Algorithm is a step-by-step procedure, which defines a phối of instructions khổng lồ be executed in a certain order lớn get the desired output. Algorithms are generally created independent of underlying languages, i.e. An algorithm can be implemented in more than one programming language.
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From the data structure point of view, following are some important categories of algorithms −
Search − Algorithm to search an thành công in a data structure.Sort − Algorithm khổng lồ sort items in a certain order.Insert − Algorithm khổng lồ insert cống phẩm in a data structure.Update − Algorithm to lớn update an existing thành quả in a data structure.Delete − Algorithm to delete an existing sản phẩm from a data structure.Characteristics of an Algorithm
Not all procedures can be called an algorithm. An algorithm should have the following characteristics −
Unambiguous − Algorithm should be clear & unambiguous. Each of its steps (or phases), & their inputs/outputs should be clear và must lead khổng lồ 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.How to lớn Write an Algorithm?
There are no well-defined standards for writing algorithms. Rather, it is problem và resource dependent. Algorithms are never written to support a particular programming code.
As we know that all programming languages mô tả basic code constructs like loops (do, for, while), flow-control (if-else), etc. These common constructs can be used khổng lồ write an algorithm.
We write algorithms in a step-by-step manner, but it is not always the case. Algorithm writing is a process & is executed after the problem tên miền is well-defined. That is, we should know the problem domain, for which we are designing a solution.
Example
Let’s try lớn learn algorithm-writing by using an example.
Problem − kiến thiết an algorithm to địa chỉ cửa hàng two numbers và display the result.
Step 1 − START
Step 2 − declare three integers a, b & c
Step 3 − define values of a & b
Step 4 − add values of a & b
Step 5 − store output đầu ra of step 4 khổng lồ c
Step 6 − print c
Step 7 − STOP
Algorithms tell the programmers how lớn code the program. Alternatively, the algorithm can be written as −
Step 1 − START ADD
Step 2 − get values of a và b
Step 3 − c ← a + b
Step 4 − display c
Step 5 − STOP
In design and analysis of algorithms, usually the second method is used lớn describe an algorithm. It makes it easy for the analyst to lớn analyze the algorithm ignoring all unwanted definitions. He can observe what operations are being used and how the process is flowing.
Writing step numbers, is optional.
We thiết kế an algorithm to lớn get a solution of a given problem. A problem can be solved in more than one ways.
Hence, many solution algorithms can be derived for a given problem. The next step is to lớn analyze those proposed solution algorithms and implement the best suitable solution.
Algorithm Analysis
Efficiency of an algorithm can be analyzed at two different stages, before implementation and after implementation. They are the following −
A Priori Analysis − This is a theoretical analysis of an algorithm. Efficiency of an algorithm is measured by assuming that all other factors, for example, processor speed, are constant và have no effect on the implementation.A Posterior Analysis − This is an 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 lượt thích running time and space required, are collected.We shall learn about a priori algorithm analysis. Algorithm analysis đơn hàng with the execution or running time of various operations involved. The running time of an operation can be defined as the number of computer instructions executed per operation.
Algorithm Complexity
Suppose X is an algorithm & n is the kích cỡ 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 − Time is measured by counting the number of key operations such as comparisons in the sorting algorithm.Space Factor − 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 the storage space required by the algorithm in terms of n as the kích thước of đầu vào data.
Space Complexity
Space complexity of an algorithm represents the amount of memory space required by the algorithm in its life cycle. The space required by an algorithm is equal khổng lồ the sum of the following two components −
A fixed part that is a space required to lớn store certain data and variables, that are independent of the size of the problem. For example, simple variables và constants used, program size, etc.A variable part is a space required by variables, whose kích cỡ depends on the kích thước of the problem. For example, dynamic memory allocation, recursion stack space, etc.Space complexity S(P) of any algorithm phường is S(P) = C + SP(I), where C is the fixed part and S(I) is the variable part of the algorithm, which depends on instance characteristic I. 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 & one constant. Hence S(P) = 1 + 3. Now, space depends on data types of given variables and constant types and it will be multiplied accordingly.
Time Complexity
Time complexity of an algorithm represents the amount of time required by the algorithm to run khổng lồ completion. Time requirements can be defined as a numerical function T(n), where T(n) can be measured as the number of steps, provided each step consumes constant time.
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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 the addition of two bits. Here, we observe that T(n) grows linearly as the input kích cỡ increases.