Find the larger exponential among two exponentials

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++

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// 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

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Java

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// 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);
    }
}

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Python3

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# 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

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C#

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// 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

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Output:

60^59


My Personal Notes arrow_drop_up

A 3rd-year Computer Science and Engineering undergraduate student at IERT, Allahabad with an interest in Programming, Data Science/AI and web development

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Improved By : ihritik, nidhiva



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