1137. N-th Tribonacci Number

Description

The Tribonacci sequence T_n is defined as follows: 

T₀ = 0, T₁ = 1, T₂ = 1, and T_n+3 = T_n + T_n+1 + T_n+2 for n >= 0.

Given n, return the value of T_n.

 

Example 1:

Input: n = 4
Output: 4
Explanation:
T_3 = 0 + 1 + 1 = 2
T_4 = 1 + 1 + 2 = 4

Example 2:

Input: n = 25
Output: 1389537

 

Constraints:

• 0 <= n <= 37
• The answer is guaranteed to fit within a 32-bit integer, ie. answer <= 2^31 - 1.

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const tribonacci = function (n) {
  const dp = new Array(n + 1);
  const fibonacci = n => {
    if (n === 0) return 0;
    if (n <= 2) return 1;
    if (dp[n]) return dp[n];

    dp[n] = fibonacci(n - 1) + fibonacci(n - 2) + fibonacci(n - 3);
    return dp[n];
  };

  return fibonacci(n);
};