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  Run time Calculations

Run time Calculations:

In Computer Science, it is very significant for Computer Scientists to know how to compute the running times of algorithms to optimize code.

Memory Allocation and Deallocation:

While executing a program written in the Binary language, we require a block of memory for global variables, and a block of memory for each of the method that has been invoked, but has not finished execution.

In the interpreter:

  • A static block of memory is allocated for global variables. This memory presents for the period of the program’s execution.
  • A dynamic block of memory (an “activation record”) is allocated while a method is invoked, and deallocated whereas the method is returned from. This memory allocation and deallocation process is stack-like, and therefore very simple to manage.
  • Memory require  for array and class instance variables is allocated “in-line” as a part of the block of memory for the construct whereas the variable is declared (either global memory or the activation record for a method).
  • String constants and a method table for each of the class type are also stored as separate blocks of memory. These never modify, and presents for the lifetime of the program.

The Run-time Environment:

The run-time environment in the Binary interpreter is shown by three pointers into run-time blocks of memory:

  • A pointer to the existing activation record (memory for the presently executing method).
  • A pointer to the current instance (“this”), which is actually a portion of the space allocated for the globals or another method.
  • A pointer to the global variables.

The layout for activation record for a method is following:

  • In the compiler’s model, but not in the interpreter’s model of an activation record, there is space for the saving registers value.
  • The space for parameters, in order.
  • The space for local variables, in order.

Measuring Running Time:

Once we have agreed that we might evaluate a program by measuring its running time, we face the problem of finding what the running time actually is. The two main approaches to summarizing the running time are following:

Benchmarking:

While comparing two or more programs designed to do the similar set of tasks, it is customary to produce a small collection of typical inputs that can serve like benchmarks. That is, we agree to admit the benchmark inputs as representative of the job mix; a program that executes well on the benchmark inputs is supposed to perform well on all inputs.

For instance, a benchmark to evaluate sorting programs may contain one small set of numbers, such like the First 20 digits of π; one medium set, such like the set of zip codes in Texas; and one big set, such like the set of phone numbers in the Brooklyn telephone directory. We might also desire to check that a program works effciently (and correctly) while given an empty set of elements to sort, a singleton set, and a list which is already in sorted order. Interestingly, some of the sorting algorithms perform poorly while given a list of elements that is already sorted.

Analysis of a Program:

In order to analyze a program, we start by grouping inputs according to size. What we select to call the size of an input can differ from program to program. For a sorting program, a good measure of the size is the number of elements to be sorted. For a program that solves out n linear equations in n unknowns, this is normal to take n to be the size of the problem. Other programs may use the value of some specific input, or the length of a list that is an input to the program, or the size of an array i.e. an input, or some combination of quantities such as these.

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