Question

Computer science

Implement these below questions in C++:
1. Given two-bit strings of length n, find the bitwise AND, bitwise OR, and bitwise XOR of these strings.
2. Looking for positive integers that are not the sum of the cubes of nine different positive integers.
3. Given subsets A and B of a set with n elements, use bit strings to find A, A ∪ B, A ∩ B, A − B, and A ⊕ B.
4. Given a finite set, list all elements of its power set.
5. Given an ordered list of n integers and an integer x in the list, find the number of comparisons used to determine the position of x in the list using a linear search and using a binary search.
6. Given a list of n integers, find the first and last occurrences of the largest integer in the list.
7. Given a positive integer, find the prime factorization of this integer.
8. Given two positive integers, find their greatest common divisor using the Euclidean algorithm.
9. Given a square matrix, determine whether it is symmetric.
10. Given a 2n × 2n checkerboard with one square missing, construct a tiling of this checkerboard using right triominoes.

Answer 1

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1)

#include<iostream>
using namespace std;

string BitwiseOR(string* array, int s1)
{
   string r;

   int ssize = min;
   for (int i = 0; i < s1; i++)
   {
       ssize = max(ssize, (int)array[i].size());
       reverse(array[i].begin(), array[i].end());
   }

   for (int i = 0; i < s; i++) {
       string s;
       for (int j = 0; j < ssize - array[i].size(); j++)
           s += '0';

       array[i] = array[i] + s;
   }
   for (int i = 0; i < ssize; i++) {
       int current = 0;
       for (int j = 0; j < s1; j++)
           current = current | (array[j][i] - '0');

       r += (current + '0');
   }
   reverse(r.begin(), r.end());
   return r;
}
int main()
{
   string array[] = { "10", "11", "1000001" };
   int s1 = sizeof(array) / sizeof(array[0]);
   cout << BitwiseOR(array, n);
   return 0;
}

2)

#include <iostream>
using namespace std;
int main()
{
int a, b, lcm;
cout<<" Enter First positive integer="<<endl;
cin>>a;
cout<<"Enter second Positive integer="<<endl;
cin>>b;
if(a>b)
{

lcm = a;
}
else
{

lcm = b;
}
while(1)
{
if( lcm%a==0 && lcm%b==0 )
   {
cout<<"The LCM of "<<a<<" and "<<b<<" is="<<lcm;
break;
}
  
lcm++;
}

return 0;
}

4)

#include <iostream>
#include <cmath>
using namespace std;
void printPowerSet(char *set, int set_size)
{
int pow_set_size = pow(2, set_size);
int j;
for(int i = 0; i < pow_set_size; i++)
{
for(j = 0; j < set_size; j++)
{
if(i & (1 << j))
{
cout << set[j];
}
}
cout << endl;
}
}
int main()

{
char set[] = {'a','b','c'};
printPowerSet(set, 3);
return 0;
}

5)

#include<iostream>
using namespace std;

int BinarySearch(int arr[], int left, int right, int elem)
{
   if (right >= left)
   {
       int mid = left + (right - left) / 2;
               if (arr[mid] == elem)
       {
           return mid;
       }
       if (arr[mid] > elem)
       {
           return BinarySearch(arr, left, mid - 1, elem);
       }
               return BinarySearch(arr, mid + 1, right, elem);
   }
   else
   {
       return -1; // when element is not present in array
   }
}
int LinearSearch(int arr1[], int n, int x)
{
   for (int i = 0; i < n; i++)
   {
       if (arr1[i] == x)
       {
           return i;
       }
   }
       return -1;
}
int main()
{
   int arr[] = { 2, 3, 4, 10, 40 };
   int size = sizeof(arr) / sizeof(arr[0]);
   int elem = 10;
   int result = BinarySearch(arr, 0, size - 1, elem);
   if (result == -1)
   {
       cout << "Element is not present in array";
   }
   else
   {
       cout << "Element is present at index " << result <<endl;
   }
   //Linear Search Calling.
   int arr1[] = { 2, 3, 4, 10, 40 };
   int x = 3;
   int n = sizeof(arr1) / sizeof(arr1[0]);
   int result1 = LinearSearch(arr1, n, x);
   if (result1 == -1)
   {
       cout << "Element is not present in array" <<endl;
   }
   else
   {
       cout << "Element is present at index " << result1 <<endl;
   }
   system("pause");
   return 0;
}

6)

#include<iostream>
#include<string>
using namespace std;

void sorting(int arr[],int size)
{
   int temp;
   for(int i=0;i<size-1;i++)
   {
      
       for(int j=i+1;j<size;j++)
       {
      
           if(arr[i]>arr[j])
           {
               temp=arr[i];
               arr[i]=arr[j];
               arr[j]=temp;
              
           }
       }
   }
  
}

int Max(int arr[],int size)
{
   int max=-999;
   for(int i=0;i<size;i++)
   {
       if(max<arr[i])
       {
           max=arr[i];
       }
   }
  
   return max;
}

int findFirstOccurrence(int arr[], int N, int x)
{
   // search space is arr[low..high]
   int low = 0, high = N - 1;

   // initialize the result by -1
   int result = -1;

   // iterate till search space contains at-least one element
   while (low <= high)
   {
       // find the mid value in the search space and
       // compares it with target value
       int mid = (low + high)/2;

       // if target is found, update the result and
       // go on searching towards left (lower indices)
       if (x == arr[mid])
       {
           result = mid;
           high = mid - 1;
       }

       // if target is less than the mid element, discard right half
       else if (x < arr[mid])
           high = mid - 1;

       // if target is more than the mid element, discard left half
       else
           low = mid + 1;
   }

   // return the leftmost index or -1 if the element is not found
   return result;
}

// Function to find last occurrence of a given number
// in sorted array of integers
int findLastOccurrence(int arr[], int N, int x)
{
   // search space is A[low..high]
   int low = 0, high = N - 1;

   // initialize the result by -1
   int result = -1;

   // iterate till search space contains at-least one element
   while (low <= high)
   {
       // find the mid value in the search space and
       // compares it with target value
       int mid = (low + high)/2;

       // if target is found, update the result and
       // go on searching towards right (higher indices)
       if (x == arr[mid])
       {
           result = mid;
           low = mid + 1;
       }

       // if target is less than the mid element, discard right half
       else if (x < arr[mid])
           high = mid - 1;

       // if target is more than the mid element, discard left half
       else
           low = mid + 1;
   }

   // return the leftmost index or -1 if the element is not found
   return result;
}

int main()
{
   int first;
   int Largest;
   int a[11]={3,2,5,1,4,6,1,5,1,6,6};
   sorting(a,11);
   for(int i=0;i<11;i++)
   {
       cout<<"i="<<i<<endl;
       cout<<a[i]<<endl;
   }
  
   Largest=Max(a,11);
   cout<<"First occurance:"<<findFirstOccurrence(a,11,Largest)<<endl;
   cout<<"Last occurance:"<<findLastOccurrence(a,11,Largest)<<endl;
  
  
  
  
  
}

7)

#include <iostream>
using namespace std;
void factors(int n)
{
int x = 2;
while (x * x <= n)
{
if (n % x == 0)
{   
cout << x<<endl;
n = (n / x);
}
else
{
x++;
}
}
if (n > 1)
{
cout << n << "\n";
}
}
int main()
{
int x;
cout << "Enter a positive integer greater than 1 : "<<endl;
cin >> x;
factors(x);
cout << "The result: " << x;
return 0;
}

8)

#include <iostream>
using namespace std;
int gcd(int a, int b)
{
if (b == 0)
{
        return a;
}
return gcd(b, a % b);
}
int main()
{
int a , b;
cout<<"Enter the values of a: "<<endl;
cin>>a;
cout<<"Enter the value of b:"<<endl;
cin>>b;
cout<<"GCD of "<< a <<" and "<< b <<" is:"<< gcd(a, b)<<endl;
}

9)

#include <iostream>
#include<string>
using namespace std;
  
int main()
{
bool check=true;
cout<<"Enter the number of rows of square matrix"<<endl;
int row;
cin>>row;
cout<<"Enter the number of coloumns"<<endl;
int col;
cin>>col;
int arr[row][col];

cout<<"Enter Elements"<<endl;
for(int i=0;i<row;i++)
{
cout<<"Row#"<<i;
for(int j=0;j<col;j++)
{
cout<<" Col#"<<j<<endl;
cin>>arr[i][j];

}
}

for(int i=0;i<row;i++)
{
for(int j=0;j<col;j++)
{
if(arr[i][j]!=arr[j][i])
{
check=false;

}
}
}

if(check==true)
{
cout<<"This is symmetric"<<endl;
}

else
{
cout<<"This is not symmetric"<<endl;

}

}

10)

#include <iostream>
using namespace std;
int calculatePower(int, int);

int calculatePower(int base, int powerRaised)
{
if (powerRaised != 0)
{
  
return (base*calculatePower(base, powerRaised-1));
}
else
{
  
return 1;
}
}

int main()
{
int base, powerRaised, result;

cout << "Enter base number: ";
cin >> base;

cout << "Enter power number(positive integer): ";
cin >> powerRaised;

result = calculatePower(base, powerRaised);
cout << base << "^" << powerRaised << " = " << result;

return 0;
}

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