open System.Collections
open System.Collections.Generic
open System.Text.RegularExpressions

type Token =
    | Num of float
    | Plus
    | Minus
    | Star
    | Hat
    | Sqrt
    | Slash
    | Negative
    | RParen
    | LParen

let hasAny (list: Stack<'T>) =
    list.Count <> 0

let tokenize (input:string) =
    let tokens = new Stack<Token>()
    let push tok = tokens.Push tok
    let regex = new Regex(@"[0-9]+(.+d*)?|+|-|*|/|^|)|(|pi|e|sqrt")
    for x in regex.Matches(input.ToLower()) do
        match x.Value with
        | "+" -> push Plus
        | "*" -> push Star
        | "/" -> push Slash
        | ")" -> push LParen
        | "(" -> push RParen
        | "^" -> push Hat
        | "sqrt" -> push Sqrt
        | "pi" -> push (Num System.Math.PI)
        | "e" -> push (Num System.Math.E)
        | "-" ->
            if tokens |> hasAny then
                match tokens.Peek() with
                | LParen -> push Minus
                | Num v -> push Minus
                | _ -> push Negative
            else
                push Negative

        | value -> push (Num (float value))
    tokens.ToArray() |> Array.rev |> Array.toList



let isUnary = function
    | Negative | Sqrt -> true
    | _ -> false


let prec = function
    | Hat -> 3
    | Star | Slash -> 2
    | Plus | Minus -> 1
    | _ -> 0



let toRPN src =
    let output = new ResizeArray<Token>()
    let stack = new Stack<Token>()
    let rec loop = function
        | Num v::tokens ->
            output.Add(Num v)
            loop tokens
        | RParen::tokens ->
            stack.Push RParen
            loop tokens
        | LParen::tokens ->
            while stack.Peek() <> RParen do
                output.Add(stack.Pop())
            stack.Pop() |> ignore // pop the "("
            loop tokens
        | op::tokens when op |> isUnary ->
            stack.Push op
            loop tokens
        | op::tokens ->
            if stack |> hasAny then
                if prec(stack.Peek()) >= prec op then
                    output.Add(stack.Pop())
            stack.Push op
            loop tokens
        | [] ->
            output.AddRange(stack.ToArray())
            output
    (loop src).ToArray()

let (@) op tok =
    match tok with
    | Num v ->
        match op with
        | Sqrt -> Num (sqrt v)
        | Negative -> Num (v * -1.0)
        | _ -> failwith "input error"
    | _ -> failwith "input error"

let (@@) op toks =
    match toks with
    | Num v,Num u ->
        match op with
        | Plus -> Num(v + u)
        | Minus -> Num(v - u)
        | Star -> Num(v * u)
        | Slash -> Num(u / v)
        | Hat -> Num(u ** v)
        | _ -> failwith "input error"
    | _ -> failwith "inpur error"


let evalRPN src =
    let stack = new Stack<Token>()
    let rec loop = function
        | Num v::tokens ->
            stack.Push(Num v)
            loop tokens
        | op::tokens when op |> isUnary ->
            let result = op @ stack.Pop()
            stack.Push result
            loop tokens
        | op::tokens ->
            let result = op @@ (stack.Pop(),stack.Pop())
            stack.Push result
            loop tokens
        | [] -> stack
    if loop src |> hasAny then
        match stack.Pop() with
        | Num v -> v
        | _ -> failwith "input error"
    else failwith "input error"

let eval input =
    input |> (tokenize >> toRPN >> Array.toList >> evalRPN)