p.1
Big-O Notation and Its Importance
What is the time complexity of the provided function in Big-O notation?
O(n) — linear complexity.
p.2
Comparison of Time Complexities
In logarithmic time complexity O(log n), how does the value of n change with each iteration?
The value of n is halved on each iteration.
p.3
Space Complexity and Its Calculation
What does space complexity include?
All variables, both global and local, dynamic pointer data-structures, and stack contents in recursion.
p.1
Dominant Operations in Algorithms
In the provided code, which line contains the dominant operation?
Line 4, where 'result += 1' is executed.
p.1
Introduction to Time Complexity
Why is accurately calculating a program's operation time labor-intensive?
It depends on the compiler and the type of computer or speed of the processor.
p.4
Dominant Operations in Algorithms
How does the fast_solution function calculate the result?
It increments the result by (i + 1) for each index i.
p.4
Dominant Operations in Algorithms
What does the slow_solution function do?
It increments the result by 1 for each pair of indices (i, j).
p.1
Dominant Operations in Algorithms
What does complexity represent in the context of time complexity?
The maximum number of primitive operations that a program may execute.
p.3
Space Complexity and Its Calculation
Why is space complexity trickier to calculate than time complexity?
Not all variables and data-structures may be needed at the same time.
p.4
Comparison of Time Complexities
What is the advantage of the model solution over the others?
It computes the result in constant time O(1).
p.3
Exponential and Factorial Time Complexities
What are the two types of time complexity mentioned that can only solve problems for small values of n?
Factorial time O(n!) and exponential time O(2^n).
p.4
Dominant Operations in Algorithms
How does the model_solution function compute the result?
It uses the formula n * (n + 1) // 2.
p.1
Comparison of Time Complexities
What should be considered when analyzing the complexity of a program?
Specific, worst-case examples of data that the program will take a long time to process.
p.1
Introduction to Time Complexity
What is the purpose of using time complexity?
To estimate the running time of a program.
p.1
Big-O Notation and Its Importance
What does the complexity O(n) imply about the number of operations?
The program may perform c · n operations, where c is a constant.
p.1
Dominant Operations in Algorithms
What are dominant operations?
Operations that are performed the largest number of times in a program.
