62.Unique Paths
1. 题目
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?
2. 思路
本题求解的是一个机器人从左上角走到右下角有多少中走法。这是一个典型的动态规划问题。这里可以设dp[i] [j]为机器人走到矩阵的第i,j步的时候的方法。那么dp[i] [j] 的递推表达式是：
dp[i] [j] = dp[i-1] [j] + dp[i] [j-1]
3. 实现
class Solution(object):
def uniquePaths(self, m, n):
"""
:type m: int
:type n: int
:rtype: int
"""
dp = [ [ 1 for i in range(n+1)] for j in range(m+1) ]
for i in range( 1 , m+1) :
for j in range( 1 , n +1 ):
dp[i][j] = dp[i-1][j] + dp[i][j-1]
return dp[m-1][n-1]