Problem:
Score : 200 points

Problem Statement

Given is an integer N. Find the number of positive integers less than or equal to N that have an odd number of digits (in base ten without leading zeros).

Constraints

1 \leq N \leq 10^5

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of positive integers less than or equal to N that have an odd number of digits.

Sample Input 1

11

Sample Output 1

9

Among the positive integers less than or equal to 11, nine integers have an odd number of digits: 1, 2, \ldots, 9.

Sample Input 2

136

Sample Output 2

46

In addition to 1, 2, \ldots, 9, another 37 integers also have an odd number of digits: 100, 101, \ldots, 136.

Sample Input 3

100000

Sample Output 3

90909

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

#if true && UTAKA_LOCAL
//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Net.Mime;
using System.Text;

namespace UtakaApp
{
    public partial class Program
    {
        public const string SiteName = "AtCoder";
        public const string ContestName = "abc136";
        public const string ProblemName = "B";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var console = new MyConsole();
            new Program().Solve(System.Console.In, console);
            console.Flush();
#endif
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
        }

        private DigitGetter digitGetter;

        public void Solve(TextReader textReader, IConsole console)
        {
            var cin = new ConsoleInput(textReader);

            int N = cin.ReadInt;

            digitGetter = new DigitGetter(10);

            long count = 0;

            for (int i = 1; i <= N; i++)
            {
                if (digitGetter.GetNumberOfDigits(i) % 2 == 1)
                {
                    count++;
                }
            }

            console.WriteLine(count.ToString());
        }
    }

    public class DigitGetter
    {
        public long B;

        private long[] table;

        public DigitGetter(long b)
        {
            if (b <= 1)
            {
                throw new InvalidOperationException($"bは2以上にする必要があります");
            }

            B = b;

            // table生成

            List<long> list = new List<long>();

            long current = 1;

            list.Add(current);

            // オーバーフローして負になったら終了
            while (true)
            {
                current *= B;

                if (current < 0)
                {
                    break;
                }

                list.Add(current);
            }

            table = list.ToArray();
        }

        /// <summary>
        /// 桁数を求める
        /// </summary>
        /// <param name="a">求める対象</param>
        /// <returns>桁数</returns>
        public int GetNumberOfDigits(long a)
        {
            if (a < 0)
            {
                throw new InvalidOperationException("aが0未満でした");
            }

            if (a == 0)
            {
                return 1;
            }

            /*
            int index = table.GetAtLeastIndex(a, (p, q) =>
            {
                if (p < q) return -1;
                else if (p > q) return 1;
                else return 0;
            });

            return index;
            */

            // base2でも64回なので2分探索しない
            for (int i = 0; i < table.Length; i++)
            {
                if (a < table[i])
                {
                    return i;
                }
            }

            return table.Length;
        }
    }

    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private readonly char _separator = ' ';
        private readonly Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            _separator = separator;
            _stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0)
                {
                    return inputStream.Dequeue();
                }

                var tmp = _stream.ReadLine().Split(_separator);
                for (var i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);

        public string[] ReadStrArray(long N)
        {
            var ret = new string[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = Read;
            }

            return ret;
        }

        public int[] ReadIntArray(long N)
        {
            var ret = new int[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadInt;
            }

            return ret;
        }

        public long[] ReadLongArray(long N)
        {
            var ret = new long[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadLong;
            }

            return ret;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(string str);
        void WriteLine(string str);
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
        }

        public void Flush()
        {
            Console.Out.Flush();
        }

        public void Write(string str)
        {
            Console.Write(str);
        }

        public void WriteLine(string str)
        {
            Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private readonly StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string GetDirectoryPath()
        {
            var problemPart = string.IsNullOrEmpty(Program.ProblemName)
                ? ""
                : $"/{Program.ProblemName}";

            return
                $"{System.Environment.GetFolderPath(Environment.SpecialFolder.UserProfile)}/AlgorithmPrac/{Program.SiteName}/{Program.ContestName}{problemPart}";
        }

        private string GetInputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.in";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.out";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsole();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems()
        {
            var isSuccessAll = true;

            var testCaseNumber = 1;
            while (true)
            {
                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    Console.WriteLine("Success");
                }
                else
                {
                    isSuccessAll = false;
                    Console.WriteLine("Failure *****");
                }

                testCaseNumber++;
            }

            if (isSuccessAll)
            {
                Console.WriteLine("!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}