title: Maximum Subsequence Sum Such That No Three Are Consecutive
signature: function maximum_subsequence_sum_such_that_no_three_are_consecutive(arr, n)
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, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(arr, n) 
      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({5, 6, 8, 9, 10, 10, 16, 17, 17, 20, 21, 22, 23, 28, 29, 32, 36, 37, 40, 41, 42, 43, 47, 47, 48, 48, 49, 49, 52, 52, 53, 59, 61, 64, 65, 79, 79, 81, 87, 91, 92, 98}, 35, 832)
      print(string.format("TEST-0...%s",result))
  
      result = driver({98, 76, -80, -30, 82, 52, -14, 28, 98, 18, 82, 52, 26, -62, -8}, 7, 308)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 1, 1, 1, 1}, 7, 2)
      print(string.format("TEST-2...%s",result))
  
      result = driver({21, 26, 85, 73, 47, 10, 54, 9, 11, 70, 42, 95, 44, 91}, 12, 419)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-94, -92, -90, -84, -76, -68, -60, -50, -34, -34, -20, -16, -6, 18, 50, 54, 66, 70, 96}, 9, -182)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1}, 16, 7)
      print(string.format("TEST-5...%s",result))
  
      result = driver({2, 3, 4, 4, 14, 14, 18, 21, 24, 26, 29, 31, 32, 34, 36, 37, 38, 40, 42, 44, 44, 54, 63, 69, 77, 77, 82, 82, 86, 87, 90, 93, 95}, 31, 895)
      print(string.format("TEST-6...%s",result))
  
      result = driver({-46, 64, -44, 88, -74, 54, 40, -2, -24, 94, 40, -44, 56, -54, -60, -86, -58, 48, -90, 12, -76, -30, 94, -34, 14, 12, 80, -40, 60}, 22, 450)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, 7, 0)
      print(string.format("TEST-8...%s",result))
  
      result = driver({4, 32, 63, 23, 44, 57, 59, 69, 88, 61, 66, 61, 65, 33, 79, 58, 71, 2, 80, 41, 83, 12, 20, 9, 7, 40, 36, 97, 10, 98, 66, 78, 71, 37, 53}, 26, 895)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def maximum_subsequence_sum_such_that_no_three_are_consecutive(arr, n):
      sum = [0 for k in range(n)]
      if (n >= 1):
          sum[0] = arr[0]
      if (n >= 2):
          sum[1] = (arr[0] + arr[1])
      if (n > 2):
          sum[2] = max(sum[1], max((arr[1] + arr[2]), (arr[0] + arr[2])))
      for i in range(3, n):
          sum[i] = max(max(sum[(i - 1)], (sum[(i - 2)] + arr[i])), ((arr[i] + arr[(i - 1)]) + sum[(i - 3)]))
      return sum[(n - 1)]
source_cpp: int maximum_subsequence_sum_such_that_no_three_are_consecutive(vector<int> arr, int n) {
    int sum [ n ];
    if ( n >= 1 ) sum [ 0 ] = arr [ 0 ];
    if ( n >= 2 ) sum [ 1 ] = arr [ 0 ] + arr [ 1 ];
    if ( n > 2 ) sum [ 2 ] = max ( sum [ 1 ], max ( arr [ 1 ] + arr [ 2 ], arr [ 0 ] + arr [ 2 ] ) );
    for ( int i = 3;
    i < n;
    i ++ ) sum [ i ] = max ( max ( sum [ i - 1 ], sum [ i - 2 ] + arr [ i ] ), arr [ i ] + arr [ i - 1 ] + sum [ i - 3 ] );
    return sum [ n - 1 ];
  }