A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 3.9 Space Bounds 85A classic example of a space/time tradeoff is the lookup table. A lookup tablepre-stores the value of a function that would otherwise be computed each time it isneeded. For example, 12! is the greatest value for the factorial function that can bestored in a 32-bit int variable. If you are writing a program that often computesfactorials, it is likely to be much more time efficient to simply pre-compute the 12storable values in a table. Whenever the program needs the value of n! for n ≤ 12,it can simply check the lookup table. (If n > 12, the value is too large to store asan int variable anyway.) Compared to the time required to compute factorials, itmay be well worth the small amount of additional space needed to store the lookuptable.Lookup tables can also store approximations for an expensive function such assine or cosine. If you compute this function only for exact degrees or are willingto approximate the answer with the value for the nearest degree, then a lookuptable storing the computation for exact degrees can be used instead of repeatedlycomputing the sine function. Note that initially building the lookup table requiresa certain amount of time. Your application must use the lookup table often enoughto make this initialization worthwhile.Another example of the space/time tradeoff is typical of what a programmermight encounter when trying to optimize space. Here is a simple code fragment forsorting an array of integers. We assume that this is a special case where there are nintegers whose values are a permutation of the integers from 0 to n − 1. This is anexample of a Binsort, which is discussed in Section 7.7. Binsort assigns each valueto an array position corresponding to its value.for (i=0; i