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By Manoochehr Azmoodeh (auth.)

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Example text

Data Abstraction and Data Hierarchies At assembly-language level, the data items used are primarily bytes and words. In most assembly languages some abstraction is provided by interpreting certain words (or groups of words) as integers, reals or sequences of characters. Corresponding operations such as arithmetic for numbers are therefore provided. In a high-levellanguage these data items are known as data types. Generally, a data type is a set of permissible objects with a number of operations defined on these objects.

For loops. The number of times the loop is executed must be multiplied by the time complexity of the body of the loop. 4. while C do S; and repeatS until C; For both these loop constructs we should find the number of times the loop will be executed and multiply this by the complexities of C and S. For instance, the loop of b_search function is executed log2 n times. Thus, its time complexity is log2 n (0(1)) = O(log2 n). This simple analysis may not work for all loops. In these cases other properties of the program should be used to infer the time complexity.

Let us return to the seq1 function and examine its time complexity. The function A is recursive. Let us first look at the asymptotic complexity of A. If F(n) denotes the time complexity of function A, in a similar way to the b_search above, we can formulate F(n) as F(n) = ~ ~ : ~ +1 ~ 1 + 1 + F(n-1) + F(n-2) + 2 + 1 + 3 : : ~ n> 1 When n = 0, one test and one assignment are necessary. For n = 1, two tests and one assignment are needed and finally for n > 1, two tests, two calls to the same function of sizes n-1 and n-2 (that is, F(n-1) and F(n-2)) and one addition, two subtractions and one assignment, are needed.

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