Create Unique Paths - Leetcode 62.py

Author: gahogg

Unique Paths - Leetcode 62.py

@@ -0,0 +1,66 @@
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        # Recursive Solution
+        # Time: O(2^(m*n))
+        # Space: O(m*n)
+        
+        def paths(i, j):
+            if i == j == 0:
+                return 1
+            elif i < 0 or j < 0 or i == m or j == n:
+                return 0
+            else:
+                return paths(i-1, j) + paths(i, j-1)
+        
+        return paths(m-1, n-1)
+
+
+
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        # Top Down DP (Memoization)
+        # Time: O(m*n)
+        # Space: O(m*n)
+
+        memo = {(0,0): 1}
+        def paths(i, j):
+            if (i,j) in memo:
+                return memo[(i,j)]
+            elif i < 0 or j < 0 or i == m or j == n:
+                return 0
+            else:
+                val = paths(i, j-1) + paths(i-1, j)
+                memo[(i,j)] = val
+                return val
+        
+        return paths(m-1, n-1)
+
+
+
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        # Bottom Up DP (Tabulation)
+        # Time: O(m*n)
+        # Space: O(m*n)
+
+        dp = []
+        for _ in range(m):
+            dp.append([0] * n)
+        
+        dp[0][0] = 1
+        
+        for i in range(m):
+            for j in range(n):
+                if i == j == 0:
+                    continue
+                    
+                val = 0
+                if i > 0:
+                    val += dp[i-1][j]
+                if j > 0:
+                    val += dp[i][j-1]
+                
+                dp[i][j] = val
+        
+        return dp[m-1][n-1]
+