Unique Paths

uniquePaths.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?
+
+# Dynamic Programming, boundary is important in this case. 
+
+class Solution:
+    # @return an integer
+    def uniquePaths(self, m, n):
+        steps = [[0 for x in range(n)] for x in range(m)] 
+        for j in range(n):
+            steps[0][j] = 1
+        for j in range(m):
+            steps[j][0] = 1
+        for i in range(1,m):
+            for j in range(1,n):
+                if i-1 < m and j-1 < n:
+                    steps[i][j] = steps[i-1][j] + steps[i][j-1]
+                elif i-1<m:
+                    steps[i][j] = steps[i-1][j]
+                elif j-1<n:
+                    steps[i][j] = steps[i][j-1]
+
+        return steps[m-1][n-1]
+