Excel file reading and writing in MATLAB - Time & Space Complexity

Time Complexity: Excel file reading and writing

O(n x m)

Understanding Time Complexity

When reading or writing Excel files in MATLAB, it is important to understand how the time taken grows as the file size increases.

We want to know how the program's work changes when the Excel file has more rows or columns.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

filename = 'data.xlsx';
data = readmatrix(filename);

% Process data (example: multiply each element by 2)
data = data * 2;

writematrix(data, 'output.xlsx');

This code reads all data from an Excel file, processes it by doubling each number, and writes the result back to a new Excel file.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Reading and writing all cells in the Excel file, and multiplying each element in the data array.
• How many times: Once for each cell in the Excel file (rows x columns).

How Execution Grows With Input

As the number of rows and columns in the Excel file grows, the number of operations grows roughly by the total number of cells.

Input Size (cells)	Approx. Operations
10 x 10 = 100	About 100 operations
100 x 100 = 10,000	About 10,000 operations
1000 x 1000 = 1,000,000	About 1,000,000 operations

Pattern observation: The work grows proportionally with the total number of cells in the Excel file.

Final Time Complexity

Time Complexity: O(n x m)

This means the time grows roughly in proportion to the number of rows (n) times the number of columns (m) in the Excel file.

Common Mistake

[X] Wrong: "Reading or writing an Excel file always takes the same time, no matter the size."

[OK] Correct: The time depends on how many cells are read or written. Larger files have more cells, so they take more time.

Interview Connect

Understanding how file size affects reading and writing time helps you explain performance in real projects and shows you can think about efficiency clearly.

Self-Check

"What if we only read a specific range of cells instead of the whole file? How would the time complexity change?"