Wipro R Programming Recently Asked Interview Questions Answers
What is R lists?
Lists are the object which Contains elements of different types – like strings, numbers, vectors and another list inside it. A list can also contain a matrix or a function as its elements. The List is created using list() Function. In other words, a list is a generic vector containing other objects. For Example, The variable x is containing copies of three vectors n, s, b and a numeric value 3.
n = c(2, 3, 5)
s = c(“aa”, “bb”, “cc”, “dd”, “ee” )
b = c(TRUE, FALSE, TRUE, FALSE, FALSE )
x = list( n, s, b, 3) # x contains copies of n, s, b)
Explain how to create a list in R?
Create a list containing string, numbers, vectors and logical values. For Example:
List_data <- list("Green", "Yellow", c(5,6,7), TRUE, 51.2)
print(list_data) When we execute the above code, it produces the following result-
[[1]]
[1] “Green”
[[2]]
[1] “Yellow”
[[3]]
[1] 5, 6, 7
[[4]]
[1] TRUE
[[5]]
[1] 51.2
How to use sapply in R?
Multipy all values by 10:
> sapply(BOD,function(x) 10 * x)
Time demand
[1,] 10 80
[2,] 20 100
[3,] 30 190
Used for array, margin set to 1:
> x <- array(1:9) > sapply(x,function(x) x * 10)
[1] 10 20 30 40 50 60 70 80 90
Two dimension array, margin can be 1 or 2:
> x <- array(1:9,c(3,3)) > x
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
> sapply(x,function(x) x * 10)
[1] 10 20 30 40 50 60 70 80 90
sapply: returns a vector, matrix or an array
# sapply : returns a vector, an array or matrix
sapply(c(1:3), function(x) x^2)
[1] 1 4 9
What is R matrices?
A matrix is a two-dimensional rectangular data set and thus it can be created using vector input to the matrix function. In addition, a matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually, the numbers are the real numbers. By using a matrix function we can reproduce a memory representation of the matrix in R. Hence, the data elements must be of the same basic type.
How many methods are available to use the matrices?
There are so many methods to solve the matrices like adding, subtraction, negative etc.
What is control structure in R?
R has the standard control structures we would expect. expr can be multiple statements by enclosing them in braces { }. It is more efficient to use built-in functions rather than control structures whenever possible. These allow us to control the flow of execution of a script typically inside of a function. Control structures define the flow of the program. The decision is been based on the evaluation of a variable.
How many control statements are present in R?
There are eight control statements are present in R.
Name all control statements present in R?
If
If-else
For
Nested loops
While
Repeat and break
Next
return.
Explain how to access list elements in R?
Create a list containing a vector, a list and a matrix.
list_data <- list(c("Feb","Mar","Apr"))
list("white",13.4)), matrix(c(3,9,5,1,-2,8), nrow = 2)
For Example: Give names to the elements in the list:
Names(list_data) <- c(“1 st Quarter”, “A Matrix”, “A Inner list”)
Access the first element of the list:
print(list_data[1])
Access the third element. As it also a list, all its elements will print:
Print(list_data[3])
By using the name of the element access the list elements:
Print(list_data$A Matrix)
It will produced the following result after executing the above code:
$”1 st Quarter” [1] “Feb”, "Mar”, "Apr”
$A_Inner_list
$A_Inner_list[[1]]
[1] “White”
$A_Inner_list[[2]]
[1] 13.4
$ “A Matrix” [1]
[1] [2] [3]
[1] 3 5 -2
[2] 9 1 8
Explain how to manipulate list elements in R?
Create a list containing a vector, a matrix and a list.
list_data <- list(c("Feb","Mar","Apr"),
matrix(c(3,9,5,1,-2,8), nrow = 2), list("green",12.3))
For Example:
Give names to the elements in the list:
names(list_data) <- c("1st Quarter", "A_Matrix", "A Inner list")
Add element at the end of the list:
list_data[4] <- "New element"
print(list_data[4])
Remove the last element:
list_data[4] <- NULL # Print the 4th Element.print(list_data[4])
Update the 3rd Element:
list_data[3] <- "updated element"
print(list_data[3])
When we execute the above code, it produces the following result:
[[1]]
[1] "New element"
$NULL
$`A Inner list`
[1] "updated element"
Explain how to generate lists in R?
We can use a colon to generate a list of numbers. For example:
-3:3
[1] -3 -2 -1 0 1 2 3
Explain how to operate on lists in R?
R allows to Operate on all list values at once. For example:
c(1,3,5) + 4
This and the Apply function allow you to avoid most for loops.
[1] 5, 7, 9
What are features of R functions?
Function component describes the three main components of a function.
Lexical scoping teaches how R finds values from names.
In R, every operation is a function call.
Function arguments discuss the three ways of supplying arguments to a function. it shows to call
The function is given a list of arguments and to the impact of lazy evaluation.
Special calls describe two special types of function infix and replacement functions.
Return values discuss how and when functions return values. it also shows how you can ensure
that a function does something before it exists.
What is function definition?
An R function is been created using the keyword function. The basic syntax of an R function definition is as follows −
function_name <- function(arg_1, arg_2, …) {
Function body
}
What are the components of R functions?
The different parts of a function are −
Function Name − It is the actual name of the function because it stored in R environment as an object with this name.
Arguments − An argument is a placeholder. When a function invokes, we pass a value to the
argument. Arguments are optional; that is, a function may contain no arguments. Also, arguments can have default values.
Functions Body – In a function body, statements can be collected. and hence, it defines what the function does.
Return Value − the return value of a function is the last expression in the function body to check.
What are Generic Functions in R?
R has three object-oriented (OO) systems: [[S3]], [[S4]] and [[R5]]. … A method is a function associated with a particular type of object. S3 implements a style of object-oriented programming called generic-function OO.
What are R packages?
Packages are collections of R functions, data, and compiled code in a well-defined format. The directory where packages are stored is called the library. R comes with a standard set of packages. Others are available for download and installation. Once installed, they have to be loaded into the session to be used.
Name the functions which helps in importing data from other applications in R?
read.table()
readlines()
read.fwf
read.delim()
scan()
read.csv()
read.csv2()
What is more functions in R and name them?
We have to load the built-in foreign command to use these functions:
>library("foreign")
R more functions:
read.xpss
read.xport
read.dta
List out some of the function that R provides?
Mean
Median
Distribution
Covariance
Regression
What is the distribution in R?
R Functions for Probability Distributions. Every distribution that R handles has four functions. There is a root name, for example, the root name for the normal distribution is the norm. This root is prefixed by one of the letters. p for “probability”, the cumulative distribution function (c. d. f.)
What are vector functions?
In R, a function is a piece of code written to carry out a specified task. R Functions are called as objects because we can work with them exactly the same way we work with any other type of object. Vector functions are those functions which we used in vectors.
For Example: rep(), seq(), using all() and any(), more on c() etc.
Most common functions which we use in vector operations are –
rep()
seq()
Explain how to repeat vectors in R?
We can use the rep() function in several ways if we want to repeat the complete vector. For examples: specify the argument times 1. To repeat the vector c(0, 0, 7) three times, use this code:
> rep(c(0, 0, 7), times = 4)
[1] 0 0 7 0 0 7 0 0 7 0 0 7 2
We can also repeat every value by specifying the argument each, like this:
> rep(c(2, 4, 2), each = 2)
[1] 2 2 4 4 2 2 3
We can tell R for each value how often it has to repeat:
> rep(c(0, 7), times = c(4,3))
[1] 0 0 0 0 7 7 7 4
In seq, we use the argument length.out to define R. it will repeat the vector until it reaches that length, even if the last repetition is incomplete.
> rep(1:3,length.out=9)
[1] 1 2 3 1 2 3 1 2 3
How to create vectors in R?
a) To create a vector using integers:
For Example, We use the colon operator (:) in R.
The code 2:6 gives you a vector with the numbers 2 to 6, and 3:-4 create a vector with the numbers 3 to –4, both in steps of 1.
b) We use the seq() to make steps in a sequence.
Seq() function used to describe by which the numbers should decrease or increase.
For Example In R, the vector with a numbers 4.5 to 3.0 in steps of 0.5.
> seq(from = 4.5, to = 3.0, by = -0.5)
[1] 4.5 4.0 3.5 3.0 c
You can specify the length of the sequence by using the argument out. R calculates the step size itself. For Example We can make a vector of nine values going from –2.7 to 1.3 like this:
> seq(from = -2.7, to = 1.3, length.out = 9)
[1] -2.7 -2.2 -1.7 -1.2 -0.7 -0.2 0.3 0.8 1.3
Can we update and delete any of the elements in a list?
We can update any of the element but we can delete only the element at the end of the list.
How many types of object are present In R?
There are 6 types of objects present in R:
Vectors
Matrices
Arrays
Lists
Data Frames
Factors
What are R Functions?
A function is a piece of code written to carry out a specified task. Thus it can or can’t accept arguments or parameters and it can or can’t return one or more values. In R, functions are objects in their own right. Hence, we can work with them exactly the same way we work with any other type of object.
What is using all() and any()?
a) na.rm – State whether NA values should ignore.
b) any(…, na.rm=FALSE) … – One or more R objects that need to be check. na.rm – State whether NA values should ignore. The any() and all() functions are shortcuts because they report any or all their arguments are TRUE.
> x <- 1:10 > any(x > 5)
[1] TRUE
> any(x > 88)
[1] FALSE
> all(x > 88)
[1] FALSE
> all(x > 0)
[1] TRUE For Example: Suppose that R executes the following:
> any(x > 5)
It first evaluates x > 5:
(FALSE, FALSE, FALSE, FALSE, FALSE)
We use any() function – that reports whether any of those values are TRUE while all() function works and
reports if all the values are TRUE.
What is R’s C interface?
R’s source code is a powerful technique for Improving Programming skills. But, many base R function was already written in C. It is been used to figure out how those functions work. All functions in R defined with the prefix Rf_ or R_.
Outline of Rs C interface
Input Validations talks about itself so that C function doesn’t crash R.
C data Structures shows how to translate data structure names from R to C.
Creating and modifying vectors teaches how to create, change, and make vectors in C.
Calling C defines the basics of creating. It also defines the functions with the inline package.
What are Prerequisites for R’s C interface?
We need a C compiler for C interface. Windows users can use Rtools. Mac users will need the Xcode command line tools. Most Linux distributions will come with the necessary compilers. In Windows, it is necessary to include Windows PATH environment variable in it:
Rtools executables directory (C:\Rtools\bin),
C compiler executables directory (C:\Rtools\gcc-4.6.3\bin).
How to call C function from R?
Generally, to call a C function it required two pieces:
C function.
R wrapper function that uses.Call().
The function below adds two numbers together:
// In C -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
#include <R.h>
#include <Rinternals.h>
SEXP add(SEXP a, SEXP b) {
SEXP result = PROTECT(allocVector(REALSXP, 1));
REAL(result)[0] = asReal(a) + asReal(b);
UNPROTECT(1);
return result;
}
# In R -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
add <- function(a, b) {
.Call("add", a, b}
}
What are R matrices and R matrices functions?
A matrix is a two-dimensional rectangular data set. Thus it can create using vector input to the matrix function. Also, a matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually, the numbers are the real numbers. We reproduce a memory representation of the matrix in R with the matrix function. Hence, the data elements must be of the same basic type. Matrices functions are those functions which we use in matrices.
There are two types of matrices functions:
apply()
sapply()
What is apply() function in R?
Return a vector or array or list of values obtained by applying a function to margins of an array or matrix.
Keywords
array, iteration
Usage
apply(X, MARGIN, FUN, …)
Arguments
X – an array, including a matrix
… – optional arguments to FUN
FUN – The function to apply: see ‘Details’
MARGIN -Functions will apply on subscripts in a vector.
What is the apply() family in R?
Apply functions are a family of functions in base R. which allow us to perform an action on many chunks of data. An apply function is a loop, but run faster than loops and often must less code. There are many different apply functions. The called function could be:
There is some aggregating function. They include meaning, or the sum(includes return a number or scalar);
Other transforming or subsetting functions.
There are some vectorized functions. They return more complex structures like lists, vectors, matrices, and arrays.
We can perform operations with very few lines of code in apply().
What is R lists?
Lists are the object which Contains elements of different types – like strings, numbers, vectors and another list inside it. A list can also contain a matrix or a function as its elements. The List is created using list() Function. In other words, a list is a generic vector containing other objects. For Example, The variable x is containing copies of three vectors n, s, b and a numeric value 3.
n = c(2, 3, 5)
s = c(“aa”, “bb”, “cc”, “dd”, “ee” )
b = c(TRUE, FALSE, TRUE, FALSE, FALSE )
x = list( n, s, b, 3) # x contains copies of n, s, b)
Explain how to create a list in R?
Create a list containing string, numbers, vectors and logical values. For Example:
List_data <- list("Green", "Yellow", c(5,6,7), TRUE, 51.2)
print(list_data) When we execute the above code, it produces the following result-
[[1]]
[1] “Green”
[[2]]
[1] “Yellow”
[[3]]
[1] 5, 6, 7
[[4]]
[1] TRUE
[[5]]
[1] 51.2
 |
| Wipro R Programming Recently Asked Interview Questions Answers |
How to use sapply in R?
Multipy all values by 10:
> sapply(BOD,function(x) 10 * x)
Time demand
[1,] 10 80
[2,] 20 100
[3,] 30 190
Used for array, margin set to 1:
> x <- array(1:9) > sapply(x,function(x) x * 10)
[1] 10 20 30 40 50 60 70 80 90
Two dimension array, margin can be 1 or 2:
> x <- array(1:9,c(3,3)) > x
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
> sapply(x,function(x) x * 10)
[1] 10 20 30 40 50 60 70 80 90
sapply: returns a vector, matrix or an array
# sapply : returns a vector, an array or matrix
sapply(c(1:3), function(x) x^2)
[1] 1 4 9
What is R matrices?
A matrix is a two-dimensional rectangular data set and thus it can be created using vector input to the matrix function. In addition, a matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually, the numbers are the real numbers. By using a matrix function we can reproduce a memory representation of the matrix in R. Hence, the data elements must be of the same basic type.
How many methods are available to use the matrices?
There are so many methods to solve the matrices like adding, subtraction, negative etc.
What is control structure in R?
R has the standard control structures we would expect. expr can be multiple statements by enclosing them in braces { }. It is more efficient to use built-in functions rather than control structures whenever possible. These allow us to control the flow of execution of a script typically inside of a function. Control structures define the flow of the program. The decision is been based on the evaluation of a variable.
How many control statements are present in R?
There are eight control statements are present in R.
Name all control statements present in R?
If
If-else
For
Nested loops
While
Repeat and break
Next
return.
Create a list containing a vector, a list and a matrix.
list_data <- list(c("Feb","Mar","Apr"))
list("white",13.4)), matrix(c(3,9,5,1,-2,8), nrow = 2)
For Example: Give names to the elements in the list:
Names(list_data) <- c(“1 st Quarter”, “A Matrix”, “A Inner list”)
Access the first element of the list:
print(list_data[1])
Access the third element. As it also a list, all its elements will print:
Print(list_data[3])
By using the name of the element access the list elements:
Print(list_data$A Matrix)
It will produced the following result after executing the above code:
$”1 st Quarter” [1] “Feb”, "Mar”, "Apr”
$A_Inner_list
$A_Inner_list[[1]]
[1] “White”
$A_Inner_list[[2]]
[1] 13.4
$ “A Matrix” [1]
[1] [2] [3]
[1] 3 5 -2
[2] 9 1 8
Explain how to manipulate list elements in R?
Create a list containing a vector, a matrix and a list.
list_data <- list(c("Feb","Mar","Apr"),
matrix(c(3,9,5,1,-2,8), nrow = 2), list("green",12.3))
For Example:
Give names to the elements in the list:
names(list_data) <- c("1st Quarter", "A_Matrix", "A Inner list")
Add element at the end of the list:
list_data[4] <- "New element"
print(list_data[4])
Remove the last element:
list_data[4] <- NULL # Print the 4th Element.print(list_data[4])
Update the 3rd Element:
list_data[3] <- "updated element"
print(list_data[3])
When we execute the above code, it produces the following result:
[[1]]
[1] "New element"
$NULL
$`A Inner list`
[1] "updated element"
Explain how to generate lists in R?
We can use a colon to generate a list of numbers. For example:
-3:3
[1] -3 -2 -1 0 1 2 3
Explain how to operate on lists in R?
R allows to Operate on all list values at once. For example:
c(1,3,5) + 4
This and the Apply function allow you to avoid most for loops.
[1] 5, 7, 9
What are features of R functions?
Function component describes the three main components of a function.
Lexical scoping teaches how R finds values from names.
In R, every operation is a function call.
Function arguments discuss the three ways of supplying arguments to a function. it shows to call
The function is given a list of arguments and to the impact of lazy evaluation.
Special calls describe two special types of function infix and replacement functions.
Return values discuss how and when functions return values. it also shows how you can ensure
that a function does something before it exists.
What is function definition?
An R function is been created using the keyword function. The basic syntax of an R function definition is as follows −
function_name <- function(arg_1, arg_2, …) {
Function body
}
What are the components of R functions?
The different parts of a function are −
Function Name − It is the actual name of the function because it stored in R environment as an object with this name.
Arguments − An argument is a placeholder. When a function invokes, we pass a value to the
argument. Arguments are optional; that is, a function may contain no arguments. Also, arguments can have default values.
Functions Body – In a function body, statements can be collected. and hence, it defines what the function does.
Return Value − the return value of a function is the last expression in the function body to check.
What are Generic Functions in R?
R has three object-oriented (OO) systems: [[S3]], [[S4]] and [[R5]]. … A method is a function associated with a particular type of object. S3 implements a style of object-oriented programming called generic-function OO.
What are R packages?
Packages are collections of R functions, data, and compiled code in a well-defined format. The directory where packages are stored is called the library. R comes with a standard set of packages. Others are available for download and installation. Once installed, they have to be loaded into the session to be used.
Name the functions which helps in importing data from other applications in R?
read.table()
readlines()
read.fwf
read.delim()
scan()
read.csv()
read.csv2()
What is more functions in R and name them?
We have to load the built-in foreign command to use these functions:
>library("foreign")
R more functions:
read.xpss
read.xport
read.dta
List out some of the function that R provides?
Mean
Median
Distribution
Covariance
Regression
What is the distribution in R?
R Functions for Probability Distributions. Every distribution that R handles has four functions. There is a root name, for example, the root name for the normal distribution is the norm. This root is prefixed by one of the letters. p for “probability”, the cumulative distribution function (c. d. f.)
What are vector functions?
In R, a function is a piece of code written to carry out a specified task. R Functions are called as objects because we can work with them exactly the same way we work with any other type of object. Vector functions are those functions which we used in vectors.
For Example: rep(), seq(), using all() and any(), more on c() etc.
Most common functions which we use in vector operations are –
rep()
seq()
Explain how to repeat vectors in R?
We can use the rep() function in several ways if we want to repeat the complete vector. For examples: specify the argument times 1. To repeat the vector c(0, 0, 7) three times, use this code:
> rep(c(0, 0, 7), times = 4)
[1] 0 0 7 0 0 7 0 0 7 0 0 7 2
We can also repeat every value by specifying the argument each, like this:
> rep(c(2, 4, 2), each = 2)
[1] 2 2 4 4 2 2 3
We can tell R for each value how often it has to repeat:
> rep(c(0, 7), times = c(4,3))
[1] 0 0 0 0 7 7 7 4
In seq, we use the argument length.out to define R. it will repeat the vector until it reaches that length, even if the last repetition is incomplete.
> rep(1:3,length.out=9)
[1] 1 2 3 1 2 3 1 2 3
How to create vectors in R?
a) To create a vector using integers:
For Example, We use the colon operator (:) in R.
The code 2:6 gives you a vector with the numbers 2 to 6, and 3:-4 create a vector with the numbers 3 to –4, both in steps of 1.
b) We use the seq() to make steps in a sequence.
Seq() function used to describe by which the numbers should decrease or increase.
For Example In R, the vector with a numbers 4.5 to 3.0 in steps of 0.5.
> seq(from = 4.5, to = 3.0, by = -0.5)
[1] 4.5 4.0 3.5 3.0 c
You can specify the length of the sequence by using the argument out. R calculates the step size itself. For Example We can make a vector of nine values going from –2.7 to 1.3 like this:
> seq(from = -2.7, to = 1.3, length.out = 9)
[1] -2.7 -2.2 -1.7 -1.2 -0.7 -0.2 0.3 0.8 1.3
Can we update and delete any of the elements in a list?
We can update any of the element but we can delete only the element at the end of the list.
How many types of object are present In R?
There are 6 types of objects present in R:
Vectors
Matrices
Arrays
Lists
Data Frames
Factors
What are R Functions?
A function is a piece of code written to carry out a specified task. Thus it can or can’t accept arguments or parameters and it can or can’t return one or more values. In R, functions are objects in their own right. Hence, we can work with them exactly the same way we work with any other type of object.
What is using all() and any()?
a) na.rm – State whether NA values should ignore.
b) any(…, na.rm=FALSE) … – One or more R objects that need to be check. na.rm – State whether NA values should ignore. The any() and all() functions are shortcuts because they report any or all their arguments are TRUE.
> x <- 1:10 > any(x > 5)
[1] TRUE
> any(x > 88)
[1] FALSE
> all(x > 88)
[1] FALSE
> all(x > 0)
[1] TRUE For Example: Suppose that R executes the following:
> any(x > 5)
It first evaluates x > 5:
(FALSE, FALSE, FALSE, FALSE, FALSE)
We use any() function – that reports whether any of those values are TRUE while all() function works and
reports if all the values are TRUE.
What is R’s C interface?
R’s source code is a powerful technique for Improving Programming skills. But, many base R function was already written in C. It is been used to figure out how those functions work. All functions in R defined with the prefix Rf_ or R_.
Outline of Rs C interface
Input Validations talks about itself so that C function doesn’t crash R.
C data Structures shows how to translate data structure names from R to C.
Creating and modifying vectors teaches how to create, change, and make vectors in C.
Calling C defines the basics of creating. It also defines the functions with the inline package.
What are Prerequisites for R’s C interface?
We need a C compiler for C interface. Windows users can use Rtools. Mac users will need the Xcode command line tools. Most Linux distributions will come with the necessary compilers. In Windows, it is necessary to include Windows PATH environment variable in it:
Rtools executables directory (C:\Rtools\bin),
C compiler executables directory (C:\Rtools\gcc-4.6.3\bin).
How to call C function from R?
Generally, to call a C function it required two pieces:
C function.
R wrapper function that uses.Call().
The function below adds two numbers together:
// In C -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
#include <R.h>
#include <Rinternals.h>
SEXP add(SEXP a, SEXP b) {
SEXP result = PROTECT(allocVector(REALSXP, 1));
REAL(result)[0] = asReal(a) + asReal(b);
UNPROTECT(1);
return result;
}
# In R -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
add <- function(a, b) {
.Call("add", a, b}
}
What are R matrices and R matrices functions?
A matrix is a two-dimensional rectangular data set. Thus it can create using vector input to the matrix function. Also, a matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually, the numbers are the real numbers. We reproduce a memory representation of the matrix in R with the matrix function. Hence, the data elements must be of the same basic type. Matrices functions are those functions which we use in matrices.
There are two types of matrices functions:
apply()
sapply()
What is apply() function in R?
Return a vector or array or list of values obtained by applying a function to margins of an array or matrix.
Keywords
array, iteration
Usage
apply(X, MARGIN, FUN, …)
Arguments
X – an array, including a matrix
… – optional arguments to FUN
FUN – The function to apply: see ‘Details’
MARGIN -Functions will apply on subscripts in a vector.
What is the apply() family in R?
Apply functions are a family of functions in base R. which allow us to perform an action on many chunks of data. An apply function is a loop, but run faster than loops and often must less code. There are many different apply functions. The called function could be:
There is some aggregating function. They include meaning, or the sum(includes return a number or scalar);
Other transforming or subsetting functions.
There are some vectorized functions. They return more complex structures like lists, vectors, matrices, and arrays.
We can perform operations with very few lines of code in apply().
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