What are the different types of time complexity in algorithms?

What are the different types of time complexity in algorithms?

Time complexity measures how the runtime of an algorithm increases with the size of the input. The main types are constant, linear, logarithmic, quadratic, and exponential.

Can you explain each type with examples?

Sure!

• Constant (O(1)): The runtime does not change with input size, like accessing an array element.
• Linear (O(n)): The runtime increases linearly with input size, like iterating through an array.
• Logarithmic (O(log n)): The runtime increases logarithmically, like binary search.
• Quadratic (O(n^2)): The runtime increases quadratically, like bubble sort.
• Exponential (O(2^n)): The runtime doubles with each additional input, like the recursive calculation of Fibonacci numbers.

Which type is the most efficient?

Generally, constant time complexity (O(1)) is the most efficient, followed by logarithmic (O(log n)), linear (O(n)), and so on. It depends on the context and the specific algorithm.

How do I analyze the time complexity of my algorithm?

To analyze time complexity, identify the basic operations in your algorithm, count how many times they are executed as a function of input size, and express that count using Big O notation.