Efficiency of Algorithms

Efficiency of algorithm depends on design and implementation of algorithm. Algorithm uses computer resources to complete its task. An efficient algorithm is judged by the factor as to how economically and efficiently the CPU time and memory are used.

Characteristics of Efficient Algorithms

1) Algorithms should be efficient and economical in use of computer time, memory and peripherals.

2) They should be simple and most generalized.

3) They should be easily understandable and clear for implementation.

4) They can be easily modified if necessary.

5) They should be well documented for to be used by those who do not have knowledge of their inner working.

6) They should not be dependent for running on a particular computer.

7) It should be possible to use them to as a sub procedure for other problems.

Causes of Inefficiency

There are many reasons due to which the efficiency of a programme decreases. Some of them are described below.

1.       Redundant computation

One of the main causes of inefficiency is redundant computation. When redundant computation is done inside a loop it reduces the efficiency considerably. The most common mistake is computing few expressions inside the loop which can be stated out of loop. The following example illustrates the point:

Let us consider 'x', 'i' as temporary variables and 'n' as input from the user and 'a','b', 'c' are constants.

x = 0;

i = 0;

a = 3.2;

b= 4.0;

c = 5.8;

while (i < n)

{

x = x + 0.1;

y = (a*a*a+c) *x*x+b*b*x;

printf('x = %f y = %f', x, y);

i = i +1;

}

In this loop there is unnecessary computation like multiplication and addition of constant terms 'a', 'b' and 'c' which can be computed outside the loop also, which is given below

x = 0;

a3c= a*a*a+c;

b2 = b*b;

For (i= 0; i<n;i++)

{

x = x + 0.1;

y = a3c *x*x+b2*x;

printf('x = %f y = %f', x,y);

}

2.       Late termination

Doing more conditional checks or tests inside the loop is called late termination. For example we have a sorted list of names. We need to find the name JAGJIT. The name may exist in the list or may not. A common mistake committed here is searching till the end of the list. Instead one can search till a name occurs which is alphabetically later then JAGJIT like JASWANT. If the name JAGJIT exists in the list, the loop should terminate as soon as the name is found. This is illustrated with the algorithms below.

3.       Inefficient algorithm

while name sought <> Current name and till end of file do get next name from list

Efficient algorithm

while name sought <> Current name and till end of file do

a) get next name from list

b) If current name is greater than the name sought exit from the loop

4.       Early determination of desired output

Sometimes it may happen that the required output may be achieved before termination condition occurs. For example in an algorithm for sorting a list of items, assume the list is already sorted. Performing the entire sorting is inefficient in this case as it is already sorted? Predetermination of the fact the list is already sorted can reduce computation. Checking whether there is any exchange in each pass and terminating the loop in case of no exchanges can reduce the iterations.

5.       Storage and inefficiency

Storage is one the main factors of efficiency. Avoid using lot of intermediate storage which are not much used later in the program Try to use dynamic storage (allocating memory as and when required) as much as possible which avoids excessive allocation of memory. Free the memory of unnecessary variables after their use in the program.