# Problem Solving: Matrix Traversals I

Learn to solve different matrix traversal problems.

## We'll cover the following

- Traversals and mappings from R2 to R world
- The complete code of 5 mapping functions

In this lesson, we’ll traverse 2-D arrays differently and map them to a 1-D array. **Mapping** here refers to the process of taking elements from a two-dimensional matrix and rearranging them in a specific order to form a one-dimensional array. The specific order will be determined by the direction specified by an arrow in the question. This direction can be row-wise, column-wise, diagonally, or any other specific direction.

For example, a row-wise mapping function would take the elements of the 2-D matrix and arrange them in the order in which they appear in each row. A column-wise mapping function, on the other hand, would arrange the elements in the order in which they appear in each column.

## Traversals and mappings from $R^2$ to $R$ world

Mapping is a way to transform complex data structures into simpler data structures. In this case it transforms a 2-D matrix into a 1-D array, making it easier to process or manipulate.

Given a `rows x cols`

two-dimensional matrix `TDA`

, write the mapping functions from $R^2$ (two dimensions) to $R$ (one dimension) for each different problem.

Implement the mapping function for each different mapping case below to convert a two-dimensional matrix `TDA`

with dimensions of `rows x cols`

to a one-dimensional array `projectionMap`

. The functions should take the elements of the 2-D array and arrange them in a specific order as indicated by the direction specified by an arrow.

### Playground for your implementation

Write your implementation of the mapping function here.

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