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?
Note: m and n will be at most 100.
Example 1:
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 -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
Tags: Math, String
一个机器人位于一个 m x n 网格的左上角 （起始点在下图中标记为“Start” ）。
机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角（在下图中标记为“Finish”）。
问总共有多少条不同的路径？
利用DP和 Problem 64类似 状态转移方程：f[x][y] = f[x-1][y] + f[x][y-1]
```go func uniquePaths(m int, n int) int { // Init DP dp := make([][]int, m) for i := 0; i < m; i++ { dp[i] = make([]int, n) }
// Calculate first row
for i := 0; i < n; i++ {
dp[0][i] = 1
}
// Calculate first col
for i := 0; i < m; i++ {
dp[i][0] = 1
}
// Calculate first other
for i := 1; i < m; i++ {
for j := 1; j < n; j++ {
dp[i][j] = dp[i-1][j] + dp[i][j-1]
}
}
return dp[m-1][n-1]
}
### 思路2
> 思路2
```go
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