EIT Computer Science and Numerical Methods

Question 1

What is the time complexity of binary search on a sorted array of n elements?

Accepted Answer

O(log n)

Answer

Binary search repeatedly halves the search space, resulting in a logarithmic number of comparisons — O(log n).

Question 2

The Newton-Raphson iterative formula for finding the root of f(x) = 0 is:

Accepted Answer

x_(n+1) = x_n - f(x_n)/f'(x_n)

Answer

The Newton-Raphson method subtracts the ratio f(x_n)/f'(x_n) from the current estimate to converge toward the root.

Question 3

What is the decimal equivalent of the binary number 1101?

Accepted Answer

13

Answer

1101 in binary equals 1×8 + 1×4 + 0×2 + 1×1 = 8 + 4 + 0 + 1 = 13.

Question 4

In numerical methods, the trapezoidal rule is used to approximate:

Accepted Answer

A definite integral

Answer

The trapezoidal rule approximates a definite integral by summing the areas of trapezoids formed under the curve.

Question 5

Which data structure follows the LIFO (Last In, First Out) access principle?

Accepted Answer

Stack

Answer

A stack removes elements in the reverse order they were added, so the last element pushed is the first one popped.

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