add: 62

Author: huyjs9

README.md

@@ -7,6 +7,7 @@
 | #    | Title                                                                                                                      | Level  | Time         | Space      | Tags                                                                | Note                          |
 | ---- | -------------------------------------------------------------------------------------------------------------------------- | ------ | ------------ | ---------- | ------------------------------------------------------------------- | ----------------------------- |
 | 57   | [Insert Interval](./src/57.insert-interval.py)                                                                             | Medium | O(N)         | O(N)       | Array, Matrix, Dynamic Programming                                  | DP (Merging Intervals)        |
+| 62   | [Unique Paths](./src/62.unique-paths.py)                                                                                   | Medium | O(M\*N)      | O(M\*N)    | Array, Matrix, Dynamic Programming                                  | DP (Distinct Ways)            |
 | 64   | [Minimum Path Sum](./src/64.minimum-path-sum.py)                                                                           | Medium | O(N\*M)      | O(N\*M)    | Array, Matrix, Dynamic Programming                                  | DP (Min - Max)                |
 | 70   | [Climbing Stairs](./src/70.climbing-stairs.py)                                                                             | Easy   | O(N)         | O(N)       | Dynamic Programming                                                 | DP (Min - Max)                |
 | 120  | [Triangle](./src/120.triangle.py)                                                                                          | Medium | O(N^2)       | O(N^2)     | Array, Dynamic Programming                                          | DP (Min - Max)                |

src/62.unique-paths.py

@@ -0,0 +1,54 @@
+# Level: Medium
+# TAGS: Math, Dynamic Programming, Combinatorics
+
+
+class Solution:
+    """
+    DP Top-Down | Time and Space: O(M*N)
+    """
+
+    def uniquePaths(self, m: int, n: int) -> int:
+        memo = {}
+
+        def dfs(i, j):
+            if i < 0 or j < 0:
+                return 0
+            if i == 0 and j == 0:
+                return 1
+
+            if (i, j) in memo:
+                return memo[(i, j)]
+
+            memo[(i, j)] = dfs(i - 1, j) + dfs(i, j - 1)
+            return memo[(i, j)]
+
+        return dfs(m - 1, n - 1)
+
+    """
+    DP Bottom-Up
+    """
+
+    def uniquePaths1(self, m: int, n: int) -> int:
+        dp = [[1] * n for i in range(m)]
+        for i in range(1, m):
+            for j in range(1, n):
+                dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
+        return dp[-1][-1]
+
+
+tests = [
+    (
+        (
+            3,
+            7,
+        ),
+        28,
+    ),
+    (
+        (
+            3,
+            2,
+        ),
+        3,
+    ),
+]