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This approach uses an iterative method with dynamic programming principles to compute the N-th Tribonacci number. We maintain a list or variables to store previously computed values to avoid redundant calculations. This approach provides an optimal solution both in terms of time and space.
Time Complexity: O(n), Space Complexity: O(1).
1def tribonacci(n):
2 if n == 0: return 0
3 if n == 1 or n == 2: return 1
4
5 t0, t1, t2 = 0, 1, 1
6 for _ in range(3, n + 1):
7 t = t0 + t1 + t2
8 t0, t1, t2 = t1, t2, t
9 return t
10
11n = 25
12print(tribonacci(n))The Python solution employs a tuple to succinctly swap and iterate through the sequence values.
This approach employs recursion with memoization to compute the Tribonacci numbers. Here, we recursively break the problem into smaller subproblems and cache the results of each computed Tribonacci number to avoid redundant calculations, thus optimizing the recursive solution in terms of performance.
Time Complexity: O(n), Space Complexity: O(n).
1def tribonacci(n, memo={0: 0,
In this Python code, a dictionary is used as a memoization cache, storing the results of each calculated Tribonacci number.