Test: Time and Space Complexity - 1 - Software Development MCQ

Time complexity in algorithms refers to the amount of time taken by an algorithm to execute or run, usually measured in terms of the number of operations or steps executed.

O(1) time complexity means that the algorithm takes a constant amount of time to run, irrespective of the input size. It indicates that the algorithm has a fixed number of operations.

The best-case time complexity of an algorithm represents the minimum amount of time it takes to run, given a particular input. O(1) represents constant time complexity, indicating that the algorithm takes a constant amount of time, regardless of the input size.

The worst-case time complexity of an algorithm represents the maximum amount of time it takes to run, given a particular input. O(n²) represents quadratic time complexity, indicating that the algorithm's running time grows exponentially with the input size.

Space complexity in algorithms refers to the amount of memory used by an algorithm to store data and variables during its execution. It measures how the space requirements of the algorithm grow with the input size.

The given code snippet has a loop that runs n times, where n is the input size. Since the loop executes n times, the time complexity is O(n).

The loop iterates until i exceeds n, where i is doubled in each iteration. The number of iterations can be calculated as log2(n), which represents the logarithmic time complexity.

The code snippet contains nested loops, with both loops iterating n times. Hence, the overall time complexity is O(n^2), indicating a quadratic time complexity.

The code snippet contains three nested loops, each running n times. Hence, the total number of iterations is n * n * n = n^3 = 5^3 = 125.

The code snippet allocates memory for an array of size n and then deallocates it using the delete[] operator. The space complexity is constant O(1) because the memory usage does not depend on the input size

The outer loop runs log2(n) times, and the inner loop runs n times. Hence, the time complexity is O(n log n).

The outer loop runs log2(n) times, and the inner loop runs i times, where i doubles in each iteration. Hence, the time complexity is O(n log n).

The outer loop runs n times, and the inner loop runs log2(i) times, where i doubles in each iteration. Hence, the time complexity is O(log n).

The outer loop runs log2(n) times, the middle loop runs i times, and the inner loop runs log2(n) times. Hence, the time complexity is O(n^2).

The outer loop runs n times, and the inner loop runs n - i times. The total number of iterations is 1 + 2 + 3 + ... + n, which is equivalent to (n * (n + 1)) / 2. Hence, the time complexity is O(n^2).