How many operations can an average computer perform in less than a second?
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10^8 operations.
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How many operations can an average computer perform in less than a second?
10^8 operations.
What is the time complexity of a function that always performs a fixed number of operations?
Constant time — O(1).
What is the expected time complexity for n approximately equal to 1,000,000?
O(n) or O(n log n).
What is the time complexity of the provided function in Big-O notation?
O(n) — linear complexity.
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.
What is the time complexity of the model solution?
O(1).
What does space complexity include?
All variables, both global and local, dynamic pointer data-structures, and stack contents in recursion.
What is the time complexity of a function that iterates over two different inputs n and m?
Linear time — O(n + m).
In the provided code, which line contains the dominant operation?
Line 4, where 'result += 1' is executed.
What is the time complexity of the slow solution?
O(n^2).
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.
How does the fast_solution function calculate the result?
It increments the result by (i + 1) for each index i.
What is the space complexity for declaring an array with n elements?
O(n).
What does the slow_solution function do?
It increments the result by 1 for each pair of indices (i, j).
What does complexity represent in the context of time complexity?
The maximum number of primitive operations that a program may execute.
Why is space complexity trickier to calculate than time complexity?
Not all variables and data-structures may be needed at the same time.
What is the space complexity for a program with a constant number of variables?
O(1).
What is the time complexity of a nested loop where both loops iterate n times?
Quadratic time — O(n^2).
What is the advantage of the model solution over the others?
It computes the result in constant time O(1).
What is the time complexity of the fast solution?
O(n).
What is the expected time complexity for n approximately equal to 500?
O(n^3).
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).
What is the expected time complexity for n approximately equal to 10,000?
O(n^2).
What is the worst-case time complexity for the linear function that checks for a zero in an array?
Linear time — O(n).
How does the model_solution function compute the result?
It uses the formula n * (n + 1) // 2.
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.
What is the purpose of using time complexity?
To estimate the running time of a program.
What does the complexity O(n) imply about the number of operations?
The program may perform c · n operations, where c is a constant.
What are dominant operations?
Operations that are performed the largest number of times in a program.
