Unique Grid Descent Paths

easy

Dynamic ProgrammingMathCombinatoricsDp 2d

Asked atAmazonGoogleUberBloomberg

Problem Description

You are given an `rows × cols` grid. Starting from the **top-left cell** (row 0, column 0), you want to reach the **bottom-right cell** (row `rows-1`, column `cols-1`). At each step you may move **only right** or **only down**.

Return the total number of distinct paths from the top-left to the bottom-right.

**Example 1:**
```
Input: rows = 3, cols = 4
Output: 10
```

**Example 2:**
```
Input: rows = 2, cols = 2
Output: 2
Explanation: Right→Down, Down→Right
```

Constraints

1 <= rows, cols <= 18

Follow-up

What if some cells are blocked and cannot be traversed? Modify the DP to handle an obstacle grid.

Hints

Try the problem first. If you get stuck, you can reveal hints one at a time.

Solution

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