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Find the larger exponential among two exponentials
  • Difficulty Level : Hard
  • Last Updated : 10 May, 2021

Given four integers A, B, C and D. The task is to find which is greater AB or CD.

Examples: 

Input: A = 2, B = 5, C = 4, D = 2 
Output: 2^5 
25 = 32 
42 = 16

Input: A = 8, B = 29, C = 60, D = 59 
Output: 60^59 
 

Naive approach: Calculate the values of AB and CD then compare them. This approach will fail when the values are greater say 562145321457.



Efficient approach: Using log, we can write the terms as log(AB) and log(CD) which can also be written as B * log(A) and D * log(C). These values are easier to calculate and compare than the original values.

Below is the implementation of the above approach:  

C++




// C++ implementation of the approach
 
#include<bits/stdc++.h>
using namespace std;
 
// Function to find whether a^b is greater or c^d
void compareValues(int a, int b, int c, int d)
{
 
    // Find b * log(a)
    double log1 = log10(a);
    double num1 = log1 * b;
 
    // Find d * log(c)
    double log2 = log10(c);
    double num2 = log2 * d;
 
    // Compare both values
    if (num1 > num2)
        cout << a  << "^"  <<  b;
    else
        cout << c << "^" << d;
}
 
// Driver code
int main ()
{
    int a = 8, b = 29, c = 60, d = 59;
    compareValues(a, b, c, d);
}
 
 
// This code is contributed by ihritik

Java




// Java implementation of the approach
class GFG {
 
    // Function to find whether a^b is greater or c^d
    static void compareValues(int a, int b, int c, int d)
    {
 
        // Find b * log(a)
        double log1 = Math.log10(a);
        double num1 = log1 * b;
 
        // Find d * log(c)
        double log2 = Math.log10(c);
        double num2 = log2 * d;
 
        // Compare both values
        if (num1 > num2)
            System.out.println(a + "^" + b);
        else
            System.out.println(c + "^" + d);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a = 8, b = 29, c = 60, d = 59;
        compareValues(a, b, c, d);
    }
}

Python3




# Python3 implementation of the approach
import math
 
# Function to find whether
# a^b is greater or c^d
def compareValues(a, b, c, d):
# Find b * log(a)
    log1 = math.log10(a)
    num1 = log1 * b
 
    # Find d * log(c)
    log2 = math.log10(c)
    num2 = log2 * d
 
    # Compare both values
    if num1 > num2 :
        print(a, '^', b)
    else :
        print(c, '^', d)
 
# Driver code
a = 8
b = 29
c = 60
d = 59
 
# Function call
compareValues(a, b, c, d)
 
# This code is contributed by nidhiva

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
    // Function to find whether
    // a^b is greater or c^d
    static void compareValues(int a, int b,
                              int c, int d)
    {
 
        // Find b * log(a)
        double log1 = Math.Log10(a);
        double num1 = log1 * b;
 
        // Find d * log(c)
        double log2 = Math.Log10(c);
        double num2 = log2 * d;
 
        // Compare both values
        if (num1 > num2)
            Console.WriteLine(a + "^" + b);
        else
            Console.WriteLine(c + "^" + d);
    }
 
    // Driver code
    public static void Main ()
    {
        int a = 8, b = 29, c = 60, d = 59;
        compareValues(a, b, c, d);
    }
}
 
// This code is contributed by ihritik

Javascript




<script>
 
// Javascript implementation of the approach
 
// Function to find whether a^b is greater or c^d
function compareValues(a, b, c, d)
{
 
    // Find b * log(a)
    let log1 = Math.log(a) / Math.log(10);
    let num1 = log1 * b;
 
    // Find d * log(c)
    let log2 = Math.log(c) / Math.log(10);
    let num2 = log2 * d;
 
    // Compare both values
    if (num1 > num2)
        document.write(a + "^" + b);
    else
        document.write(c + "^" + d);
}
 
// Driver code
let a = 8, b = 29, c = 60, d = 59;
compareValues(a, b, c, d);
 
// This code is contributed by souravmahato348
 
</script>
Output: 
60^59

 

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