The largest magnitude of integers is limited, so we are not able to add 18,274,3

Question

The largest magnitude of integers is limited, so we are not able to add 18,274,364,583,929,273,748,459,595,684,373 and 8,129,498,165,026,026,350,236(1)(notation),since integer variables cannot hold such large values, let alone their sum. The program can be solved if we treat these numbers as sequences of numerals, store the numbers corresponding to these numerals on two stacks, and then perform addition by popping numbers from the stacks. The pseudocode for this algorithm is:

addingLargeNumebrs():

   read the numerals of the first number and store them on one stack;

   read the numerals of the second numbers and store them on another stack;?result = 0;

   while at least one stack is not empty;pop a number from each non-empty stack and add them to result;

   store carry in result;push carry on the result stack if it is not zero;

   pop numbers from the result stack and display them

Write a modular C++ program to perform the four basic arithmetic operations, +,-, X, and / on very large integers; the result of division should also be an integer. Use the std::stack template class in design.

Apply these operations to compute the following:

   1) 123(45) ( to the 45th)

   2) The hundredth number in the sequence(1*2(to the 1st) + 3),(2*3(to the 2nd)+4),(3*4(to the 3rd) + 5),......

Explanation / Answer

ANS:-

PROGRAM:-

/*
* largeNumbers.cpp
*
* Created on: 19-Mar-2017
* Author: kasturi
*/

#include <iostream>
#include <vector>

using namespace std;
void addLargeNumbers(const char *pNum1, const char *pNum2);

int main()
{
   addLargeNumbers("134567892", "7634956");
   addLargeNumbers("235682760926", "1824986235");
   addLargeNumbers("99999999999923", "888888888888843");
   return 0;
}

void addLargeNumbers(const char *pNum1, const char *pNum2)
{
   vector<int> v1, v2, resultStack;
   int result = 0, counter=0;
   if(strlen(pNum1) > strlen(pNum2))
   {
       counter = strlen(pNum1);
       for(int i=strlen(pNum2); i<counter; i++)
           v2.push_back(0);
   }
   else if(strlen(pNum2) > strlen(pNum1))
   {
       counter = strlen(pNum2);
       for(int i=strlen(pNum1); i<counter; i++)
           v1.push_back(0);
   }
   else
       counter = strlen(pNum1);
   for(int i=0; i<strlen(pNum1); i++)
   {
       v1.push_back(pNum1[i] - '0');
   }
   for(int i=0; i<strlen(pNum2); i++)
   {
       v2.push_back(pNum2[i] - '0');
   }
   while(!v1.empty() && !v2.empty())
   {
       //cout<<v1[counter-1]<<" "<<v2[counter-1]<<endl;
       result += v1[counter-1]+ v2[counter-1];
       resultStack.push_back(result%10);
       result = result/10;
       v1.pop_back();
       v2.pop_back();
       counter--;
   }
   if(result > 0)
       resultStack.push_back(result);
   cout<<"Adding "<<pNum1<< " and "<<pNum2<<endl;
   cout<<"Result: ";
   for(int i=resultStack.size()-1; i>=0; i--)
   {
       cout<<resultStack[i];
   }
   cout<<endl<<endl;
}

OUTPUT:

Adding 134567892 and 7634956

Result: 142202848

Adding 235682760926 and 1824986235

Result: 237507747161

Adding 99999999999923 and 888888888888843

Result: 988888888888766

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