Find Minimum Value to Assign All Array Elements for Greater Product in C++

Suppose we have an array of n elements. Update all elements of the given array to some min value x, such that arr[i] = x. Such that product of all elements in the new array is strictly greater than the product of all elements of the initial array, where i <= arr[i] <= 10^10, and 1 <= n <= 10^5. So if the array is like [4, 2, 1, 10, 6]. So 4 is the smallest element. 4 * 4 * 4 * 4 * 4 > 4 * 2 * 1 * 10 * 6

As we know that the product of n elements is P. If we have to find nth root of P, to find the nth root of product, we simply divide n from sum of log of n elements of the array and then the ceiling of antilog will be the result.

res = ceil(antilog(log(x) / 10))

or res = ceil(10 ^ (log(x) / 10))

Example

 Live Demo

#include <iostream>
#include <cmath>
#define EPS 1e-15
using namespace std;
long long findMinValue(long long arr[], long long n) {
   long double sum = 0;
   for (int i=0; i<n; i++)
   sum += (long double)log10(arr[i])+EPS;
   long double xl = (long double)(sum/n+EPS);
   long double res = pow((long double)10.0, (long double)xl) + EPS;
   return (long long)ceil(res+EPS);
}
int main() {
   long long arr[] = {4, 2, 1, 10, 6};
   long long n = sizeof(arr)/sizeof(arr[0]);
   cout << "Min value is: "<< findMinValue(arr, n);
}

Output

Min value is: 4