62.py

'''
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?
'''

classSolution(object):
defuniquePaths(self, m, n):
"""
 :type m: int
 :type n: int
 :rtype: int
 """
dp= [[0for_inrange(n)] for_inrange(m)]
forindexinrange(m):
dp[index][0] =1

forindexinrange(n):
dp[0][index] =1

forindex_iinrange(1, m):
forindex_jinrange(1, n):
dp[index_i][index_j] =dp[index_i-1][index_j] +dp[index_i][index_j-1]

returndp[m-1][n-1]