Running time

An algorithm's running time is its computational work on an input, measured either as elapsed time on a specified system or as an operation count under a cost model. Time complexity expresses how that count grows with input size. For binary search in a random-access sorted array, halving the candidate interval needs $O(\log n)$ comparisons. The same index-based code on a linked representation need not have that cost. Worst-case, average-case and amortized bounds quantify different questions; a measured duration alone does not prove any asymptotic guarantee.