Efficiency and complexity

Efficiency is a measure of how well an algorithm performs in terms of time and space resource consumption.
Time efficiency refers to the running time of an algorithm, i.e., how long it takes to execute.
Space efficiency measures the amount of memory an algorithm uses to accomplish its task.
The goal is to use the least amount of time and memory possible while still effectively addressing the problem at hand.

Time complexity is a function describing the amount of time an algorithm takes in terms of the quantity of input to the algorithm.
The two types of time complexities are worst-case time complexity and average case time complexity.
The worst-case time complexity represents the maximum time an algorithm can take for an input of size n. It is denoted as O(n), where n is the size of the input to the algorithm.
Average case time complexity is the amount of time required for an algorithm to complete if it had average performance for any input of size n.

Space complexity of an algorithm quantifies the amount of space or memory the algorithm requires relative to the size of the input.
It is represented using Big O notation. For example, an algorithm that needs space proportional to the input size would have a space complexity of O(n).
Sometimes, improving space complexity can negatively impact time complexity, and vice versa. This is known as a trade-off.

The complexity of an algorithm is a function describing the amount of resources such as time and space required by an algorithm as a function of the size of the input to the algorithm.
Big O notation, Big Omega notation, and Big Theta notation are commonly used to express the upper bound, lower bound, and tight bound, respectively, of an algorithm’s time complexity or space complexity.
Time complexity prefigures how an algorithm’s running time changes as the quantity of input to the function increases.
Space complexity governs how much memory an algorithm needs to run efficiently.

Developers often face a trade-off between time and space complexity - an algorithm that uses less memory might run slower and vice versa.
As a programmer, it is important to understand these trade-offs and make decisions based on the specific constraints and requirements of your application.