Find the Cheapest Right-and-Down Grid Path
Company: Infosys
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
Each entry in the rectangular grid `costs` is a nonnegative cost. A path starts in the upper-left cell, finishes in the lower-right cell, and advances one cell at a time to the right or downward.
Return the smallest total cost of any such path. Add the costs of every visited cell, including both endpoints.
### Examples
**Example 1**
```text
Input: costs = [[2,8,1],[3,1,1]]
Output: 7
```
Moving down, right, and right visits costs `2`, `3`, `1`, and `1`, for a total of `7`. Every other permitted path costs more.
**Example 2**
```text
Input: costs = [[5],[0],[4]]
Output: 9
```
There is only one column, so the path visits all three cells.
### Constraints
- The grid has between `1` and `200` rows and between `1` and `200` columns.
- All rows have equal length.
- `0 <= costs[i][j] <= 200`
Overview: Find the minimum total cell cost of a grid path that advances right or down, including the starting and ending cell costs.