题目
There is a robot on an m x n
grid. The robot is initially located at the top-left corner (i.e., grid[0][0]
). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]
). The robot can only move either down or right at any point in time.
Given the two integers m
and n
, return the number of possible unique paths that the robot can take to reach the bottom-right corner.
The test cases are generated so that the answer will be less than or equal to 2 * 109
.
Example 1:
Input: m = 3, n = 7
Output: 28
Example 2:
Input: m = 3, n = 2
Output: 3
Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down
Constraints:
1 <= m, n <= 100
思路
动态规划,dp[i][j] = dp[i-1][j]+dp[i][j-1]
,边界的路径都是1。
代码
python版本:
class Solution:
def uniquePaths(self, m: int, n: int) -> int:
dp = [[1 for _ in range(n)] for _ 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]