The time complexity to access an element in a 2D matrix by row-major order is:O(1)O(log n)O(n)O(n^2)

Break Down the Problem

1. Understanding Row-Major Order: In row-major order, a two-dimensional array is stored in a contiguous block of memory, with all elements of a row stored sequentially.
2. Accessing Elements: We need to determine the time complexity for accessing an element in such a 2D structure.

Relevant Concepts

1. Time Complexity Assumption:
   • The time complexity for accessing an element generally depends on the structure of the data and how it is stored in memory.
   • For arrays, accessing an element by index is usually O(1) time complexity since it can be computed directly using the formula.

Analysis and Detail

1. Access Formula:
   • When accessing the element at position $(i, j)$ in a 2D matrix of size $m \times n$, the formula used in row-major order to access the element is: $\text{Address}(i, j) = \text{Base Address} + (i \times n + j) \times \text{Size of Element}$
   • Here, you can compute the address in constant time $O(1)$.

Verify and Summarize

1. Since we can directly compute the position of any element without needing to traverse other elements, the access time complexity is indeed constant.
2. Therefore, the correct answer is $O(1)$ for accessing an element in a 2D matrix stored in row-major order.

Final Answer

The time complexity to access an element in a 2D matrix by row-major order is: O(1).