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 = 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++
// 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 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
# 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
Time complexity: O(1)
Auxiliary space: O(1)
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