Fibonacci Number

Problem

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

Solution

/**
 * @param {number} n
 * @return {number}
 */
var fib = function(n) {
    let dp = Array(n >= 2 ? n + 1 : 2).fill(null);
    dp[0] = 0;
    dp[1] = 1;
    for (let i = 2; i <= n; ++i) {
        dp[i] = dp[i - 1] + dp[i - 2];
    }
    return dp[n];
};

We will implement a DP solution. Let dp[i] be the value of F(i).

For the base case, if i = 0 or i = 1, then dp[0] = 0 and dp[1] = 1 by definition.
For the recursive case, dp[i] = dp[i - 1] + dp[i - 2] by definition.

Problem​

Solution​

Problem

Solution