1...m {
+            for x in 1...n {
+                if x == 1 || y == 1 {
+                    cache[y - 1][x - 1] = 1
+                } else {
+                    cache[y - 1][x - 1] = cache[y - 2][x - 1] + cache[y - 1][x - 2]
+                }
+            }
+        }
+        return cache[m - 1][n - 1]
+    }
+}
+
+```
+
