Solution for Unique Paths problem using dynamic programming

Author: BarthJr

unique_paths.py

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+# 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?
+#
+# Note: m and n will be at most 100.
+"""
+>>> uniquePaths(3, 2)
+3
+>>> uniquePaths(7, 3)
+28
+>>> uniquePaths(0, 0)
+0
+>>> uniquePaths(0, 2)
+0
+>>> uniquePaths(2, 0)
+0
+"""
+
+
+def uniquePaths(m: int, n: int) -> int:
+    if not m or not n:
+        return 0
+    dp = [[1 for col in range(n)] for row 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]