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1013. Fibonacci Number

Math Dynamic Programming Recursion Memoization

Problem - Fibonacci Number

Easy

The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,

F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.

Given n, calculate F(n).

 

Example 1:

Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

Example 2:

Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

Example 3:

Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

 

Constraints:

  • 0 <= n <= 30

Solutions

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class Solution:
    def fib(self, n: int) -> int:
        def matrix_mul(a, b):
            return [
                [a[0][0] * b[0][0] + a[0][1] * b[1][0],
                a[0][0] * b[0][1] + a[0][1] * b[1][1]],
                [a[1][0] * b[0][0] + a[1][1] * b[1][0],
                 a[1][0] * b[0][1] + a[1][1] * b[1][1]]
            ]

        def matrix_power(m, power):
            result = [[1, 0], [0, 1]]
            while power:
                if power & 1:
                    result = matrix_mul(result, m)
                m = matrix_mul(m, m)
                power >>= 1
            return result

        if n == 0:
            return 0

        base = [[1, 1], [1, 0]]
        result = matrix_power(base, n - 1)
        return result[0][0]

Submission Stats:

  • Runtime: 26 ms (98.33%)
  • Memory: 18 MB (23.59%)