Perfect Cubes

For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that aⁿ+bⁿ+cⁿ, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the ``perfect cube'' equation a³=b³+c³+d³ (e.g. a quick calculation will show that the equation 12³=6³+8³+10³ is indeed true). This problem requires that you write a program to find all sets of numbers {a, b, c, d} which satisfy this equation for a<=200.

Output

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

The first part of the output is shown here:

Cube = 6, Triple = (3,4,5)

Cube = 12, Triple = (6,8,10)

Cube = 18, Triple = (2,12,16)

Cube = 18, Triple = (9,12,15)

Cube = 19, Triple = (3,10,18)

Cube = 20, Triple = (7,14,17)

Cube = 24, Triple = (12,16,20)

 

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace Cubes

{

    class Program

    {

        static void Main(string[] args)

        {

            for (int i = 6; i < 200; i++)

            {

                for (int j = 2; j < 200; j++)

                {

                    for (int k = j + 1; k < 200; k++)

                    {

                        for (int l = k + 1; l < 200; l++)

                        {

                            if ((i*i*i) == (j*j*j) + (k*k*k) + (l*l*l))

                            {

                                Console.WriteLine(i +" "+ j +" "+ k +" "+ l);

                            }

                        }

                    }

                }

            }

        }

    }

}

Encoder and Decoder

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace Scores

{

    class Program

    {

        static void Main(string[] args)

        {

            string s = Console.ReadLine();

            if (!char.IsDigit(s[0]))//Encoder Section.

            {

                string s1 = "";

                string s2 = "";

                for (int i = 0; i < s.Length; i++)

                {

                    int ch = s[i];//Retreivimg the ASCII code of ith character.

                    s1 = s1 + ch.ToString();//COnctenating it into a string.

                }

                //Reversing the string of ASCII values.

                for (int i = s1.Length - 1; i >= 0; i--)

                {

                    s2 = s2 + s1[i];

                }

                Console.WriteLine(s2);

            }

            else//Decoder Section.

            {

                string s1 = "";

                string s2 = "";

                //Reversing the input encoded string.

                for (int j = s.Length - 1; j >= 0; j--)

                {

                    s1 = s1 + s[j];

                }

                int i = 0;

                while (i < s1.Length)

                {

                    int count = 0;

                    string s3 = "";

                    while (count < 2)//Taking two digits at a time.

                    {

                        s3 = s3 + s1[i];

                        i++;

                        count++;

                    }

                    count = int.Parse(s3);

                    if (count < 32)//Condition for taking three digits at a time.

                    {

                        s3 = s3 + s1[i];

                        i++;

                        count = int.Parse(s3);

                    }

                    s2 = s2 + char.ConvertFromUtf32(count);//Concatenating the character to the string.

                }

                Console.WriteLine(s2);

            }

        }

    }

}

Inheritance in C#

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace Test_in_cs

{

    class publisher

    {

        String title;

        float price;

        public publisher(String t, float p)

        {

            title = t;

            price = p;

        }

        public void displaydata()

        {

            Console.WriteLine("Title: " + title);

            Console.WriteLine("Price: " + price);

        }

    }

    class book : publisher

    {

        int page;

        public book(String t, float p, int c)

            : base(t, p)//Syntax for declaring a derived class.

        {

            page = c;

        }

        public void display()

        {

            base.displaydata();

            Console.WriteLine("Total pages: " + page);

        }

    }

    class Program

    {

        static void Main(string[] args)

        {

            book b = new book("Let us C#", 180.0f, 475);

            b.display();

        }

    }

}

Static members in C#

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace Test_in_cs

{

    //Class for demonstration of static member.

    class staticdemo

    {

        private static int count;

        private int info;

        public staticdemo()//Constructor.

        {

            count++;//Static member increments with every instantiation.

        }

        public static void num()//Static method.

        {

            Console.WriteLine("Number of objects is: " + count);

        }

        public int setter(int a)

        {

            info = a;

            return info;

        }

    }

    class Program

    {

        static void Main(string[] args)

        {

            Console.Write("Enter the number of objects to be created: ");

            String s = Console.ReadLine();

            int n = int.Parse(s);

            staticdemo[] obj = new staticdemo[n];//Only memory allocation.

            staticdemo.num();

            for (int i = 0; i < n; i++)

            {

                obj[i] = new staticdemo();//Actual instantiation.

                Console.Write("Information in object " + (i+1));

                Console.WriteLine("is " + obj[i].setter(i + 1));

            }

            staticdemo.num();

        }

    }

}

Classes and Objects in C#

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

 

namespace Test_in_cs

{

    class cone

    {

        private float height, radius;

        public cone(float h, float r)

        {

            height = h;

            radius = r;

        }

        public void setdata(float h, float r)

        {

            height = h;

            radius = r;

        }

        public void displaydata()

        {

            Console.WriteLine("Height= " + height);

            Console.WriteLine("Radius= " + radius);

        }

        public void volume()

        {

            float v;

            v = (1 / 3.0f) * 3.14f * radius * radius * height;

            Console.WriteLine("Volume= " + v);

        }

    }

    class Program

    {

        static void Main(string[] args)

        {

            //Class instantiation and member calling.

            cone c1 = new cone(10.0f, 3.5f);

            cone c2 = new cone(20.0f, 6.2f);

            c1.displaydata();

            c1.volume();

            c2.displaydata();

            c2.volume();

            Console.WriteLine("\nData after setting:");

            c1.setdata(100.0f,100.0f);

            c1.displaydata();

            //Class instantiation and member calling.

            Console.Write("Enter the string: ");

            String s2 = Console.ReadLine();

            for (int i = 0; i < s2.Length; i++)

            {

                if (s2[i] == ' ')

                {

                    s2 = s2.Remove(i, 1);

                    s2 = s2.Insert(i,"space");

                }

            }

            Console.WriteLine(s2);

        }

    }

}

Longest Common Subsequence

Given two sequences of characters, print the length of the longest common subsequence of both sequences. For example, the longest common subsequence of the following two sequences:

abcdgh

aedfhr

is adh of length 3.

Input consists of pairs of lines. The first line of a pair contains the first string and the second line contains the second string. Each string is on a separate line and consists of at most 1,000 characters. 

For each subsequent pair of input lines, output a line containing one integer number which satisfies the criteria stated above.

 

Sample input

a1b2c3d4e

zz1yy2xx3ww4vv

abcdgh

aedfhr

abcdefghijklmnopqrstuvwxyz

a0b0c0d0e0f0g0h0i0j0k0l0m0n0o0p0q0r0s0t0u0v0w0x0y0z0

abcdefghijklmnzyxwvutsrqpo

opqrstuvwxyzabcdefghijklmn

 

Output for the sample input

4

3

26

14

#include "stdafx.h"

#include "string.h"

 

int _tmain(int argc, _TCHAR* argv[])

{

      int lena,lenb,i,j,k,ind,maxlen,templen,found;

      char A[100],B[100];

      while(scanf("%s",A))

      {

            maxlen=0;templen=0;found=0;

            scanf("%s",B);

            lena=strlen(A);

            lenb=strlen(B);

            for(i=0;i<lena;i++)

            {

                  ind=-1;j=i;templen=0;

                  while(j<lena)

                  {

                        found=0;

                        for(k=ind+1;k<lenb;k++)

                        {

                              if(A[j]==B[k] && j<lena)

                              {

                                    templen++;

                                    ind=k;

                                    j++;

                                    found=1;

                                    break;

                              }

                        }

                        if(found!=1)

                        {

                              j++;

                        }

                  }

                  if(maxlen<templen)

                  {

                        maxlen=templen;

                  }

            }

            printf("%d\n",maxlen);

      }

      return 0;

}

Big Mod

Calculate
R:=B^P
mod M, meaning remainder R when B raised to the power of P is divided by M.
for large values of B, P, and M using an efficient algorithm.
(That's right, this problem has a time dependency !!!.)

Input

Three integer values (in the order B, P, M) will be read one number per line. B and P are integers in the range 0 to 2147483647 inclusive. M is an integer in the range 1 to 46340 inclusive.

Output

The result of the computation. A single integer.

Sample Input

3
18132
17

17
1765
3

2374859
3029382
36123

Sample Output

13
2
13195

// Big-Mod.cpp : Defines the entry point
for the console application.

//

 

#include "stdafx.h"

int _tmain(int argc, _TCHAR* argv[])
{
                void
bigmod(long int x,long int y,long int z);
                long int B,P,M;
                while(cin>>B)
                {
                                cin>>P;
                                cin>>M;
                                bigmod(B,P,M);
                }
                return 0;
}
void bigmod(long int x,long int y,long int z)
{
                int pow,rem;
                rem=x%z;
                for(pow=1;pow<y;pow++)
                {
                                rem=(rem*(x%z))%z;
                }
                cout<<rem<<endl;
}