Adds Longest Arithmetic Subsequence

dynamic_programming/longest_arithmetic_subsequence.py

@@ -0,0 +1,66 @@
+from typing import List
+"""
+Longest Arithmetic Subsequence Problem: Given an array nums of integers, return the length of the longest arithmetic subsequence in nums.
+
+Note that:
+- A subsequence is an array that can be derived from another array by deleting some or no elements
+  without changing the order of the remaining elements.
+- A sequence seq is arithmetic if seq[i + 1] - seq[i] are all the same value (for 0 <= i < seq.length - 1).
+"""
+
+def longest_arithmetic_subsequence(nums: List[int]) -> int:
+    """
+    Finds the length of the longest arithmetic subsequence in a given array of integers.
+
+    Parameters
+    ----------
+    nums : List[int]
+        The input array of integers.
+
+    Returns
+    -------
+    int
+        The length of the longest arithmetic subsequence.
+
+    Examples
+    --------
+    >>> longest_arithmetic_subsequence([3, 6, 9, 12])
+    4
+    >>> longest_arithmetic_subsequence([9, 4, 7, 2, 10])
+    3
+    >>> longest_arithmetic_subsequence([20, 1, 15, 3, 10, 5, 8])
+    4
+    >>> longest_arithmetic_subsequence([])  # Empty array
+    0
+    >>> longest_arithmetic_subsequence(None)  # Null array
+    Traceback (most recent call last):
+        ...
+    ValueError: Input array cannot be None
+    """
+    if nums is None:
+        raise ValueError("Input array cannot be None")
+    
+    if len(nums) <= 1:
+        return len(nums)
+
+    dp = [{} for _ in range(len(nums))]
+    max_length = 2
+
+    for i in range(len(nums)):
+        for j in range(i):
+            diff = nums[i] - nums[j]
+            dp[i][diff] = dp[j].get(diff, 1) + 1
+            max_length = max(max_length, dp[i][diff])
+
+    return max_length
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
+    # sample test case
+    nums = [3, 6, 9, 12]
+    expected_length = 4
+
+    result = longest_arithmetic_subsequence(nums)
+    print("Length of longest arithmetic subsequence:", result)