Convert 1D index to 2D

Converting a 1D index to a 2D index is a common task when working with matrices or 2D arrays. Here’s a simple explanation:

Imagine you have a 2D array with rows and columns, and you want to find the 2D coordinates (row, column) of an element based on its position in the 1D representation of that array.

Determine the number of columns: You need to know the number of columns in the 2D array since this information is essential for the conversion.
Calculate the row: Divide the 1D index by the number of columns and take the integer part. This gives you the row number.
```
row = 1D_index // number_of_columns
```
Calculate the column: Find the remainder of the division of the 1D index by the number of columns. This gives you the column number.
```
column = 1D_index % number_of_columns
```

Together, the row and column give you the 2D coordinates corresponding to the 1D index.

Example

Consider a 2D array with 3 rows and 4 columns. If you have a 1D index of 5, and you want to find the corresponding 2D coordinates:

number_of_columns = 4
row = 5 // 4 = 1
column = 5 % 4 = 1

So the 2D coordinates for the 1D index 5 are (1, 1).

This method works for 2D arrays where the 1D index is a representation of the elements read row by row from the 2D array.

Here’s a simple Python code snippet to convert a 1D index to a 2D index for a given number of columns.

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def convert_1D_to_2D(index_1D, number_of_columns):
    row = index_1D // number_of_columns
    column = index_1D % number_of_columns
    return row, column

# Example usage
index_1D = 5
number_of_columns = 4

row, column = convert_1D_to_2D(index_1D, number_of_columns)
print("2D coordinates are:", row, column) # Output will be: 2D coordinates are: 1 1

Here, we have used // for integer division and % for finding the remainder. This code will convert the 1D index 5 in an array with 4 columns to the 2D coordinates (1, 1). You can change the values of index_1D and number_of_columns to test other scenarios.

This is one of the key ingredients in solving the Search a 2D Matrix problem.