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src/main/java/com/thealgorithms/dynamicprogramming/Fibonacci.java
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@ -91,21 +91,22 @@ public class Fibonacci {
res = next;
}
return res;
}
}
/**
* We have only defined the nth Fibonacci number in terms of the two before it. Now, we will look at Binet's formula to calculate the nth Fibonacci number in constant time.
* The Fibonacci terms maintain a ratio called golden ratio denoted by Φ, the Greek character pronounced ‘phi'.
* First, let's look at how the golden ratio is calculated: Φ = ( 1 + √5 )/2 = 1.6180339887...
* Now, let's look at Binet's formula: Sn = Φⁿ–(– Φ⁻ⁿ)/√5
* We first calculate the squareRootof5 and phi and store them in variables. Later, we apply Binet's formula to get the required term.
* Time Complexity will be O(1)
*/
* We have only defined the nth Fibonacci number in terms of the two before it. Now, we will
* look at Binet's formula to calculate the nth Fibonacci number in constant time. The Fibonacci
* terms maintain a ratio called golden ratio denoted by Φ, the Greek character pronounced
* ‘phi'. First, let's look at how the golden ratio is calculated: Φ = ( 1 + √5 )/2
* = 1.6180339887... Now, let's look at Binet's formula: Sn = Φⁿ–(– Φ⁻ⁿ)/√5 We first calculate
* the squareRootof5 and phi and store them in variables. Later, we apply Binet's formula to get
* the required term. Time Complexity will be O(1)
*/
public static int fibBinet(int n) {
double squareRootOf5 = Math.sqrt(5);
double phi = (1 + squareRootOf5)/2;
int nthTerm = (int) ((Math.pow(phi, n) - Math.pow(-phi, -n))/squareRootOf5);
double phi = (1 + squareRootOf5) / 2;
int nthTerm = (int) ((Math.pow(phi, n) - Math.pow(-phi, -n)) / squareRootOf5);
return nthTerm;
}
}