Can't increase range of numbers in a program in C++ - c++

Question

Here is the question:
Comparing two numbers written in index form like 2^11 and 3^7 is not difficult, as any calculator would confirm that 2^11=2048<3^7=2187.
However, confirming that 632382^518061>519432^525806 would be much more difficult, as both numbers contain over three million digits.
You are given N base exponent pairs, each forming a large number you have to find the Kth smallest number of them. K is 1−indexed.
Input Format
First line containts an integer N, number of base exponent pairs. Followed by N lines each have two space separated integers B and E, representing base and exponent.
Last line contains an integer K, where K<=N
Constraints
1≤N≤105
1≤K≤N
1≤B≤109
1≤E≤109
No two numbers are equal.
Here is my code:
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
int N,i = 0,k,j=0,x,m;
long long int *arr,*arr2,*arr3;
cin >> N;
arr = (long long int *)malloc(sizeof(long long int)*2*N);
arr2 = (long long int *)calloc(N,sizeof(long long int));
arr3 = (long long int *)calloc(N,sizeof(long long int));
x = 2*N;
while(x>0)
{
cin >> arr[i];
i++;
x--;
}
cin >> k;
for(i=0;i<2*N;i+=2)
{
arr2[j] = pow(arr[i],arr[i+1]);
j++;
}
arr3 = arr2;
sort(arr2,arr2+N);
for(i=0;i<N;i++)
{
if(arr3[i] == arr2[k-1])
{
m = i;
break;
}
}
cout << arr[2*m] << " " << arr[2*m + 1];
return 0;
}
The program works for small numbers only, can't make it work for large numbers. what to do?

Answer 1

Maybe you are generating an overflow on the big numbers. You could consider using a multiprecision arithmetic library such as https://gmplib.org/. I haven't used this library myself.
Have a look at this post How to detect integer overflow? on how to detect integer overflow.

Answer 2

From your choosing of long long int type I guess you calculated the a^b of the numbers in order to sort them, which leads to very big numbers and may lead to overflow.
Note that in order to sort the numbers there is no need for this calculation, for knowing if a^b > d^c it is sufficient to check log(a^b) > log(c^d) and therefore b*log(a) > d*log(c).
And it's better to use a struct or class to create a data structure for this big numbers.
This is the code for it:
#include <iostream>
#include <algorithm>
#include <math.h>
using namespace std;
struct BigNumber{
int base;
int exponent;
};
int Compare(BigNumber x, BigNumber y);
void Sort(BigNumber* arr, int N);
int main() {
int N,i = 0,k;
BigNumber *numbers;
cout<<"\nEnter N:";
cin >> N;
numbers = (BigNumber *)calloc(N,sizeof(BigNumber));
for(i=0; i<N; i++)
{
cout<<"\nEnter base and exponent for number "<<i<<":";
cin >> numbers[i].base>>numbers[i].exponent;
}
cout<<"\nEnter K:";
cin >> k;
Sort(numbers,N);
cout << "Kth number is :" << numbers[k].base << "^" << numbers[k].exponent;
return 0;
}
void Sort(BigNumber* arr, int N){
for(int i=0; i< N; i++ ){
for(int j=0; j< N; j++){
if(Compare(arr[i], arr[j])<0){
BigNumber temp = arr[j];
arr[j] = arr[i];
arr[i] = arr[j];
}
}
}
}
int Compare(BigNumber x, BigNumber y){
double X = x.exponent * log10(x.base);
double Y = y.exponent * log10(x.base);
return X == Y? 0: X > Y ? 1: -1;
}

Answer 3

I changed the code a little. Only problem I was having was I was calculating the exponent rather than comparing log of exponent.
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
int N,i = 0,k,j=0,x,m;
int *arr;
double *arr2,*arr3;
cin >> N;
arr = (int *)malloc(sizeof(int)*2*N);
arr2 = (double *)calloc(N,sizeof(double));
arr3 = (double *)calloc(N,sizeof(double));
x = 2*N;
while(x>0)
{
cin >> arr[i];
i++;
x--;
}
cin >> k;
for(i=0;i<2*N;i+=2)
{
arr2[j] = arr[i+1]*log10(arr[i]);
j++;
}
for (i = 0; i < N; i++) {
arr3[i] = arr2[i];
}
sort(arr2,arr2+N);
for(i=0;i<N;i++)
{
if(arr3[i] == arr2[k-1])
{
m = i;
break;
}
}
cout << arr[2*m] << " " << arr[2*m + 1];
return 0;
}