[Verse 1] Listen up, I'm bout to break down the sort that's quick Divide and conquer algorithm, that's the trick Pick a pivot element, partition left and right Smaller goes left side, larger takes flight Recursively sort both sides till it's done Time complexity varies on how this thing runs Best case scenario got me feeling blessed When that pivot splits the array at its best [Chorus] Big O of n log n when the pivot's splitting even Best and average cases got your sorting believing But watch out for that worst case, Big O of n squared When the pivot's at the end, performance gets impaired Quick-sort, quick-sort, divide that array Time complexity changes based on how you play [Verse 2] Average case performance, that's the golden mean Random pivot selection keeps your runtime clean Each partition roughly cuts the size in half Logarithmic depth with linear work, do the math Master theorem tells us n log n's the cost Most of the time your efficiency ain't lost Probabilistic analysis shows us the way Expected performance keeps the big numbers at bay [Chorus] Big O of n log n when the pivot's splitting even Best and average cases got your sorting believing But watch out for that worst case, Big O of n squared When the pivot's at the end, performance gets impaired Quick-sort, quick-sort, divide that array Time complexity changes based on how you play [Bridge] Worst case creeping when your data's already sorted Pivot at the minimum, maximum gets distorted One element left, n minus one right Linear depth recursion, performance takes flight Down to quadratic time, that's n squared pain Randomized pivots help break that chain [Verse 3] In-place sorting, memory efficient and clean Space complexity logarithmic, know what I mean Stack frames for recursion, that's your overhead Tail call optimization keeps the memory well-fed Choose your pivot wisely, median of three Random selection strategy sets your data free Industry standard for a reason, you see When implemented right, it's quick as can be [Chorus] Big O of n log n when the pivot's splitting even Best and average cases got your sorting believing But watch out for that worst case, Big O of n squared When the pivot's at the end, performance gets impaired Quick-sort, quick-sort, divide that array Time complexity changes based on how you play [Outro] From best to worst case, now you understand Quicksort performance is all in your hands Pick your pivots smart, keep that runtime tight Divide and conquer till your array's sorted right
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