62. Unique Paths
A robot is located at the top-left corner of a m × 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?
Above is a 3 × 7 grid. How many possible unique paths are there?
Note:
m and n will be at most 100.
Solution: DP
class Solution(object):
def uniquePaths(self, m, n):
"""
:type m: int
:type n: int
:rtype: int
"""
paths = [1] * n
for row in xrange(1, m):
for col in xrange(1, n):
paths[col] += paths[col - 1]
return paths[-1]