update ch 2 exercises
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Bogumił Kamiński
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@ -16,10 +16,32 @@ y[1] = 10
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```
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What is the value of `x[1]` and why?
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<details>
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<summary>Solution</summary>
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`x[1]` will be `10` because `y = x` is not copying data but it binds
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the same value both to variable `x` and `y`.
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</details>
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### Exercise 2
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How can you type `⚡ = 1`. Check if this operation succeeds and what is its result.
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<details>
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<summary>Solution</summary>
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In help mode (activated by `?`) copy-paste `⚡` to get:
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```
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help?> ⚡
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"⚡" can be typed by \:zap:<tab>
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```
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After the `⚡ = 1` operation a new variable `⚡` is defined and it is bound
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to value `1`.
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</details>
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### Exercise 3
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What will be the value of variable `x` after running of the following code and why?
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@ -31,62 +53,8 @@ end
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x /= 1_000_000
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```
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### Exercise 4
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Express the type `Matrix{Bool}` using `Array` type.
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### Exercise 5
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Let `x` be a vector. Write code that prints an error if `x` is empty
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(has zero elements)
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### Exercise 6
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Write a function called `exec` that takes two values `x` and `y` and a function
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accepting two arguments, call it `op` and returns `op(x, y)`. Make `+` to be
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the default value of `op`.
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### Exercise 7
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Write a function that calculates a sum of absolute values of values stored in
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a collection passed to it.
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### Exercise 8
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Write a function that swaps first and last element in an array in place.
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### Exercise 9
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Write a loop in global scope that calculates the sum of cubes of numbers from
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`1` to `10^6`. Next use the `sum` function to perform the same computation.
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What is the difference in timing of these operations?
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### Exercise 10
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Explain the value of the result of summation obtained in exercise 9.
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# Solutions
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<details>
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<summary>Show!</summary>
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### Exercise 1
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`x[1]` will be `10` because `y = x` is not copying data but it binds
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the same value both to variable `x` and `y`.
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### Exercise 2
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In help mode (activated by `?`) copy-paste `⚡` to get:
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```
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help?> ⚡
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"⚡" can be typed by \:zap:<tab>
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```
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After the `⚡ = 1` operation a new variable `⚡` is defined and it is bound
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to value `1`.
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### Exercise 3
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<summary>Solution</summary>
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`x` will have value `0.9999999999242748`. This value is below `1.0` because
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representation of `1/7` using `Float64` type is less than rational number 1/7,
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@ -105,16 +73,31 @@ julia> 1/big(7) # construct high-precision float directly
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As you can see there is a difference at 17th place after decimal dot where we
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have `4` vs `5`.
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</details>
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### Exercise 4
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Express the type `Matrix{Bool}` using `Array` type.
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<details>
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<summary>Solution</summary>
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It is `Array{Bool, 2}`. You immediately get this information in REPL:
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```
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julia> Matrix{Bool}
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Matrix{Bool} (alias for Array{Bool, 2})
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```
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</details>
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### Exercise 5
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Let `x` be a vector. Write code that prints an error if `x` is empty
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(has zero elements)
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<details>
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<summary>Solution</summary>
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You can do it like this:
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```
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length(x) == 0 && println("x is empty")
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@ -127,8 +110,17 @@ passed as an argument to the function):
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isempty(x) && throw(ArgumentError("x is not allowed to be empty"))
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```
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</details>
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### Exercise 6
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Write a function called `exec` that takes two values `x` and `y` and a function
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accepting two arguments, call it `op` and returns `op(x, y)`. Make `+` to be
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the default value of `op`.
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<details>
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<summary>Solution</summary>
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Here are two ways to define the `exec` function:
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```
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exec1(x, y, op=+) = op(x, y)
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@ -144,15 +136,30 @@ julia> exec2(2, 3; op=*)
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6
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```
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</details>
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### Exercise 7
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Write a function that calculates a sum of absolute values of values stored in
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a collection passed to it.
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<details>
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<summary>Solution</summary>
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Such a function can be written as:
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```
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sumabs(x) = sum(abs, x)
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```
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</details>
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### Exercise 8
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Write a function that swaps first and last element in an array in place.
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<details>
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<summary>Solution</summary>
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This can be written for example as:
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```
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function swap!(x)
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@ -184,8 +191,17 @@ Note the differences in the code:
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is technically called tuple destructuring; we discuss it in later chapters of
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the book)
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</details>
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### Exercise 9
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Write a loop in global scope that calculates the sum of cubes of numbers from
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`1` to `10^6`. Next use the `sum` function to perform the same computation.
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What is the difference in timing of these operations?
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<details>
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<summary>Solution</summary>
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We used `@time` macro in chapter 1.
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Version in global scope:
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@ -246,8 +262,15 @@ julia> @time sum3loop(10^6)
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```
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This is also much faster than a loop in global scope.
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</details>
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### Exercise 10
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Explain the value of the result of summation obtained in exercise 9.
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<details>
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<summary>Solution</summary>
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In exercise 9 we note that the result is `-8222430735553051648` which is a
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negative value, although we are adding cubes of positive values. The
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reason of the problem is that operations on integers overflow. If you
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