Adds Longest Arithmetic Subsequence (Review Reqd)

dynamic_programming/longest_arithmetic_subsequence.py

@@ -0,0 +1,83 @@
+"""
+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) == 0:
+        return 0
+
+    if len(nums) == 1:
+        return 1
+
+    dp: list[dict[int, int]] = [{} 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()
+
+    # test cases
+    test_cases = [
+        ([3, 6, 9, 12], 4),
+        ([3, 6, 9, 12, 15], 5),
+        ([1, 7, 10, 13, 14, 19], 4),
+        ([1, 2, 3, 4], 4),
+        ([], 0),
+        ([10], 1),
+        ([9, 4, 7, 2, 10], 3),
+        ([1, 2, 2, 2, 2, 5], 4),
+    ]
+
+    for nums, expected_length in test_cases:
+        result = longest_arithmetic_subsequence(nums)
+        print(f"Test case {nums}: Expected {expected_length}, Got {result}")
+        assert result == expected_length, f"Test failed for input {nums}"