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 = 16Input: 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 the log, we can write the terms 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++ 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 implementation of the approach import java.io.*;
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 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# 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 |
<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> |
60^59
Time complexity: O(1)
Auxiliary space: O(1)