Create 2024-05-01-Leetcode-1137.md

Author: hyeonukim

_posts/Leetcode/DP/2024-05-01-Leetcode-1137.md

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+---
+title: Leetcode 1137. N-th Tribonacci Number
+description: Explanation for Leetcode 1137 - N-th Tribonacci Number, and its solution in Python.
+date: 2025-05-01
+categories: [Leetcode, Dynamic Programming, Easy]
+tags: [Leetcode, Python, Study, Dynamic Programming, Easy]
+math: true
+---
+
+## Problem
+[Leetcode 1137 - N-th Tribonacci Number](https://leetcode.com/problems/n-th-tribonacci-number/description/)
+
+Example:
+```
+Input: n = 4
+Output: 4
+Explanation:
+T_3 = 0 + 1 + 1 = 2
+T_4 = 1 + 1 + 2 = 4
+
+Input: n = 25
+Output: 1389537
+```
+
+## Approach
+
+Using array, we can store the all previous values. For example, we can save T_0, T_1, T_2. With the information, we can calculate T_3, T_4, and up to T_n in the saved array.
+
+Thus we can return T_n at the end
+
+Here is the Python code for the solution:
+```python
+class Solution:
+    def tribonacci(self, n: int) -> int:
+        dp = [0, 1, 1]
+        
+        if n < 3:
+            return dp[n]
+        
+        for i in range(3, n+1):
+            total = dp[i-1] + dp[i-2] + dp[i-3]
+            dp.append(total)
+
+        return dp[-1]
+```
+## Time Complexity and Space Complexity
+
+Time Complexity: $O(n)$
+
+Space Complexity: $O(n)$