title: Minimize The Maximum Difference Between The Heights
signature: function minimize_the_maximum_difference_between_the_heights(arr, n, k)
source_py: def minimize_the_maximum_difference_between_the_heights(arr, n, k):
      if (n == 1):
          return 0
      arr.sort()
      ans = (arr[(n - 1)] - arr[0])
      small = (arr[0] + k)
      big = (arr[(n - 1)] - k)
      if (small > big):
          (small, big) = (big, small)
      for i in range(1, (n - 1)):
          subtract = (arr[i] - k)
          add = (arr[i] + k)
          if ((subtract >= small) or (add <= big)):
              continue
          if ((big - subtract) <= (add - small)):
              small = subtract
          else:
              big = add
      return min(ans, (big - small))
source_cpp: int minimize_the_maximum_difference_between_the_heights(vector<int> arr, int n, int k) {
    if ( n == 1 ) return 0;
    sort(arr.begin(), arr.end());
    int ans = arr [ n - 1 ] - arr [ 0 ];
    int small = arr [ 0 ] + k;
    int big = arr [ n - 1 ] - k;
    if ( small > big ) swap ( small, big );
    for ( int i = 1;
    i < n - 1;
    i ++ ) {
      int subtract = arr [ i ] - k;
      int add = arr [ i ] + k;
      if ( subtract >= small || add <= big ) continue;
      if ( big - subtract <= add - small ) small = subtract;
      else big = add;
    }
    return min ( ans, big - small );
  }
question_info.entry_fn_name: minimize_the_maximum_difference_between_the_heights
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({31, 33, 40, 43, 44, 51, 52, 56, 60, 64, 66, 79, 91, 93, 99}, 10, 13, 19)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-86, -62, -16, 34, 54}, 3, 4, 62)
      print(string.format("TEST-1...%s",result))
  
      result = driver({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, 1, 1, 1, 1}, 29, 22, 1)
      print(string.format("TEST-2...%s",result))
  
      result = driver({3, 5, 5, 7, 9, 11, 16, 17, 21, 27, 36, 38, 41, 44, 45, 45, 48, 51, 55, 57, 58, 59, 59, 60, 67, 67, 67, 68, 70, 74, 77, 84, 86, 88, 90, 90, 91, 91, 92, 99}, 28, 28, 52)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-88, -84, -78, -72, -66, -66, -58, -56, -56, -56, -54, -50, -50, -38, -24, -18, -12, -10, -8, -4, 0, 6, 8, 10, 14, 40, 44, 50, 58, 64, 64, 68}, 22, 28, 44)
      print(string.format("TEST-4...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, 10, 8, 1)
      print(string.format("TEST-5...%s",result))
  
      result = driver({6, 11, 13, 14, 22, 25, 26, 28, 30, 31, 37, 37, 55, 57, 61, 62, 64, 67, 69, 70, 71, 73, 73, 75, 80, 81, 82, 88, 90, 98}, 29, 26, 35)
      print(string.format("TEST-6...%s",result))
  
      result = driver({-90, -86, -80, -78, -70, -64, -62, -38, -36, -32, -22, -18, -10, 4, 6, 20, 20, 24, 44, 52, 66, 82, 88, 92, 98}, 23, 18, 142)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 20, 19, 1)
      print(string.format("TEST-8...%s",result))
  
      result = driver({2}, 0, 0, 0)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.test_list: [{"idx": 0, "outputs": 19, "inputs": {"arr": [31, 33, 40, 43, 44, 51, 52, 56, 60, 64, 66, 79, 91, 93, 99], "n": 10, "k": 13}}, {"idx": 1, "outputs": 62, "inputs": {"arr": [-86, -62, -16, 34, 54], "n": 3, "k": 4}}, {"idx": 2, "outputs": 1, "inputs": {"arr": [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, 1, 1, 1, 1], "n": 29, "k": 22}}, {"idx": 3, "outputs": 52, "inputs": {"arr": [3, 5, 5, 7, 9, 11, 16, 17, 21, 27, 36, 38, 41, 44, 45, 45, 48, 51, 55, 57, 58, 59, 59, 60, 67, 67, 67, 68, 70, 74, 77, 84, 86, 88, 90, 90, 91, 91, 92, 99], "n": 28, "k": 28}}, {"idx": 4, "outputs": 44, "inputs": {"arr": [-88, -84, -78, -72, -66, -66, -58, -56, -56, -56, -54, -50, -50, -38, -24, -18, -12, -10, -8, -4, 0, 6, 8, 10, 14, 40, 44, 50, 58, 64, 64, 68], "n": 22, "k": 28}}, {"idx": 5, "outputs": 1, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], "n": 10, "k": 8}}, {"idx": 6, "outputs": 35, "inputs": {"arr": [6, 11, 13, 14, 22, 25, 26, 28, 30, 31, 37, 37, 55, 57, 61, 62, 64, 67, 69, 70, 71, 73, 73, 75, 80, 81, 82, 88, 90, 98], "n": 29, "k": 26}}, {"idx": 7, "outputs": 142, "inputs": {"arr": [-90, -86, -80, -78, -70, -64, -62, -38, -36, -32, -22, -18, -10, 4, 6, 20, 20, 24, 44, 52, 66, 82, 88, 92, 98], "n": 23, "k": 18}}, {"idx": 8, "outputs": 1, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 20, "k": 19}}, {"idx": 9, "outputs": 0, "inputs": {"arr": [2], "n": 0, "k": 0}}]