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Merged
itsvinayak merged 2 commits into from
Dec 20, 2020
Merged

Add extra testcases for Fibonacci and improve code #544

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7751836
Add extra testcases for Fibonacci and improve code
rahul1995 Nov 1, 2020
6e5ce76
Fix typos in Fibonacci.js
rahul1995 Nov 1, 2020
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15 changes: 10 additions & 5 deletions Maths/Fibonacci.js
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Original file line number Diff line number Diff line change
Expand Up @@ -102,14 +102,17 @@ const matrixMultiply = (A, B) => {
return C
}

/**
* Computes A raised to the power n i.e. pow(A, n) where A is a square matrix
* @param {*} A the square matrix
* @param {*} n the exponent
*/
// A is a square matrix
const matrixExpo = (A, n) => {
A = copyMatrix(A)
if (n === 0) return Identity(A.length) // Identity matrix
if (n === 1) return A

// Just like Binary exponentiation mentioned in ./BinaryExponentiationIterative.js
let result = Identity(A.length)
let result = Identity(A.length) // Identity matrix
while (n > 0) {
if (n % 2 !== 0) result = matrixMultiply(result, A)
n = Math.floor(n / 2)
Expand All @@ -127,15 +130,17 @@ const FibonacciMatrixExpo = (n) => {
// | | = | | * | |
// |F(n-1)| |1 0| |F(n-2)|

// F(n, n-1) = pow(A, n-1) * F(1, 0)
// Let's rewrite it as F(n, n-1) = A * F(n-1, n-2)
// or F(n, n-1) = A * A * F(n-2, n-3)
// or F(n, n-1) = pow(A, n-1) * F(1, 0)

if (n === 0) return 0

const A = [
[1, 1],
[1, 0]
]
const poweredA = matrixExpo(A, n - 1) // A raise to the power n
const poweredA = matrixExpo(A, n - 1) // A raised to the power n-1
let F = [
[1],
[0]
Expand Down
5 changes: 5 additions & 0 deletions Maths/test/Fibonacci.test.js
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Expand Up @@ -30,6 +30,11 @@ describe('Fibonanci', () => {
})

it('should return number for FibonnaciMatrixExpo', () => {
expect(FibonacciMatrixExpo(0)).toBe(0)
expect(FibonacciMatrixExpo(1)).toBe(1)
expect(FibonacciMatrixExpo(2)).toBe(1)
expect(FibonacciMatrixExpo(3)).toBe(2)
expect(FibonacciMatrixExpo(4)).toBe(3)
expect(FibonacciMatrixExpo(5)).toBe(5)
})
})