# Efficiency and complexity

## Efficiency and complexity

### Efficiency in Algorithms

• 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.

### Understanding Time Complexity

• 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.

### Understanding Space Complexity

• 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.

### Analysis of Algorithm Complexity

• 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.

### Trade-Off Between Time and Space Complexity

• 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.