I am trying to return a pair of sums using the let construct in sml. Every way I have tried will only return one value. I have tried creating a list by using cons (::) and then returning the list, but that gives an error as well.
val t = [(3,4), (4,5), (5,6)];
fun sumPairs(nil) = 0
| sumPairs((x,y)::zs) =
let
val sumFirst = x + sumPairs(zs)
val sumSecond = y + sumPairs(zs)
in
(sumFirst, sumSecond) <how would I return this as a tuple or list?>
end;
sumPairs(t);
The problem is not with (sumFirst, sumSecond) or with let specifically, but with the rest of your code.
The base case and the recursions say that sumPairs produces an int, not a pair of ints.
Because of this, there is a conflict when you try produce a pair.
Your base case should be (0,0), not 0, since it must be a pair.
You also need to deconstruct the result from the recursion since that produces a pair, not an integer.
Like this
fun sumPairs nil = (0, 0)
| sumPairs ((x,y)::zs) =
let
val (sumFirst, sumSecond) = sumPairs zs
in
(x + sumFirst, y + sumSecond)
end;
Related
The Binary Tree Maximum Path problem can be solved in using DFS.
Here is a possible solution using this approach in Python.
def maxPathSum(self, root):
def maxSum(root):
if not root:
return 0
l_sum = maxSum(root.left)
r_sum = maxSum(root.right)
l = max(0, l_sum)
r = max(0, r_sum)
res[0] = max(res[0], root.val + l + r)
return root.val + max(l, r)
res = [-float('inf')]
maxSum(root)
return res[0]
I am trying to use the same approach in Erlang. Assuming a node would look like:
{Value, Left, Right}
I came up with:
max_sum(undefined) -> 0;
max_sum({Value, Left, Right}) ->
LeftSum = max(0, max_sum(Left)),
RightSum = max(0, max_sum(Right)),
%% Where to store the max? Should I use the process dictionary?
%% Should I send a message?
Value + max(LeftSum, RightSum).
max_path_sum(Root) ->
%% Bonus question: how to represent -infinity in Erlang?
max_sum(Root)
There are no global variables in Erlang. How can I keep track of the maximum during DFS? The only things that come to my mind are to use the process dictionary or an ETS table or maybe have a different process that can keep the maximum, but maybe I am overthinking and there is a more simple and idiomatic way?
The most "erlangish" way would be to pass the global maximum as a second parameter, and return it along with the local maximum:
max_sum(undefined, GlobalMax) -> {0, GlobalMax};
max_sum({Value, Left, Right}, GlobalMax0) ->
{LeftSum, GlobalMax1} = max(0, max_sum(Left, GlobalMax0)),
{RightSum, GlobalMax2} = max(0, max_sum(Right, GlobalMax1)),
NewGlobalMax =
case GlobalMax2 of
undefined ->
Value + LeftSum + RightSum
_ ->
max(GlobalMax2, Value + LeftSum + RightSum)
end,
{Value + max(LeftSum, RightSum), NewGlobalMax}.
max_path_sum(Root) ->
{_, GlobalMax} = max_sum(Root, undefined),
GlobalMax.
Erlang doesn't support infinity values in floats, so I used the atom undefined to represent a smallest value instead.
If I have two unknown values, lets say x and y, what is the best way loop through all of the values between between those values?
For example, given the values x = 0 and y = 5 I would like to do something with the values 0, 1, 2, 3, 4, and 5. The result could exclude 0 and 5 if this is simpler.
Using Swift's Range operator, I could do something like this:
for i in x...y {
// Do something with i
}
Except I do not know if x or y is the greater value.
The Swift documentation for Range Operators states:
The closed range operator (a...b) defines a range that runs from a to b, and includes the values a and b. The value of a must not be greater than b.
There are a number of solutions here. A pretty straight forward one is:
let diff = y - x
for i in 0...abs(diff) {
let value = min(x, y) + i
// Do something with value
}
Is there a better, or more elegant way to achieve this?
I guess the most explicit way of writing it would be:
for i in min(a, b)...max(a, b) {
// Do something with i
}
To exclude the first and last value, you can increment your lower limit and use the Swift ..< syntax:
let lowerLimit = min(a, b) + 1
let upperLimit = max(a, b)
for i in lowerLimit..<upperLimit {
// Do something with i
}
I can't understand why this one works:
var arr = [4,5,6,7]
arr.map() {
x in
return x + 2
}
while this one not
arr.map() {
x in
var y = x + 2
return y
}
with error
Playground execution failed: MyPlayground.playground:13:5: error:
cannot invoke 'map' with an argument list of type '((_) -> _)'
arr.map() {
The problem here is there error message. In general, when you see something like cannot invoke .. with ... it means that the compiler's type inference has just not worked.
In this case, you've run up against one of the limitations of inference within closures. Swift can infer the type of single-statement closures only, not multiple-statement ones. In your first example:
arr.map() {
x in
return x + 2
}
There's actually only one statement: return x + 2. However, in the second:
arr.map() {
x in
var y = x + 2
return y
}
There's an assignment statement (var y = x + 2), and then the return. So the error is a little misleading: it doesn't mean you "can't invoke map() with this type of argument", what it means to say is "I can't figure out what type x or y is".
By the way, in single-statement closures, there are two other things that can be inferred. The return statement:
arr.map() {
x in
x + 2
}
And the variable name itself:
arr.map() { $0 + 2 }
It all produces the same compiled code, though. So it's really a matter of taste which one you choose. (For instance, while I think the inferred return looks clean and easier to read, I don't like the $0, so I generally always put x in or something, even for very short closures. It's up to you, though, obviously.)
One final thing: since this is all really just syntax stuff, it's worth noting that the () isn't needed either:
arr.map { x in x + 2 }
As #MartinR pointed out, the compiler can infer some types from outer context as well:
let b: [Int] = arr.map { x in
var y = x + 2
return y
}
Which is worth bearing in mind. (it seems that the "one-statement" rule only applies when there's no other type info available)
Swift can't infer type every time. Even though it should see that y = x + 2 means y is an Int too. My guess is that Swift parses the closure in a certain order that makes it not aware of the return type ahead of time in your case.
This works:
arr.map() {
x -> Int in
var y = x + 2
return y
}
I am very green when it comes to F#, and I have run across a small issue dealing with recursive functions that I was hoping could help me understand.
I have a function that is supposed to spit out the next even number:
let rec nextEven(x) =
let y = x + 1
if y % 2 = 0 then y
else nextEven y
// This never returns..
nextEven 3;;
I use the 'rec' keyword so that it will be recursive, although when I use it, it will just run in an endless loop for some reason. If I rewrite the function like this:
let nextEven(x) =
let y = x + 1
if y % 2 = 0 then y
else nextEven y
Then everything works fine (no rec keyword). For some reason I though I needed 'rec' since the function is recursive (so why don't I?) and why does the first version of the function run forever ?
EDIT
Turns out this was a total noob mistake. I had created multiple definitions of the function along the way, as is explained in the comments + answers.
I suspect you have multiple definitions of nextEven. That's the only explanation for your second example compiling. Repro:
module A =
let rec nextEven(x) =
let y = x + 1
if y % 2 = 0 then y
else nextEven y
open A //the function below will not compile without this
let nextEven(x) =
let y = x + 1
if y % 2 = 0 then y
else nextEven y //calling A.nextEven
Try resetting your FSI session.
I have created the following type using implicit type construction:
open System
type Matrix(sourceMatrix:double[,]) =
let rows = sourceMatrix.GetUpperBound(0) + 1
let cols = sourceMatrix.GetUpperBound(1) + 1
let matrix = Array2D.zeroCreate<double> rows cols
do
for i in 0 .. rows - 1 do
for j in 0 .. cols - 1 do
matrix.[i,j] <- sourceMatrix.[i,j]
//Properties
///The number of Rows in this Matrix.
member this.Rows = rows
///The number of Columns in this Matrix.
member this.Cols = cols
///Indexed Property for this matrix.
member this.Item
with get(x, y) = matrix.[x, y]
and set(x, y) value =
this.Validate(x,y)
matrix.[x, y] <- value
//Methods
/// Validate that the specified row and column are inside of the range of the matrix.
member this.Validate(row, col) =
if(row >= this.Rows || row < 0) then raise (new ArgumentOutOfRangeException("row is out of range"))
if(col >= this.Cols || col < 0) then raise (new ArgumentOutOfRangeException("column is out of range"))
However now I need to add the following overloaded constructor to this type (which is in C# here):
public Matrix(int rows, int cols)
{
this.matrix = new double[rows, cols];
}
The problem that I have is that it seems any overloaded constructors in an implicit type must have a parameter list that is a subset of the first constructor. Obviously the constructor I want to add does not meet this requirement. Is there any way to do this using implicit type construction? Which way should I do this? I'm pretty new to F# so if you could show the whole type with your changes in it I would greatly appreciate it.
Thanks in advance,
Bob
P.S. If you have any other suggestions to make my class more in the functional style please feel free to comment on that as well.
I would probably just do this:
type Matrix(sourceMatrix:double[,]) =
let matrix = Array2D.copy sourceMatrix
let rows = (matrix.GetUpperBound 0) + 1
let cols = (matrix.GetUpperBound 1) + 1
new(rows, cols) = Matrix( Array2D.zeroCreate rows cols )
unless we are talking about very large arrays which are created very often (i.e. copying the empty array becomes a performance bottleneck).
If you want to emulate the C# version, you need an explicit field that can be accessed from both constructors, like so:
type Matrix(rows,cols) as this =
[<DefaultValue>]
val mutable matrix : double[,]
do this.matrix <- Array2D.zeroCreate rows cols
new(source:double[,]) as this =
let rows = source.GetUpperBound(0) + 1
let cols = source.GetUpperBound(1) + 1
Matrix(rows, cols)
then
for i in 0 .. rows - 1 do
for j in 0 .. cols - 1 do
this.matrix.[i,j] <- source.[i,j]
BTW, there is also a matrix type in the F# PowerPack.