as with insertionsdiscovering the value of in this equation would require timing search for some (probably largevalue of and then using the resulting value of to calculate when you know kyou can calculate for any other value of for handier formulawe could lump the into the our new is equal to the old divided by now we have = * this equation says that average linear search times are proportional to the size of the array if an array is twice as bigsearching it will take twice as long binary searchproportional to log(nsimilarlywe can concoct formula relating and for binary searcht log (nas we saw earlierthe time is proportional to the base logarithm of actuallybecause any logarithm is related to any other logarithm by constant ( to go from base to base )we can lump this constant into as well then we don' need to specify the baset log(ndon' need the constant big notation looks like the formulas just describedbut it dispenses with the constant when comparing algorithmsyou don' really care about the particular microprocessor chip or compilerall you want to compare is how changes for different values of nnot what the actual numbers are thereforethe constant isn' needed big notation uses the uppercase letter owhich you can think of as meaning "order of in big notationwe would say that linear search takes (ntimeand binary search takes (log ntime insertion into an unordered array takes ( )or constant time (that' the numeral in the parentheses table summarizes the running times of the algorithms we've discussed so far table running times in big notation algorithm running time in big notation linear search binary search insertion in unordered array insertion in ordered array deletion in unordered array deletion in ordered array (no(log no( (no(no(