Time Complexity Analysis Questions

The video tutorial covers the analysis of different types of loops to determine their time complexity. It starts with basic loops, moves on to decrementing loops, and then explores loops incrementing by two. The tutorial also delves into nested loops and more complex loop structures, providing a comprehensive understanding of how to calculate time complexity in various scenarios.

What is the time complexity of a simple loop that runs from 1 to n?

• O(n)

• O(1)

• O(n^2)

• O(log n)

If a loop starts at n and decrements until 0, what is its time complexity?

• O(n^2)

• O(log n)

• O(n log n)

• O(n)

How does the time complexity change if a loop increments by 2 instead of 1?

• It becomes O(log n)

• It becomes O(n/2)

• It remains O(n)

• It becomes O(n^2)

What is the time complexity of a nested loop where both loops run from 1 to n?

• O(log n)

• O(n^2)

• O(n)

• O(n log n)

In a nested loop where the inner loop runs from 0 to i, what is the time complexity?

• O(n)

• O(log n)

• O(n^2)

• O(n^3)

What is the sum of the series 1 + 2 + 3 + ... + n?

• n(n-1)/2

• n^2/2

• n^2

• n(n+1)/2

How does the time complexity change if a loop's condition is based on a cumulative sum?

• It becomes O(log n)

• It becomes O(n)

• It becomes O(n^2)

• It becomes O(sqrt(n))

What is the time complexity of a loop that stops when a cumulative sum exceeds n?

• O(n^2)

• O(n)

• O(sqrt(n))

• O(log n)

If a loop's condition is based on a sum of integers, what is the approximate number of iterations?

• n^2

• log n

• sqrt(n)

• n

What is the time complexity of a loop that increments a variable by adding the loop index each time?

• O(n)

• O(sqrt(n))

• O(n^2)

• O(log n)