find Nth digit of n

Author: jackzhenguo

Math/.vs/Math/v15/.suo

@@ -10,16 +10,16 @@
 
 namespace Math.Lib
 {
-    Write an algorithm to determine if a number is "happy".
+//    Write an algorithm to determine if a number is "happy".
 
-A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.
+//A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.
 
-Example: 19 is a happy number
+//Example: 19 is a happy number
 
-1^2 + 9^2 = 82
-8^2 + 2^2 = 68
-6^2 + 8^2 = 100
-1^2 + 0^2 + 0^2 = 1
+//1^2 + 9^2 = 82
+//8^2 + 2^2 = 68
+//6^2 + 8^2 = 100
+//1^2 + 0^2 + 0^2 = 1
 public class HappyNumberSln {
     public bool IsHappy(int n) {
         int slow =n, fast = n;

Math/Math.Lib/HappyNumber.cs

@@ -40,10 +40,19 @@
     <Reference Include="System.Xml" />
   </ItemGroup>
   <ItemGroup>
+    <Compile Include="AddStringsSln.cs" />
+    <Compile Include="HappyNumber.cs" />
+    <Compile Include="MinimumMovesSln.cs" />
     <Compile Include="MissingNumberSln.cs" />
+    <Compile Include="Nthdigit.cs" />
     <Compile Include="PerfectNumberSln.cs" />
     <Compile Include="PowerOfTwoSln.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
+    <Compile Include="ReverseIntegarSln - Copy.cs" />
+    <Compile Include="ReverseIntegarSln.cs" />
+  </ItemGroup>
+  <ItemGroup>
+    <Content Include="Floyd%27sTortoiseandHare.jpg" />
   </ItemGroup>
   <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
   <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 

Math/Math.Lib/Math.Lib.csproj

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="12.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup>
+    <ProjectView>ShowAllFiles</ProjectView>
+  </PropertyGroup>
+</Project>

Math/Math.Lib/Math.Lib.csproj.user

@@ -0,0 +1,56 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+namespace Math.Lib
+{
+    //    Find the nth digit of the infinite integer sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...
+
+    //Note:
+    //n is positive and will fit within the range of a 32-bit signed integer (n < 231).
+
+    //Example 1:
+
+    //Input:
+    //3
+
+    //Output:
+    //3
+    //Example 2:
+
+    //Input:
+    //11
+
+    //Output:
+    //0
+
+    //Explanation:
+    //The 11th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is a 0, which is part of the number 10.
+    public class Nthdigit
+    {
+        //for this issue, there are two different ways to decribe a number
+        //1 element. this is our common way
+        //2 Nth digit. this is a new way
+        public int FindNthDigit(int n)
+        {
+            long bas = 9;
+            int digits = 1, i = 0;
+            //first: getting n which digit is in
+            while (n > bas * digits) // prevent overflowing. Since bas is long, so result of bas*digits is auto imporved as long
+            {
+                n -= (int)(bas * (digits++)); //nth
+                i += (int)bas; //number of pasted elements
+                bas *= 10; //1 digit->9; 2 digits->90; 3 digits->900, ...   
+            }
+            //second: Nth digit ->element
+            //in all numbers containing digits, pasted numbers
+            int pasted = (int)((n - 1) / digits);
+            int element = pasted + i + 1;
+            //third: once getting the element Nth digits stands,
+            //(n-1)%digits of element is solution
+            int nth = (n - 1) % digits;
+            return element.ToString()[nth] - '0';
+        }
+    }
+}

Math/Math.Lib/Nthdigit.cs

@@ -0,0 +1,57 @@
+/* ==============================================================================
+ * 功能描述：ReverseIntegarSln  
+ * 创 建 者：gz
+ * 创建日期：2017/5/18 13:05:38
+ * ==============================================================================*/
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+//Reverse digits of an integer.
+
+//Example1: x = 123, return 321
+//Example2: x = -123, return -321
+//Note: 
+//The input is assumed to be a 32-bit signed integer. Your function should return 0 when the reversed integer overflows.
+namespace lt
+{
+    /// <summary>
+    /// ReverseIntegarSln
+    /// </summary>
+    public class ReverseIntegarSln
+    {
+        public  int Reverse(int x)
+        {
+            bool isNegative = x < 0;
+            long rtn = 0;
+            while (x != 0)
+            {
+                int postBit = x % 10;
+                long iterval = rtn * 10 + postBit;
+                if (isNegative && iterval < -2147483648) return 0;
+                if (iterval > 2147483647) return 0;
+                rtn = iterval;
+                x /= 10;
+            }
+            return (int)rtn;
+        }
+
+        public  int Reverse2(int x)
+        {
+            int rtn = 0;
+
+            while (x != 0)
+            {
+                int postBit = x % 10;
+                int iterval = rtn * 10 + postBit; //if happens overflow, result != (newResult - post)/10
+                if ((iterval - postBit) / 10 != rtn) //solve the overflow
+                {
+                    return 0;
+                }
+                rtn = iterval;
+                x = x / 10;
+            }
+            return rtn;
+        }
+    }
+}

Math/Math.Lib/ReverseIntegarSln - Copy.cs

@@ -13,7 +13,7 @@
 //Example2: x = -123, return -321
 //Note: 
 //The input is assumed to be a 32-bit signed integer. Your function should return 0 when the reversed integer overflows.
-namespace lt
+namespace Math.Lib
 {
     /// <summary>
     /// ReverseIntegarSln

Math/Math.Lib/ReverseIntegarSln.cs

@@ -46,6 +46,12 @@
     <Compile Include="Program.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
   </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="..\Math.Lib\Math.Lib.csproj">
+      <Project>{8b0938a8-8d54-4ad6-8717-3ec40291a67f}</Project>
+      <Name>Math.Lib</Name>
+    </ProjectReference>
+  </ItemGroup>
   <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
   <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 
        Other similar extension points exist, see Microsoft.Common.targets.

Math/Math.v12.suo

@@ -1,4 +1,5 @@
-using System;
+using Math.Lib;
+using System;
 using System.Collections.Generic;
 using System.Linq;
 using System.Text;
@@ -9,6 +10,12 @@ class Program
     {
         static void Main(string[] args)
         {
+            Nthdigit nth = new Nthdigit();
+            if(Int32.MaxValue == 2147483647)
+            {
+                int n = nth.FindNthDigit(2147483647);
+            } 
+            
         }
     }
 }