Longest Arithmetic Sequence

Author: anantkaushik

1027-longest-arithmetic-sequence.py

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+"""
+Problem Link: https://leetcode.com/problems/longest-arithmetic-sequence/
+
+Given an array A of integers, return the length of the longest arithmetic subsequence in A.
+Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 
+0 <= i_1 < i_2 < ... < i_k <= A.length - 1, and that a sequence B is arithmetic if B[i+1] - B[i] 
+are all the same value (for 0 <= i < B.length - 1).
+
+Example 1:
+Input: [3,6,9,12]
+Output: 4
+Explanation: 
+The whole array is an arithmetic sequence with steps of length = 3.
+
+Example 2:
+Input: [9,4,7,2,10]
+Output: 3
+Explanation: 
+The longest arithmetic subsequence is [4,7,10].
+
+Example 3:
+Input: [20,1,15,3,10,5,8]
+Output: 4
+Explanation: 
+The longest arithmetic subsequence is [20,15,10,5].
+ 
+Note:
+2 <= A.length <= 2000
+0 <= A[i] <= 10000
+"""
+# Time Complexity: O(n^2)
+# Space Complexity: O(n^2)
+import collections
+class Solution:
+    def longestArithSeqLength(self, A: List[int]) -> int:
+        dp = collections.defaultdict(dict)
+        maxLength = 1
+        for i in range(1,len(A)):
+          for j in range(i):
+            diff = A[i] - A[j]
+            dp[i][diff] = 1 + dp[j].get(diff, 1)
+            maxLength = max(maxLength, dp[i][diff])
+        return maxLength
+
+class Solution1:
+    def longestArithSeqLength(self, A: List[int]) -> int:
+        dp = {}
+        for i in range(len(A)):
+          for j in range(i+1, len(A)):
+            diff = A[j] - A[i]
+            dp[j, diff] = dp.get((i, diff), 1) + 1
+        return max(dp.values())