Worksheet 4 - Loops and Flow Statements - Answers

In class we explored basic loop structures.

Loops and Outputs

Often the hardest task is not the computation, but controlling the data structure of outputing the loop. Try these variants:

require(ggplot2)

## Loading required package: ggplot2

1. Create a for loop from 1:100 that sticks x * 2 into a list

j <- list()

for (x in 1:100){
  j[[x]] <- x*2
}

head(j)

## [[1]]
## [1] 2
## 
## [[2]]
## [1] 4
## 
## [[3]]
## [1] 6
## 
## [[4]]
## [1] 8
## 
## [[5]]
## [1] 10
## 
## [[6]]
## [1] 12

2. Create a for loop from 1:100 that sticks x * 2 into a vector

j <- vector()

for(x in 1:100){
  j[x]<-x*2
}
head(j)

## [1]  2  4  6  8 10 12

3. Create a for loop from 1:100 that sticks x * 2 into a dataframe, with the first column as x.

j <- data.frame(X=1:100,OUT=NA)

for(x in 1:100){
  j[x,"OUT"] <- x*2
}

head(j)

##   X OUT
## 1 1   2
## 2 2   4
## 3 3   6
## 4 4   8
## 5 5  10
## 6 6  12

4. Create a for loop that skips odd rows in the dataframe using next, don’t cheat when using the seq statement iterator. Google if you need help!

j <- data.frame(X=1:100,OUT=NA)

for(x in 1:100){
    is.even <- function(x) x %% 2 == 0
    
    if(!is.even(x)){next} 

    j[x,"OUT"] <- x*2
}

head(j)

##   X OUT
## 1 1  NA
## 2 2   4
## 3 3  NA
## 4 4   8
## 5 5  NA
## 6 6  12

Using user defined functions within a loop.

Here is a generic function for finding prime numbers,

http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

The function is a bit slow, so don’t go too high!

sieve <- function(n) {
   n <- as.integer(n)
   
   if(n > 1e6) stop("n too large")
   
   primes <- rep(TRUE, n)
   
   primes[1] <- FALSE
   
   last.prime <- 2L
   
   for(i in last.prime:floor(sqrt(n))){
      primes[seq.int(2L*last.prime, n, last.prime)] <- FALSE
      last.prime <- last.prime + min(which(primes[(last.prime+1):n]))
   }
   which(primes)
}

#Test
paste(sieve(10),"is prime")

## [1] "2 is prime" "3 is prime" "5 is prime" "7 is prime"

5. How many prime numbers are below 50?

length(sieve(50))

## [1] 15

6. How many prime numbers are below 50, but above 10?

a <- sieve(50)
length(which(a > 10))

## [1] 11

Now for the loops.

7. Plot the number of prime numbers from 100 to 1000, by intervals of 100.

s <- seq(100,1000,100)
j <- data.frame(Size=s, NumberPrimes=NA)

for (x in s){
  a <- sieve(x)
  j[which(x == s),"NumberPrimes"] <- length(a)
}

qplot(j$Size, j$NumberPrimes)

8. Break the loop when the number of primes is greater than 1000.

s <- seq(100,1000,100)
j <- data.frame(Size=s, NumberPrimes=NA)

for (x in s){
  a <- sieve(x)
  j[which(x == s),"NumberPrimes"]<-length(a)
  if(length(a)>1000) break
}

qplot(j$Size,j$NumberPrimes)