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Find maximum among x^(y^2) or y^(x^2) where x and y are given in C++
In this problem, we are given two values x and y. Our task is to find maximum among x^(y^2) or y^(x^2) where x and y are given.
Let’s take an example to understand the problem,
Input: x = 4, y = 3
Output: 3^(4^2)
Explanation:
x^(y^2) = 4^(3^2) = 4^9 = 262144
y^(x^2) = 3^(4^2) = 3^16 = 43046721
Solution approach
One approach can be to calculate both values and then print the maximum of both. But this method does not work when the values are large.
A simple and easy approach is using natural log (ln) which will be the solution easier.
ln(x^(y^2)) = (y^2) * ln(x)
ln(y^(x^2)) = (x^2) * ln(y)
Here, the values are not directly proportional to x and y. So, let’s divide the values by (x^2)*(y^2). This makes the value,
ln(x^(y^2)) / (x^2)*(y^2) = ln(x) / (x^2)
ln(y^(x^2)) / (x^2)*(y^2) = ln(y)/ (y^2)
These values are inversely proportional to the resulting value.
If x > y, then x^(y^2) < y^(x^2)
Program to illustrate the working of our solution,
Example
#include <iostream>
using namespace std;
bool checkGreaterVal(int x, int y) {
if (x > y)
return false;
else
return true;
}
int main() {
int x = 3;
int y = 5;
cout<<"The greater value is ";
if(checkGreaterVal(x, y))
cout<<x<<"^("<<y<<"^2)";
else
cout<<y<<"^("<<x<<"^2)";
return 0;
}Output
The greater value is 3^(5^2)
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