Algorithm is a step by step procedure, which defines a set of instructions to be executed in certain order to get the desired output.
Algorithms are generally created independent of underlying languages.
An algorithm can be implemented in more than one programming language.
From data structure point of view, following are some important categories of algorithms −
Search − Algorithm to search an item in a data-structure.
Sort − Algorithm to sort items in certain order
Insert − Algorithm to insert item in a data-structure
Update − Algorithm to update an existing item in a data-structure
Delete − Algorithm to delete an existing item from a data-structure
Not all procedures can be called an algorithm. An algorithm should have the below mentioned characteristics −
Unambiguous − Algorithm should be clear and unambiguous. Each of its steps (or phases), and their input/outputs should be clear and must lead to only one meaning.
Input − An algorithm should have 0 or more well defined inputs.
Output − An algorithm should have 1 or more well defined outputs, and should match the desired output.
Finiteness − Algorithms must terminate after a finite number of steps.
Feasibility − Should be feasible with the available resources.
Independent − An algorithm should have step-by-step directions which should be independent of any programming code.
There are no well-defined standards for writing algorithms. Rather, it is problem and resource dependent. Algorithms are never written to support a particular programming code.
As we know that all programming languages share basic code constructs like loops (
while), flow-control (
These common constructs can be used to write an algorithm.
We write algorithms in step by step manner, but it is not always the case. Algorithm writing is a process and is executed after the problem domain is well-defined. That is, we should know the problem domain, for which we are designing a solution.
Sum of Two Numbers: step 1 − START ADD step 2 − get values of a & b step 3 − c ← a + b step 4 − display c step 5 − STOP
Efficiency of an algorithm can be analyzed at two different stages, before implementation and after implementation, as mentioned below −
A priori analysis − This is theoretical analysis of an algorithm. Efficiency of algorithm is measured by assuming that all other factors e.g. processor speed, are constant and have no effect on implementation.
A posterior analysis − This is empirical analysis of an algorithm. The selected algorithm is implemented using programming language. This is then executed on target computer machine. In this analysis, actual statistics like running time and space required, are collected.
We shall learn here a priori algorithm analysis. Algorithm analysis deals with the execution or running time of various operations involved. Running time of an operation can be defined as no. of computer instructions executed per operation.
Suppose X is an algorithm and n is the size of input data, the time and space used by the Algorithm X are the two main factors which decide the efficiency of X.
Time Factor − The time is measured by counting the number of key operations such as comparisons in sorting algorithm
Space Factor − The space is measured by counting the maximum memory space required by the algorithm.
The complexity of an algorithm f(n) gives the running time and / or storage space required by the algorithm in terms of n as the size of input data.
Time Complexity of an algorithm represents the amount of time required by the algorithm to run to completion. Time requirements can be defined as a numerical function
T(n) can be measured as the number of steps, provided each step consumes constant time.
For example, addition of two n-bit integers takes n steps. Consequently, the total computational time is
T(n) = c*n, where
c is the time taken for addition of two bits. Here, we observe that
T(n) grows linearly as input size increases.
Space complexity of an algorithm represents the amount of memory space required by the algorithm in its life cycle. Space required by an algorithm is equal to the sum of the following two components −
A fixed part that is a space required to store certain data and variables, that are independent of the size of the problem. For example simple variables & constant used, program size etc.
A variable part is a space required by variables, whose size depends on the size of the problem. For example dynamic memory allocation, recursion stack space etc.
Space complexity S(I) of any algorithm I is S(I) = C + SP(P) Where b>C is the fixed part and S(P) is the variable part of the algorithm which depends on instance characteristic P.
Following is a simple example that tries to explain the concept −
Algorithm: SUM(A, B) Step 1 - START Step 2 - C ← A + B + 10 Step 3 - Stop
Here we have three variables A, B and C and one constant. Hence
S(I) = 1+3. Now space depends on data types of given variables and constant types and it will be multiplied accordingly.
Discuss the complexity of an algorithm with its uses new and simple formated