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Worst-case, best-case, and average-case analysis

When analyzing algorithms, it is common to consider the worst-case, best-case, and average-case scenarios. Let’s explore each of these types of analysis:

1. Worst-Case Analysis:

• The worst-case analysis determines the upper bound on the running time or space requirements of an algorithm for the input that results in the maximum execution time or space usage.
• It assumes that the input is chosen in such a way that it leads to the most inefficient behavior of the algorithm.
• It provides a guarantee on the performance of the algorithm, ensuring that it will not exceed a certain time complexity or space complexity for any input of size ‘n’.
• The worst-case analysis helps identify scenarios in which the algorithm may perform poorly and assists in assessing its efficiency in the worst possible scenario.

2. Best-Case Analysis:

• The best-case analysis determines the lower bound on the running time or space requirements of an algorithm for the input that results in the minimum execution time or space usage.
• It assumes that the input is chosen in such a way that it leads to the most efficient behavior of the algorithm.
• The best-case analysis is often used to showcase the algorithm’s potential when the input is already in an ideal or sorted state.
• However, the best-case scenario is not always realistic or representative of the algorithm’s typical performance.

3. Average-Case Analysis:

• The average-case analysis considers the expected or average running time or space requirements of an algorithm for all possible inputs of size ‘n’.
• It takes into account the likelihood of different inputs occurring and assigns probabilities to them.
• It requires a probability distribution of the inputs and calculates the average running time or space usage by considering the weighted sum of the running times or space usages for different inputs.
• The average-case analysis is generally more informative and practical than the worst-case analysis alone, as it provides insight into the expected behavior of the algorithm under typical conditions.