old_contents: """Leetcode 1027. Longest Arithmetic Sequence
  Medium
  
  URL: 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
  """
  
  class SolutionPosDiffCountDp(object):
      def longestArithSeqLength(self, A):
          """
          :type A: List[int]
          :rtype: int
  
          Time complexity: O(n^2).
          Space complexity: O(n^2).
          """
          # Use dict:pos+diff->count to memorize previous pos's diff count.
          posdiff_count_d = {}
  
          n = len(A)
  
          for i in range(n):
              for j in range(i + 1, n):
                  diff = A[j] - A[i]
                  if (i, diff) not in posdiff_count_d:
                      # Initialize pos diff's count = 1+1.
                      posdiff_count_d[(j, diff)] = 2
                  else:
                      posdiff_count_d[(j, diff)] = posdiff_count_d[(i, diff)] + 1
  
          return max(posdiff_count_d.values())
  
  
  def main():
      # Output: 4
      A = [3,6,9,12]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
      # Output: 3
      A = [9,4,7,2,10]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
      # Output: 4
      A = [20,1,15,3,10,5,8]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
  
  if __name__ == '__main__':
      main()
  
new_contents: """Leetcode 1027. Longest Arithmetic Sequence
  Medium
  
  URL: 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
  """
  
  class SolutionPosDiffLenDp(object):
      def longestArithSeqLength(self, A):
          """
          :type A: List[int]
          :rtype: int
  
          Time complexity: O(n^2).
          Space complexity: O(n^2).
          """
          # Use dict:pos+diff->len to memorize previous pos's diff length.
          posdiff_len_d = {}
  
          n = len(A)
  
          for i in range(n):
              for j in range(i + 1, n):
                  diff = A[j] - A[i]
                  if (i, diff) not in posdiff_len_d:
                      # Initialize pos diff's count = 1+1.
                      posdiff_len_d[(j, diff)] = 2
                  else:
                      posdiff_len_d[(j, diff)] = posdiff_len_d[(i, diff)] + 1
  
          return max(posdiff_len_d.values())
  
  
  def main():
      # Output: 4
      A = [3,6,9,12]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
      # Output: 3
      A = [9,4,7,2,10]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
      # Output: 4
      A = [20,1,15,3,10,5,8]
      print SolutionPosDiffCountDp().longestArithSeqLength(A)
  
  
  if __name__ == '__main__':
      main()
  
subject: Revise to better var name: posdiff_len_d from London