Algorithm Analysis and Big O Notation

# Best Case Time Complexity

## When is it important to consider the best case time complexity of an algorithm?

While Big O notation typically describes the worst-case time complexity of an algorithm, in some situations, it can be useful to consider the best-caseÂ complexity.

### When the Best Case is Likely

If the input data for your algorithm is often in a form that triggers the best-case performance, then the best case might be more relevant than the worst case. ForÂ example:

int linearSearch(int arr[], int n, int x) {
for (int i = 0; i < n; i++) {
if (arr[i] == x)
return i;
}
return -1;
}

Linear search has a best-case complexity of $O(1)$ if the element is found at the first position. If the input data is often sorted or if the searched-for element is often at the beginning, this best-case performance might be moreÂ relevant.

### When the Worst Case is Unacceptable

In some critical systems, the worst-case performance might be catastrophic, even if it's unlikely. In such cases, you might need to ensure that even the worst case isÂ acceptable.

### When Comparing Algorithms

When choosing between different algorithms for a problem, considering the best, average, and worst cases can give a more complete picture than just the worstÂ case.

### Optimistic Algorithms

Some algorithms are designed to take advantage of best-case scenarios. These are known as optimistic algorithms. They hope for the best but prepare for theÂ worst.

An example is the Quicksort algorithm, which has a best-case complexity of $O(n log n)$ when the pivot always splits the array in the middle, but a worst-case complexity of $O(n^2)$ when the pivot is always the smallest or largestÂ element.

However, in most cases, worst-case complexity is more important, as it gives an upper bound on the running time. Average-case complexity is also often more practical than best-case complexity. But understanding all three can provide a fuller picture of an algorithm's performanceÂ characteristics.

This Question is from the Lesson:

### Algorithm Analysis and Big O Notation

An introduction to algorithms - the foundations of computer science. Learn how to design, analyze, and compare them.

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This Question is from the Lesson:

### Algorithm Analysis and Big O Notation

An introduction to algorithms - the foundations of computer science. Learn how to design, analyze, and compare them.

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