The distance will be calculated like the example given in the problem,

A time-series is a sequence of integers a1, a2,... , an, where aj represents (some) signal at time i. Often- times, we need to be able to compare two time-series and declare whether they are similar or not (e.g imagine these are the time-series of heart beats: of a patient, and of "normal heart beat"). One way to compare two such time series, called a1, a2,... an and bi, b2,...bm is as follows. Define a matching to be a non-decreasing map f : In] ? [m], thought of as a map from indeces of a to indeces of , such that f(i) f(j) whenever i