> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/grid-unique-paths.md).

# Grid Unique Paths

A robot is located at the top-left corner of an **A x B grid** (marked ‘Start’ in the diagram below).

![Path Sum: Example 1](http://i.imgur.com/3eaivQ5.png)

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: A and B will be such that the resulting answer fits in a 32 bit signed integer.*

**Example :**

```
Input : A = 2, B = 2
Output : 2

2 possible routes : (0, 0) -> (0, 1) -> (1, 1) 
              OR  : (0, 0) -> (1, 0) -> (1, 1)
```

```java
class Solution {
    public int uniquePaths(int m, int n) {
        int dp[][] = new int[m + 1][n + 1];
        dp[m][n] = 1;
        for (int r = m; r >= 1; r--) {
            for (int c = n; c >= 1; c--) {
                if (r == m && c == n)
                    continue;
                else if (c == n)
                    dp[r][c] = dp[r + 1][c];
                else if (r == m)
                    dp[r][c] = dp[r][c + 1];
                else
                    dp[r][c] = dp[r + 1][c] + dp[r][c + 1];
            }
        }
        return dp[1][1];
    }
}
```


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