Leetcode
2020.04.09 12:47

# 62. Unique Paths

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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?

Above is a 7 x 3 grid. How many possible unique paths are there?

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
```

Constraints:

• `1 <= m, n <= 100`
• It's guaranteed that the answer will be less than or equal to `2 * 10 ^ 9`.

```class Solution {
public int uniquePaths(int m, int n) {
if(m == 0 || n == 0){
return 0;
}

int[][] dp = new int[m][n];

for(int i=0; i<m; i++){
dp[i][0] = 1;
}

for(int i=0; i<n; i++){
dp[0][i] = 1;
}

for(int i=1; i<m; i++){
for(int j=1; j<n; j++){
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}

return dp[m-1][n-1];
}
}```

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