Given two numbers A and B, the task is to check that A and B are in the golden ratio.
Golden Ratio: Two numbers are said to be in the golden ratio if their ratio is the same as the ratio of the sum of the two numbers to the larger number. Here a > b > 0, Below is the geometric representation of the Golden ratio:
Examples:
Input: A = 1, B = 0.618 Output: Yes Explanation: These two numbers together forms Golden ratio
Input: A = 61.77, B = 38.22 Output Yes Explanation: These two numbers together forms Golden ratio
Approach: The idea is to find two ratios and check that this ratio is equal to the Golden ratio. That is 1.618.
// Here A denotes the larger number
Below is the implementation of the above approach:
C++
// C++ implementation to check // whether two numbers are in // golden ratio with each other #include <bits/stdc++.h>using namespace std;// Function to check that two // numbers are in golden ratio bool checkGoldenRatio(float a, float b){ // Swapping the numbers such // that A contains the maximum // number between these numbers if(a <= b) { float temp = a; a = b; b = temp; } // First Ratio std::stringstream ratio1; ratio1 << std :: fixed << std :: setprecision(3) << (a / b); // Second Ratio std::stringstream ratio2; ratio2 << std :: fixed << std :: setprecision(3) << (a + b) / a; // Condition to check that two // numbers are in golden ratio if((ratio1.str() == ratio2.str()) && ratio1.str() == "1.618") { cout << "Yes" << endl; return true; } else { cout << "No" << endl; return false; }} // Driver codeint main(){ float a = 0.618; float b = 1; // Function Call checkGoldenRatio(a, b); return 0;}// This code is contributed by divyeshrabadiya07 |
Java
// Java implementation to check // whether two numbers are in // golden ratio with each other class GFG{ // Function to check that two // numbers are in golden ratio public static Boolean checkGoldenRatio(float a, float b){ // Swapping the numbers such // that A contains the maximum // number between these numbers if (a <= b) { float temp = a; a = b; b = temp; } // First Ratio String ratio1 = String.format("%.3f", a / b); // Second Ratio String ratio2 = String.format("%.3f", (a + b) / a); // Condition to check that two // numbers are in golden ratio if (ratio1.equals(ratio2) && ratio1.equals("1.618")) { System.out.println("Yes"); return true; } else { System.out.println("No"); return false; }}// Driver code public static void main(String []args){ float a = (float)0.618; float b = 1; // Function Call checkGoldenRatio(a, b);}}// This code is contributed by rag2127 |
Python3
# Python3 implementation to check # whether two numbers are in # golden ratio with each other# Function to check that two # numbers are in golden ratiodef checkGoldenRatio(a, b): # Swapping the numbers such # that A contains the maximum # number between these numbers a, b = max(a, b), min(a, b) # First Ratio ratio1 = round(a/b, 3) # Second Ratio ratio2 = round((a+b)/a, 3) # Condition to check that two # numbers are in golden ratio if ratio1 == ratio2 and\ ratio1 == 1.618: print("Yes") return True else: print("No") return False # Driver Codeif __name__ == "__main__": a = 0.618 b = 1 # Function Call checkGoldenRatio(a, b) |
C#
// C# implementation to check // whether two numbers are in // golden ratio with each other using System;using System.Collections.Generic;class GFG { // Function to check that two // numbers are in golden ratio static bool checkGoldenRatio(float a, float b) { // Swapping the numbers such // that A contains the maximum // number between these numbers if(a <= b) { float temp = a; a = b; b = temp; } // First Ratio string ratio1 = String.Format("{0:0.000}", a / b); // Second Ratio string ratio2 = String.Format("{0:0.000}", (a + b) / a); // Condition to check that two // numbers are in golden ratio if(ratio1 == ratio2 && ratio1 == "1.618") { Console.WriteLine("Yes"); return true; } else { Console.WriteLine("No"); return false; } } // Driver code static void Main() { float a = (float)0.618; float b = 1; // Function Call checkGoldenRatio(a, b); }}// This code is contributed by divyesh072019 |
Javascript
<script>// Javascript implementation to check // whether two numbers are in // golden ratio with each other// Function to check that two // numbers are in golden ratiofunction checkGoldenRatio(a, b){ // Swapping the numbers such // that A contains the maximum // number between these numbers if (a <= b) { let temp = a; a = b; b = temp; } // First Ratio let ratio1 = (a / b).toFixed(3); // Second Ratio let ratio2 = ((a + b) / a).toFixed(3); // Condition to check that two // numbers are in golden ratio if ((ratio1 == ratio2) && ratio1 == "1.618") { document.write("Yes"); return true; } else { document.write("No"); return false; }}// Driver Code let a = 0.618; let b = 1; // Function Call checkGoldenRatio(a, b);</script> |
Output:
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
References: https://en.wikipedia.org/wiki/Golden_ratio
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