Data Structures and Algorithm Analysis - Computer Science at ...

82 Chap. 3 Algorithm Analysisdeal with variations of this problem. Most such implementations involvethe following tuning step. Directly testing whether a given complex objectcontains the point in question is relatively expensive. Instead, we canscreen for whether the point is contained within a bounding box for theobject. The bounding box is simply the smallest rectangle (usually definedto have sides perpendicular to the x and y axes) that contains the object.If the point is not in the bounding box, then it cannot be in the object. Ifthe point is in the bounding box, only then would we conduct the full comparisonof the object versus the point. Note that if the point is outside thebounding box, we saved time because the bounding box test is cheaper thanthe comparison of the full object versus the point. But if the point is insidethe bounding box, then that test is redundant because we still have to comparethe point against the object. Typically the amount of work avoided bymaking this test is greater than the cost of making the test on every object.Example 3.20 Section 7.2.3 presents a sorting algorithm named SelectionSort. The chief distinguishing characteristic of this algorithm is thatit requires relatively few swaps of records stored in the array to be sorted.However, it sometimes performs an unnecessary swap operation where ittries to swap a record with itself. This work could be avoided by testingwhether the two indices being swapped are the same. However, this eventdoes not occurr often. Because the cost of the test is high enough comparedto the work saved when the test is successful, adding the test typically willslow down the program rather than speed it up.Be careful not to use tricks that make the program unreadable. Most code tuningis simply cleaning up a carelessly written program, not taking a clear programand adding tricks. In particular, you should develop an appreciation for the capabilitiesof modern compilers to make extremely good optimizations of expressions.“Optimization of expressions” here means a rearrangement of arithmetic or logicalexpressions to run more efficiently. Be careful not to damage the compiler’s abilityto do such optimizations for you in an effort to optimize the expression yourself.Always check that your “optimizations” really do improve the program by runningthe program before and after the change on a suitable benchmark set of input. Manytimes I have been wrong about the positive effects of code tuning in my own programs.Most often I am wrong when I try to optimize an expression. It is hard todo better than the compiler.The greatest time and space improvements come from a better data structure oralgorithm. The final thought for this section isFirst tune the algorithm, then tune the code.