STATISTICS WITH R PROGRAMMING Unit - 2

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R Programming Structures: Control Statements - Loops, Looping Over Non-vector Sets, If-Else,
Arithmetic and Boolean Operators and values, Default Values for Argument, Return Values -
Deciding Whether to explicitly call return, Returning Complex Objects, Functions are Objective, No
Pointers in R, Recursion - A Quick sort Implementation, Extended Extended Example: A Binary
Search Tree.

Control Statements: The statements in an R program are executed sequentially from the top of the
program to the bottom. But some statements are to be executed repetitively, while only executing other
statements if certain conditions are met. R has the standard control structures.

Loops: Looping constructs repetitively execute a statement or series of statements until a condition isn‘t
true. These include the for, while and repeat structures with additional clauses break and next.
1) FOR :- The for loop executes a statement repetitively until a variable‘s
value is no longer contained in the sequence seq.
 The syntax is for (var in sequence)
{
statement
}
Here, sequence is a vector and var takes on each of its value
during the loop. In each iteration, statement is evaluated.
 for (n in x) { - - - }
It means that there will be one iteration of the loop for each
component of the vector x, with taking on the values of those
components—in the first iteration, n = x[1]; in the second
iteration, n = x[2]; and so on.
 In this example for (i in 1:10) print("Hello") the word Hello is
printed 10 times.
 Square of every element in a vector:
> x <- c(5,12,13)
> for (n in x) print(n^2)
[1] 25
[1] 144
[1] 169

 Program to find the multiplication

# take input from the user
num = as.integer(readline(prompt = "Enter a number: "))
# use for loop to iterate 10 times
for(i in 1:10) {
print(paste(num,'x', i, '=', num*i)) }

2) WHILE:- A while loop executes a statement repetitively until the

condition is no longer true.
Syntax:
while (expression)
{
statement
}
 Here, expression is evaluated and the body of the loop is entered if
the result is TRUE.

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 The statements inside the loop are executed and the flow returns to evaluate
the expression again.
 This is repeated each time until expression evaluates to FALSE, in which case, the loop exits.
 Example
> i <- 1
> while (i<=10) i <- i+4
>i
[1] 13

 Program to find the sum of first n natural numbers

sum = 0
# take input from the user
num = as.integer(readline(prompt = "Enter a number: ")) Output:
# use while loop to iterate until zero Enter a number: 4
while(num > 0) [1] "The sum is 10"
{
sum = sum + num
num = num - 1
}
print(paste("The sum is", sum))

3) Break statement: A break statement is used inside a loop

(repeat, for, while) to stop the iterations and flow the control outside of
the loop.In a nested looping situation, where there is a loop inside
another loop, this statement exits from the innermost loop that is being
evaluated.
Syntax:- break
Example
x <- 1:5
Output:
for (val in x) {
[1] 1
if (val == 3){
[1] 2
break
}
print(val)
}

4) Next statement:- A next statement is useful when we want to skip the

current iteration of a loop without terminating it. On encountering next,
the R parser skips further evaluation and starts next iteration of the loop.
Syntax:- next
Example
x <- 1:5
for (val in x) { Output:
if (val == 3){ [1] 1
next [1] 2
} [1] 4
print(val) [1] 5
}

5) Repeat:- Repeat loop is used to iterate over a block of code multiple number of times. There is no
condition check in repeat loop to exit the loop.

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We must ourselves put a condition explicitly inside the body of the loop and use the break statement to
exit the loop. Failing to do so will result into an infinite loop.

Syntax:
repeat
{
statement
}

Example:

x <- 1
repeat Output:
{ [1] 1
print(x) [1] 2
x = x+1 [1] 3
if (x == 6) [1] 4
break [1] 5
}

Looping Over Non-vector Sets:- R does not directly support iteration over nonvector sets, but there
are a couple of indirect yet easy ways to accomplish it:
 apply( ):- Applies on 2D arrays (matrices), data frames to find aggregate functions like
sum, mean, median, standard deviation.
syntax:- apply(matrix,margin,fun,....)
margin = 1 indicates row
= 2 indicates col
> x <- matrix(1:20,nrow = 4,ncol=5)
>x
[,1] [,2] [,3] [,4] [,5]
[1,] 1 5 9 13 17
[2,] 2 6 10 14 18
[3,] 3 7 11 15 19
[4,] 4 8 12 16 20
> apply(x,2,sum)
[1] 10 26 42 58 74

 Use lapply( ), assuming that the iterations of the loop are independent of each other, thus
allowing them to be performed in any order. Lapply( ) can be applies on dataframes,lists
and vectors and return a list. lapply returns a list of the same length as X, each element of
which is the result of applying FUN to the corresponding element of X.
Syntax: lapply(X, FUN, ...)
> x <- matrix(1:4,2,2)
>x
[,1] [,2] lapply( ) function is applied on every
[1,] 1 3 elements of the object.
[2,] 2 4
> lapply(x,sqrt)
[[1]]
[1] 1

[[2]]
[1] 1.414214

[[3]]
[1] 1.732051

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[[4]]
[1] 2
 Use get( ), As its name implies, this function takes as an argument a character string
representing the name of some object and returns the object of that name. It sounds simple,
but get() is a very powerful function.
Syntax: get(“character string”)
> get("sum")
function (..., na.rm = FALSE) .Primitive("sum")
> get("g")
function(x)
{
return(x+1)
}
> get("num")
[1] "45"

Note:- Reserved words in R programming are a set of words that have special meaning and cannot be
used as an identifier (variable name, function name etc.).This list can be viewed by
typing help(reserved) or ?reserved at the R command prompt.

Reserved words in R

if else repeat while function

for in next break TRUE

FALSE NULL Inf NaN NA

NA_integer_ NA_real_ NA_complex_ NA_character_ ...

If –Else:- The if-else control structure executes a statement if a given condition is true. Optionally, a
different statement is executed if the condition is false.
The syntax is
if (cond) if (cond)
{ {
statements statement1
} } else
{
statement2
}

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x <- 8
if(x>3) {y <- 10 Output:
} else {y<-0} [1] 10
print(y)

y <- ifelse(x>3, 10, 0)

y Output:
[1] 0
x <- 4
if(x==4) Output: Error.
x <- 1
else The right brace before the else is used by the R parser to
{ deduce that this is an if-else rather than just an if.
x <- 3
y <- 4
}

An if-else statement works as a function call, and as such, it returns the last value assigned.
v <- if (cond) expression1 else expression2
This will set v to the result of expression1 or expression2, depending on whether cond is true. You
can use this fact to compact your code. Here‘s a simple example:
> x <- 2
> y <- if(x == 2) x else x+1
>y
[1] 2

> x <- 2
>if(x == 2) y <- x else y <- x+1
>y
[1] 2

Operators:- R has many operators to carry out different

mathematical and logical operations.
Types of operators
1. Arithmetic operators.
2. Relational operators.
3. Logical operators.
4. Assignment operators.
5. Miscellaneous Operators

1.Arithmetic operators:- These operators are used to carry out mathematical operations like addition
and multiplication. Here is a list of arithmetic operators available in R.
Operator Description Example

v <- c( 2,5.5,6)
t <- c(8, 3, 4)
+ Adds two vectors print(v+t)
it produces the following result −
[1] 10.0 8.5 10.0

v <- c( 2,5.5,6)
Subtracts second t <- c(8, 3, 4)
−
vector from the first print(v-t)
it produces the following result −

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[1] -6.0 2.5 2.0

v <- c( 2,5.5,6)
t <- c(8, 3, 4)
Multiplies both print(v*t)
*
vectors
it produces the following result −
[1] 16.0 16.5 24.0

v <- c( 2,5.5,6)
t <- c(8, 3, 4)
Divide the first vector
/ print(v/t)
with the second
When we execute the above code, it produces the following result −
[1] 0.250000 1.833333 1.500000

v <- c( 2,5.5,6)
Give the remainder of t <- c(8, 3, 4)
%% the first vector with print(v%%t)
the second it produces the following result −
[1] 2.0 2.5 2.0

v <- c( 2,5.5,6)
The result of division t <- c(8, 3, 4)
%/% of first vector with print(v%/%t)
second (quotient) it produces the following result −
[1] 0 1 1

v <- c( 2,5.5,6)
The first vector raised t <- c(8, 3, 4)
^ to the exponent of print(v^t)
second vector it produces the following result −
[1] 256.000 166.375 1296.000

2.Relational Operator:- Relational operators are used to compare between values.Each element of the
first vector is compared with the corresponding element of the second vector. The result of comparison
is a Boolean value.

Operator Description Example

v <- c(2,5.5,6,9)
Checks if each element of the first vector is t <- c(8,2.5,14,9)
> greater than the corresponding element of the print(v>t)
second vector. it produces the following result −
[1] FALSE TRUE FALSE FALSE

v <- c(2,5.5,6,9)
Checks if each element of the first vector is less t <- c(8,2.5,14,9)
< than the corresponding element of the second print(v < t)
vector. it produces the following result −
[1] TRUE FALSE TRUE FALSE

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v <- c(2,5.5,6,9)
Checks if each element of the first vector is t <- c(8,2.5,14,9)
== equal to the corresponding element of the print(v == t)
second vector. it produces the following result −
[1] FALSE FALSE FALSE TRUE

v <- c(2,5.5,6,9)
Checks if each element of the first vector is less t <- c(8,2.5,14,9)
<= than or equal to the corresponding element of print(v<=t)
the second vector. it produces the following result −
[1] TRUE FALSE TRUE TRUE

v <- c(2,5.5,6,9)
Checks if each element of the first vector is t <- c(8,2.5,14,9)
>= greater than or equal to the corresponding print(v>=t)
element of the second vector. it produces the following result −
[1] FALSE TRUE FALSE TRUE

v <- c(2,5.5,6,9)
t <- c(8,2.5,14,9)
Checks if each element of the first vector is print(v!=t)
!= unequal to the corresponding element of the
second vector. it produces the following result −
[1] TRUE TRUE TRUE FALSE

3)Logical Operators:- It is applicable only to vectors of type logical, numeric or complex. Zero is
considered FALSE and non-zero numbers are taken as TRUE. Each element of the first vector is
compared with the corresponding element of the second vector. The result of comparison is a Boolean
value.
Operator Description Example

It is called Element-wise Logical AND v <- c(3,1,TRUE,2+3i)

operator. It combines each element of the first t <- c(4,1,FALSE,2+3i)
vector with the corresponding element of the print(v&t)
& second vector and gives a output TRUE if both
the elements are TRUE. it produces the following result −
[1] TRUE TRUE FALSE TRUE

v <- c(3,0,TRUE,2+2i)
It is called Element-wise Logical OR operator. t <- c(4,0,FALSE,2+3i)
It combines each element of the first vector print(v|t)
| with the corresponding element of the second
vector and gives a output TRUE if one the it produces the following result −
elements is TRUE. [1] TRUE FALSE TRUE TRUE

v <- c(3,0,TRUE,2+2i)
It is called Logical NOT operator. Takes each print(!v)
! element of the vector and gives the opposite
logical value. it produces the following result −
[1] FALSE TRUE FALSE FALSE

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The logical operator && and || considers only the first element of the vectors and give a vector
of single element as output.
Operator Description Example

v <- c(3,0,TRUE,2+2i)
Called Logical AND operator. Takes t <- c(1,3,TRUE,2+3i)
first element of both the vectors and print(v&&t)
&&
gives the TRUE only if both are
TRUE. it produces the following result −
[1] TRUE

Called Logical OR operator. Takes v <- c(0,0,TRUE,2+2i)

first element of both the vectors and t <- c(0,3,TRUE,2+3i)
|| print(v||t)
gives the TRUE if one of them is
TRUE. it produces the following result −[1] FALSE

4) Assignment Operators:- These operators are used to assign values to vectors.

Operator Description Example

v1 <- c(3,1,TRUE,2+3i)
v2 <<- c(3,1,TRUE,2+3i)
v3 = c(3,1,TRUE,2+3i)
<− print(v1)
or print(v2)
= Called Left Assignment print(v3)
or it produces the following result −
<<− [1] 3+0i 1+0i 1+0i 2+3i
[1] 3+0i 1+0i 1+0i 2+3i
[1] 3+0i 1+0i 1+0i 2+3i

c(3,1,TRUE,2+3i) -> v1
c(3,1,TRUE,2+3i) ->> v2
-> print(v1)
print(v2)
or Called Right Assignment
->> it produces the following result −
[1] 3+0i 1+0i 1+0i 2+3i
[1] 3+0i 1+0i 1+0i 2+3i

5) Miscellaneous Operators:- These operators are used to for specific purpose and not general
mathematical or logical computation.
Operator Description Example

Colon v <- 2:8

operator. It print(v)
creates the
: series of it produces the following result −
numbers in [1] 2 3 4 5 6 7 8
sequence
for a vector.

This v1 <- 8
operator is v2 <- 12
%in%
used to t <- 1:10
identify if print(v1 %in% t)

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an element print(v2 %in% t)

belongs to a it produces the following result −
vector.
[1] TRUE
[1] FALSE

M = matrix( c(2,6,5,1,10,4), nrow = 2,ncol = 3,byrow =

This TRUE)
operator is t = M %*% t(M)
used to print(t)
%*% multiply a
it produces the following result −
matrix with
its [,1] [,2]
transpose. [1,] 65 82
[2,] 82 117

Functions:- A function is a block or chunck of code having a

specific structure, which is often singular or atomic nature,
and can be reused to accomplish a specific nature. A function
helps to divide a large program into modules to enhance
readability and code reuse. or A function is a group of
instructions that takes inputs, uses them to compute other
values, and returns a result.
structure of a function
function_name <- function(arguments)
{
statements Built-in functions in R
}
 The word ‗function‘ is a keyword which is used to specify the statements enclosed within the
curly braces are part of the function.
 Function_name is used to identify the function
 Function consists of formal arguments and body
 The function is called using the following statement: function_name(arguments)
Example:
say.hello <- function() g <- function(x)
{ {
print("Hello, World!") x<- x+1
} return(x)
say.hello() }
[1] "Hello, World!" g(2)
[1] 3

 Functions are assigned to objects just like any other variable, using <- operator.
 Function are a set of parentheses that can either be empty – not have any arguments – or
contain any number of arguments.
 The body of the function is enclosed in curly braces ({ and }).This is not necessary if the
function contains only one line.
 A semicolon(;) can be used to indicate the end of the line but is not necessary.

# counts the number of odd integers in x

> oddcount <- function(x)
{
k <- 0 # assign 0 to k
for (n in x) {
if (n %% 2 == 1) k <- k+1 # %% is the modulo operator
}

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return(k)
}
> oddcount(c(1,3,5))
[1] 3
> oddcount(c(1,2,3,7,9))
[1] 4

Variables created outside functions are global and are available within functions as well. Example:
> f <- function(x) return(x+y)
> y <- 3
> f(5)
[1] 8
Here y is a global variable. A global variable can be written to from within a function by using R‘s
superassignment operator, <<-.

Default Arguments:- R also makes frequent use of default arguments. Consider a function definition
like this:
> g <- function(x,y=2,z=T) { ... }

Here y will be initialized to 2 if the programmer does not specify y in the call. Similarly, z will have the
default value TRUE. Now consider this call:

> g(12,z=FALSE)
Here, the value 12 is the actual argument for x, and we accept the default value of 2 for y, but we
override the default for z, setting its value to FALSE.

Default Values for Arguments:-

> my_matrix<- matrix (1:12,4,3,byrow= TRUE)
The argument byrow= TRUE tells R that the matrix should be filled in row wise. In this example the
default argument is byrow = FALSE, the matrix is filled in column wise.

Lazy Evaluation of Function:- Arguments to functions are evaluated lazily, which means so they are
evaluated only when needed by the function body.
# Create a function with arguments.
new.function <- function(a, b) {
print(a^2)
print(a)
print(b)
}
# Evaluate the function without supplying one of the arguments.
new.function(6)
When we execute the above code, it produces the following result −
[1] 36
[1] 6
Error in print(b) : argument "b" is missing, with no default

Return Values:- Functions are generally used for computing some value, so they need a mechanism to
supply that value back to the caller.This is called returning.

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 The return value of a function can be any R object. Although the return value is often a list, it
could even be another function.
 You can transmit a value back to the caller by explicitly calling return(). Without this call, the
value of the last executed statement will be returned by default.
 If the last statement in the call function is a for( ) statement, which returns the value NULL.

# First build it without an explicit return # Now build it with an explicit return
num <- function(x) num <- function(x)
{ {
x*2 return(x*2)
} }
> num(5) > num(5)
[1] 10 [1] 10

# build it again, this time with another argument after the explicit return
num <- function(x)
{
return(x*2)
#below here is not executed because the return function already exists.
print("VISHNU")
return(17)
}
> num(5)
[1] 10

# if the last statement is for loop or any empty statement then it return NULL.
num <- function(x)
{ }
> num(5)
[1] NULL

Deciding Whether to Explicitly Call return():-The R idiom is to avoid explicit calls to return(). One of
the reasons cited for this approach is that calling that function lengthens execution time. However,
unless the function is very short, the time saved is negligible, so this might not be the most compelling
reason to refrain from using return(). But it usually isn‘t needed.
#Example to count the odd numbers with no return statement
oddcount <- function(x) {
k <- 0 Both programs
for (n in x) { results in same
if (n %% 2 == 1) k <- k+1 output with and
}
k without return
}
> oddcount(c(12,2,5,9,7))
[1] 3

#Example to count the odd numbers with return statement

oddcount <- function(x) {
k <- 0
for (n in x) {
if (n %% 2 == 1) k <- k+1
}
return(k)
}
> oddcount(c(12,2,5,9,7))
[1] 3

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Good software design, can glance through a function‘s code and immediately spot the various
points at which control is returned to the caller. The easiest way to accomplish this is to use an
explicit return() call in all lines in the middle of the code that cause a return.

Returning Complex Objects:- The return value can be any R object, you can return complex objects.
Here is an example of a function being returned:
g<-function() {
x<- 3
t <- function(x) return(x^2)
return(t)
}

> g()
function(x) return(x^2)
<environment: 0x16779d58>
If your function has multiple return values, place them in a list or other container.

Functions are Objective:- R functions are first-class objects (of the class "function"), meaning that they
can be used for the most part just like other objects. This is seen in the syntax of function creation:
g <- function(x)
{
return(x+1)
}
function( ) is a built-in R function whose job is to create functions.On the right-hand side, there are really
two arguments to function(): The first is the formal argument list for the function i.e, x and the second is
the body of that function return(x+1). That second argument must be of class "expression". So, the point
is that the right-hand side creates a function object, which is then assigned to g.
> ?"{" Its job is the make a single unit of what could be several statements.
 formals( ) :- Get or set the formal arguments of a function
> formals(g) # g is a function with formal arguments ―x‖
$x
 body( ) :- Get or set the body of a function
> body(g) # g is a function
{
x <- x + 1
return(x)
}
 Replacing body of the function: quote( ) is used to substitute expression
> g <- function(x) return(x+1)
> body(g) <- quote(2*x+3)
>g
function (x)
2*x+3
 Typing the name of an object results in printing that object to the screen which is similar to
all objects
>g
function(x)
{
return(x+1)
}
 Printing out a function is also useful if you are not quite sure what an R library function
does. Code of a function is displayed by typing the built-in function name.
> sd
function (x, na.rm = FALSE)
sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x),
na.rm = na.rm))
<bytecode: 0x17b49740> <environment: namespace:stats>

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 Some of R‘s most fundamental built-in functions are written directly in C, and thus they
are not viewable in this manner.
> sum
function (..., na.rm = FALSE) .Primitive("sum")
 Since functions are objects, you can also assign them, use them as arguments to other
functions, and so on.
> f1 <- function(a,b) return(a+b)
> f2 <- function(a,b) return(a-b)
> f <- f1 # Assigning function object to other object
> f(3,2)
[1] 5
> g <- function(h,a,b) h(a,b) # passing function object as an arguments
> g(f1,3,2)
[1] 5
> g(f2,3,2)
[1] 1

No Pointers in R:- R does not have variables corresponding to pointers or references like C language.
This can make programming more difficult in some cases.
The fundamental thought is to create a class constructor and have every instantiation of the
class be its own environment. One can then pass the object/condition into a function and it will be
passed by reference instead of by value, because unlike other R objects, environments are not copied
when passed to functions. Changes to the object in the function will change the object in the calling
frame. In this way, one can operate on the object and change internal elements without having to create
a copy of the object when the function is called, nor pass the entire object back from the function. For
large objects, this saves memory and time.
For example, you cannot write a function that directly changes its arguments.

> x <- c(12,45,6)

> sort(x)
[1] 6 12 45
>x
[1] 12 45 6
The argument to sort() does not change. If we do want x to change in this R code, the solution is to
reassign the arguments:
> x <- sort(x)
>x
[1] 6 12 45

If a function has several output then a solution is to gather them together into a list, call the function
with this list as an argument, have the function return the list, and then reassign to the original list.
An example is the following function, which determines the indices of odd and even numbers in a
vector of integers:
> y <-function(v){
odds <- which(v %% 2 == 1)
evens <- which(v %% 2 == 0)
list(o=odds,e=evens)
}
> y(c(2,34,1,5))
$o
[1] 3 4

$e
[1] 1 2

Recursion:- Recursion is a programming technique in which, a function calls itself repeatedly for some
input.

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To solve a problem of type X by writing a recursive function f():

1. Break the original problem of type X into one or more smaller
problems of type X.
2. Within f(), call f() on each of the smaller problems.
3. Within f(), piece together the results of (b) to solve the original
problem.
# Recursive function to find factorial
recursive.factorial <- function(x)
{
if (x == 0) return (1)
else return (x * recursive.factorial(x-1))
}
> recursive.factorial(5)
[1] 120

r = fact(4)
24
return(4*(fact(3))
6
return(3*(fact(2))
2
return(2*(fact(1))
1
return(1)

A Quicksort Implementation:- Quick sort is also known as Partition-Exchange sort and is based on
Divide and conquer Algorithm design method. This was proposed by C.A.R Hoare. The basic idea of
quick sort is very simple. We consider one element at a time (pivot element). We have to move the pivot
element to the final position that it should occupy in the final sorted list. While identifying this position,
we arrange the elements, such that the elements to the left of the pivot element will be less than pivot
element & elements to the right of the pivot element will be greater than pivot element. There by
dividing the list by 2 parts. We have to apply quick sort on these 2 parts recursively until the entire list is
sorted.

For instance, suppose we wish to sort the vector (5,4,12,13,3,8,88). We first compare everything to the
first element, 5, to form two subvectors: one consisting of the elements less than 5 and the other
consisting of the elements greater than or equal to 5. That gives us subvectors (4,3) and (12,13,8,88). We
then call the function on the subvectors, returning (3,4) and (8,12,13,88). We string those together with
the 5, yielding (3,4,5,8,12,13,88), as desired. R‘s vector-filtering capability and its c() function make
implementation of Quicksort quite easy.

# Quicksort recursive function

qs <- function(x) {
if (length(x) <= 1) return(x)
pivot <- x[1]
therest <- x[-1]
sv1 <- therest[therest < pivot]
sv2 <- therest[therest >= pivot] > qs(c(12,6,7,34,3))
sv1 <- qs(sv1) [1] 3 6 7 12 34
sv2 <- qs(sv2)
return(c(sv1,pivot,sv2)) }

14 U.Padma Jyothi, CSE Dept , VITB

STATISTICS WITH R PROGRAMMING Unit - 2

Binary search tree:- The nature of binary search trees implies that at any node, all of the elements in
the node‘s left subtree are less than or equal to the value stored in this node, while the right subtree
stores the elements that are larger than the value in this mode. In our example tree, where the root
node contains 8, all of the values in the left subtree-5, 2 and 6-are less than 8, while 20 is greater than 8.

The code follows. Note that it includes only routines to insert new items and to traverse the tree.
# storage is in a matrix, say m, one row per node of the tree; a link i in the tree means the vector
#m[i,] = (u,v,w); u and v are the left and right links, and w is the stored value; null links have the value
#NA; the matrix is referred to as the list (m,nxt,inc), where m is the matrix, nxt is the next empty row to
#be used, and inc is the number of rows of expansion to be allocated when the matrix becomes full

# initializes a storage matrix, with initial stored value firstval

newtree <- function(firstval,inc) {
m <- matrix(rep(NA,inc*3),nrow=inc,ncol=3)
m[1,3] <- firstval
return(list(mat=m,nxt=2,inc=inc))
}

# inserts newval into nonempty tree whose head is index hdidx in the storage space treeloc; note that
#return value must be reassigned to tree; inc is as in newtree() above
ins <- function(hdidx,tree,newval,inc) {
tr <- tree
# check for room to add a new element
tr$nxt <- tr$nxt + 1
if (tr$nxt > nrow(tr$mat))
tr$mat <- rbind(tr$mat,matrix(rep(NA,inc*3),nrow=inc,ncol=3))
newidx <- tr$nxt # where we'll put the new tree node
tr$mat[newidx,3] <- newval
idx <- hdidx # marks our current place in the tree
node <- tr$mat[idx,]
nodeval <- node[3]
while (TRUE) {
# which direction to descend, left or right?
if (newval <= nodeval) dir <- 1 else dir <- 2
# descend
# null link?
if (is.na(node[dir])) {
tr$mat[idx,dir] <- newidx
break
} else {
idx <- node[dir]
node <- tr$mat[idx,]
nodeval <- node[3]
}
}
return(tr)
}

15 U.Padma Jyothi, CSE Dept , VITB

STATISTICS WITH R PROGRAMMING Unit - 2

# print sorted tree via inorder traversal

printtree <- function(hdidx,tree) {
left <- tree$mat[hdidx,1]
if (!is.na(left)) printtree(left,tree)
print(tree$mat[hdidx,3])
right <- tree$mat[hdidx,2]
if (!is.na(right)) printtree(right,tree)
}

sapply( ):- sapply is wrapper class to lapply with difference being it returns vector or matrix instead of
list object.
Syntax: sapply(X, FUN, ...,)
# create a list with 2 elements
x = (a=1:10,b=11:20) # mean of values using sapply
sapply(x, mean)
a b
5.5 15.5

tapply( ):- tapply() applies a function or operation on subset of the vector broken down by a given factor
variable.
To understand this, imagine we have ages of 20 people (male/females), and we need to know the
average age of males and females from this sample. To start with we can group ages by the gender
(male or female), ages of 12 males, and ages of 8 females, and later calculate the average age for
males and females.
Syntax of tapply: tapply(X, INDEX, FUN, …)
X = a vector, INDEX = list of one or more factor, FUN = Function or operation that needs to be
applied, … optional arguments for the function
> ages <- c(25,26,55,37,21,42)
> affils <- c("R","D","D","R","U","D")
> tapply(ages,affils,mean)
DRU
41 31 21

16 U.Padma Jyothi, CSE Dept , VITB