What is the time complexity of the following code snippet?

Correct option is C

The time complexity of the given code is O(n³). The code uses three nested loops to iterate over each element in an n x n x n 3D matrix. Each loop runs n times, resulting in n * n * n = n³ total iterations. Therefore, the time complexity of this code is O(n³), which is typical for operations that involve processing every element in a 3D matrix.
Important Key Points:
1. Nested Loops for 3D Matrix: The code uses three nested loops, each iterating n times, to traverse the entire 3D matrix.
2. Initialization and Access in 3D Array: The code assigns values to each element in the 3D matrix based on the sum of its indices (i + j + k).
3. Complexity Growth with n: As n increases, the time complexity grows cubically, making this operation inefficient for large values of n.
Knowledge Booster:
· O(n³) Complexity: Often seen in algorithms that perform operations on 3D data structures or complex nested loops. Processing all elements in a 3D matrix typically has O(n³) complexity.
· Difference from O(n²): O(n²) complexity involves two nested loops, commonly seen in 2D matrix operations. In contrast, O(n³) involves three nested loops, making it more computationally intensive.
· Improving Efficiency: When working with large datasets, avoid O(n³) algorithms if possible, as they can become very slow. For large 3D datasets, techniques like reducing dimensionality or optimizing operations within the loops may be needed.