Champernowne's Constant - Project Euler Problem 40

Problem

An irrational decimal fraction is created by concatenating the positive integers:

0.12345678910
It can be seen that the 12^th digit of the fractional part is 1.

If d_n represents the n^th digit of the fractional part, find the value of the following expression.

d₁ x d₁₀ x d₁₀₀ x d₁₀₀₀ x d₁₀₀₀₀ x d₁₀₀₀₀₀ x d_1000000
Original Problem Source


Solution

 //speed depends on using StringBuilder, non-idiomatic since it is mutable  
 let rec NumArray start max maxLength (numString:System.Text.StringBuilder) =   
             if start = max || numString.Length >= maxLength then  
               numString.Append(start.ToString())  
             else  
               let newString = numString.Append(start.ToString())  
               let nextNum = start + 1  
               NumArray nextNum max maxLength newString  
   
 //cast string to int  
 let convertStringToInt32 (value:string) =   
   let mutable result = 0  
   let found = System.Int32.TryParse(value, &result)  
   result  
   
 //test for conversion  
 //let test_conversion = convertStringToInt32("1")  
   
 //starts timer  
 let startChampernowne = System.DateTime.Now  
   
 //create string builder and initialize it  
 let numStringStart = new System.Text.StringBuilder()  
 let startString = numStringStart.Append(".")  
   
 //variety of tests  
 //let test_numArray = NumArray 1 100 100000 numStringStart  
 //let test_stringPosition1 = test_numArray.Chars(0)  
 //let test_stringPosition10 = test_numArray.Chars(9)  
 //let test_stringPosition100 = test_numArray.Chars(99)  
 //let test_stringPosition12 = test_numArray.Chars(11)  
   
 //Create Champernowne's constant nd convert to string  
 let GetNumArray = NumArray 1 1000000 1000000 startString  
 let NumArrayToString = GetNumArray.ToString()  
   
 //find solution  
 let ProdOfValues =   
   convertStringToInt32(NumArrayToString.Chars(1).ToString())  
    * convertStringToInt32(NumArrayToString.Chars(10).ToString())  
    * convertStringToInt32(NumArrayToString.Chars(100).ToString())  
     * convertStringToInt32(NumArrayToString.Chars(1000).ToString())  
     * convertStringToInt32(NumArrayToString.Chars(10000).ToString())  
      * convertStringToInt32(NumArrayToString.Chars(100000).ToString())  
      * convertStringToInt32(NumArrayToString.Chars(1000000).ToString())  
   
 //end times  
 printfn "%s" ((System.DateTime.Now - startChampernowne).ToString())