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#
# PROBLEMS:
#
# 1.  Construct a vector that contains elements: 1,2,3,...,19,20.
      v <- c(1:20)
      #v
#
#
# 2.  Construct a vector that contains elements: 1,2,3,...,19,20,19,...,3,2,1.
      v1 <- 1:20
      v2 <- 20:1
      j <- c(v1, v2)
      #j
#
# 3.  Construct a vector that contains elements: 1,3,5,1,3,5,...,1,3,5 
#     where there are 10 occurrences of element 5.
      h <- rep(seq(from=1, to=5, by=2), times=5)
      #h
#
#
# 4.  Calculate the values of sin(x) at 0, 0.1, 0.2, 0.3, ..., 1.0
      s <- seq(from=0.0, to=1.0, by=0.1)
      s <- sin(s)
      #s
#
# 5.  Suppose we have measured the heights and weights of ten individuals:
#
      # the vector of heights in 'cm'
      height <- c(179, 185, 183, 172, 174, 185, 193, 169, 173, 168)

      # the vector of weights in 'kg'
      weight <- c(95, 89, 70, 80, 92, 86, 100, 63, 72, 70)

#     Calculate the body mass index (bmi) for each individual using the formula:
#     bmi = weight_in_kg / (height_in_m)^2
#
#     HINT: first convert heights from 'cm' to 'm', then use the formula above.  
      height <- height / 100
      bmi <- weight / (height ^ 2)
      #bmi
#
# 6.  Consider a vector:
# 
      x <- c(1, -2, 3, -4, 5, -6, 7, -8)
      x[x < 0] <- 0
      x[x >= 0] <- x[] * 10
      x

#     Edit the vector x as follows. Replace all elements with a negative value 
#     with 0. Multiply the elements with a positive value by 10.
#
#
# 7.  Without using R, determine the result of the following computation:
#
      x <- c(1,2,3) # x = [1, 2, 3]
      # 1 / 2^2 - 1 + 2 * 3 - 2 -> 1/4 - 1 + 6 -2 ->  1/4 + 3 -> 3.25
      x[1]/x[2]^2-1+2*x[3]-x[1+1]
      #x

#
#
# 8.  Consider a vector:
#
      x <- 1:200
      length(x[x %% 11 == 0])
#     Determine how many elements in the vector are exactly divisible by 11.
#
#     HINT: the integer division operator is %/%
#           the modulus operator is %%              
#
#
# 9.  Consider a data frame:
#
      height <- c(179, 185, 183, 172, 174, 185, 193, 169, 173, 168)
      weight <- c(95, 89, 70, 80, 92, 86, 100, 63, 72, 70)
      gender <- factor(c("f","m","m","m","f","m","f","f","m","f"))
      student <- c(T, T, F, F, T, T, F, F, F, T)
      age = c(20, 21, 30, 25, 27, 19, 24, 27, 28, 24)
      name = c("Joan","Tom","John","Mike","Anna","Bill","Tina","Beth","Steve","Kim")
 
      df <- data.frame(name, gender, age, height, weight, student)
 
#     
#     - calculate the average age of persons in our dataset. 
#       (HINT: use the mean() function)
        mean(age)
#
#     - calculate the average age of students in our dataset.
        mean(df$age[df$student == T])
#
#     - how many males and females are in our dataset? 
#       (HINT: use the table() function)
        table(df$gender)
#
#     - print persons that are students.
        df$name[df$student == T]
#
#     - print persons who are between 1.8m and 1.9m tall (inclusive). 
        df$name[df$height >= 180 & df$height <= 190]
#
#     - print students who are above average height 
#       (considering all persons in the dataset).
        df$name[df$height > mean(df$height)] 
#
#     - arrange persons by their age. 
#       (HINT: use the order function)
        # order(df$age, decreasing=TRUE)
        df[order(df$age, decreasing=TRUE), ]
        df
#
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