title: Maximum Sum Pairs Specific Difference
signature: function maximum_sum_pairs_specific_difference(arr, n, k)
source_py: def maximum_sum_pairs_specific_difference(arr, N, K):
      arr.sort()
      dp = ([0] * N)
      dp[0] = 0
      for i in range(1, N):
          dp[i] = dp[(i - 1)]
          if ((arr[i] - arr[(i - 1)]) < K):
              if (i >= 2):
                  dp[i] = max(dp[i], ((dp[(i - 2)] + arr[i]) + arr[(i - 1)]))
              else:
                  dp[i] = max(dp[i], (arr[i] + arr[(i - 1)]))
      return dp[(N - 1)]
source_cpp: int maximum_sum_pairs_specific_difference(vector<int> arr, int N, int K) {
    sort(arr.begin(), arr.end());
    int dp [ N ];
    dp [ 0 ] = 0;
    for ( int i = 1;
    i < N;
    i ++ ) {
      dp [ i ] = dp [ i - 1 ];
      if ( arr [ i ] - arr [ i - 1 ] < K ) {
        if ( i >= 2 ) dp [ i ] = max ( dp [ i ], dp [ i - 2 ] + arr [ i ] + arr [ i - 1 ] );
        else dp [ i ] = max ( dp [ i ], arr [ i ] + arr [ i - 1 ] );
      }
    }
    return dp [ N - 1 ];
  }
question_info.entry_fn_name: maximum_sum_pairs_specific_difference
question_info.entry_cls_name: Solution
question_info.test_case_ids: ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
question_info.test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(arr, n, k, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(arr, n, k) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver({48, 53, 67, 78, 78, 93, 95}, 6, 4, 156)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-70, -32, -2, 18, 30, 32, 52, 70, 72, 88}, 8, 8, 62)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 37, 31, 10)
      print(string.format("TEST-2...%s",result))
  
      result = driver({2, 3, 5, 5, 6, 10, 12, 13, 13, 16, 23, 23, 34, 36, 39, 40, 42, 45, 45, 47, 51, 51, 52, 56, 57, 58, 60, 60, 60, 60, 61, 63, 67, 68, 71, 73, 75, 80, 80, 82, 84, 86, 86, 86, 86, 89, 90, 98, 99}, 31, 37, 1083)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-84, -56, 68, 78}, 3, 3, 0)
      print(string.format("TEST-4...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1}, 14, 9, 5)
      print(string.format("TEST-5...%s",result))
  
      result = driver({1, 2, 3, 9, 12, 12, 16, 17, 18, 19, 20, 21, 21, 26, 29, 42, 44, 45, 48, 48, 48, 54, 54, 55, 60, 63, 63, 64, 64, 67, 67, 68, 69, 74, 78, 78, 79, 83, 95, 95, 95, 96, 97, 99}, 27, 42, 849)
      print(string.format("TEST-6...%s",result))
  
      result = driver({-92, -58, -56, -48, -42, -16, -14, 28, 40, 42, 54, 60, 64}, 9, 8, 0)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 21, 19, 9)
      print(string.format("TEST-8...%s",result))
  
      result = driver({25, 64, 96}, 1, 1, 0)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.test_list: [{"idx": 0, "outputs": 156, "inputs": {"arr": [48, 53, 67, 78, 78, 93, 95], "n": 6, "k": 4}}, {"idx": 1, "outputs": 62, "inputs": {"arr": [-70, -32, -2, 18, 30, 32, 52, 70, 72, 88], "n": 8, "k": 8}}, {"idx": 2, "outputs": 10, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 37, "k": 31}}, {"idx": 3, "outputs": 1083, "inputs": {"arr": [2, 3, 5, 5, 6, 10, 12, 13, 13, 16, 23, 23, 34, 36, 39, 40, 42, 45, 45, 47, 51, 51, 52, 56, 57, 58, 60, 60, 60, 60, 61, 63, 67, 68, 71, 73, 75, 80, 80, 82, 84, 86, 86, 86, 86, 89, 90, 98, 99], "n": 31, "k": 37}}, {"idx": 4, "outputs": 0, "inputs": {"arr": [-84, -56, 68, 78], "n": 3, "k": 3}}, {"idx": 5, "outputs": 5, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], "n": 14, "k": 9}}, {"idx": 6, "outputs": 849, "inputs": {"arr": [1, 2, 3, 9, 12, 12, 16, 17, 18, 19, 20, 21, 21, 26, 29, 42, 44, 45, 48, 48, 48, 54, 54, 55, 60, 63, 63, 64, 64, 67, 67, 68, 69, 74, 78, 78, 79, 83, 95, 95, 95, 96, 97, 99], "n": 27, "k": 42}}, {"idx": 7, "outputs": 0, "inputs": {"arr": [-92, -58, -56, -48, -42, -16, -14, 28, 40, 42, 54, 60, 64], "n": 9, "k": 8}}, {"idx": 8, "outputs": 9, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 21, "k": 19}}, {"idx": 9, "outputs": 0, "inputs": {"arr": [25, 64, 96], "n": 1, "k": 1}}]