Algorithms

Sorting, searching, and traversal — with the comparison counter running, so the complexity is a number you watch rather than a claim you accept.

• SortingWhy the comparison sorts stop at n log n, why the library beats your quicksort, and why stability is the property that actually decides which one you need.core· best O(n log n)· average O(n log n)· worst O(n²) quicksort· space O(n) merge
• SearchingBinary search, the off-by-one that survives every test, and why the useful version is not "find x" but "find the boundary".core· linear O(n)· binary O(log n)· hash O(1)*
• Two PointersTurning a nested loop into a single pass by proving that one direction of movement is always safe — plus fast/slow pointers, which detect cycles in constant space.core· time O(n)· space O(1)
• Sliding WindowReusing the previous answer instead of recomputing it — and the monotonicity requirement that decides whether the window is allowed to shrink.core· time O(n)· space O(k)
• RecursionTrusting the recursive call, counting the stack, and why Python and JavaScript will not save you with tail-call optimisation.foundational· depth O(d) stack· fib-naive O(2ⁿ)· fib-memo O(n)