Average case and expectation are two different measures used to describe the performance of an algorithm. The average case refers to the average number of operations or steps an algorithm takes to solve a problem, while the expectation refers to the expected number of operations or steps an algorithm takes based on a probability distribution of inputs. In other words, the average case is a specific value, while the expectation is a theoretical value based on probability.
Yes, it is possible for an algorithm to have the same average case and expectation. This would occur when the probability distribution of inputs is evenly distributed, meaning that each input has an equal chance of occurring. In this case, the average case and expectation would be the same, as they both represent the same value.
The average case is calculated by taking the sum of the number of operations for each possible input and dividing by the total number of inputs. The expectation is calculated by taking the sum of the number of operations for each possible input multiplied by its probability of occurring.
Considering both average case and expectation provides a more comprehensive understanding of an algorithm's performance. While the average case gives a specific value, the expectation takes into account the likelihood of different inputs and provides a more realistic estimate of an algorithm's performance in real-world scenarios. This allows for better comparison and selection of algorithms for different applications.
Yes, an algorithm can have a good average case but a poor expectation. This would occur when the probability distribution of inputs is skewed, meaning that certain inputs are more likely to occur than others. In this case, the average case may be low as it is influenced by the most common inputs, but the expectation may be much higher as it considers the less common inputs as well.