title: Dynamic Programming Set 14 Maximum Sum Increasing Subsequence
signature: function dynamic_programming_set_14_maximum_sum_increasing_subsequence(arr, n)
source_py: def dynamic_programming_set_14_maximum_sum_increasing_subsequence(arr, n):
      max = 0
      msis = [0 for x in range(n)]
      for i in range(n):
          msis[i] = arr[i]
      for i in range(1, n):
          for j in range(i):
              if ((arr[i] > arr[j]) and (msis[i] < (msis[j] + arr[i]))):
                  msis[i] = (msis[j] + arr[i])
      for i in range(n):
          if (max < msis[i]):
              max = msis[i]
      return max
source_cpp: int dynamic_programming_set_14_maximum_sum_increasing_subsequence(vector<int> arr, int n) {
    int i, j, max = 0;
    int msis [ n ];
    for ( i = 0;
    i < n;
    i ++ ) msis [ i ] = arr [ i ];
    for ( i = 1;
    i < n;
    i ++ ) for ( j = 0;
    j < i;
    j ++ ) if ( arr [ i ] > arr [ j ] && msis [ i ] < msis [ j ] + arr [ i ] ) msis [ i ] = msis [ j ] + arr [ i ];
    for ( i = 0;
    i < n;
    i ++ ) if ( max < msis [ i ] ) max = msis [ i ];
    return max;
  }
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, 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({4, 5, 7, 12, 23, 31, 31, 45, 47, 60, 67, 70, 84, 85, 91, 96}, 11, 301)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-88, -38, -50, -14, 36, -32, 0, -8, -12, -62, -46, 66, -46, -26, 6, -44, 14, -74, -84, 52, -28}, 18, 102)
      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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 39, 1)
      print(string.format("TEST-2...%s",result))
  
      result = driver({85, 42, 7, 35, 35, 21, 97, 59, 88, 50, 12, 44, 85, 22, 38, 23, 42, 61, 44, 63, 23, 69, 28, 17, 73, 20, 71, 80, 15, 42, 28, 10, 56, 77, 43}, 26, 396)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-92, -82, -82, -74, -72, -68, -68, -66, -60, -54, -42, -38, -36, -32, -30, -16, -14, -12, -10, 14, 24, 28, 34, 34, 38, 42, 44, 52, 70, 72, 80, 84, 86, 94}, 32, 582)
      print(string.format("TEST-4...%s",result))
  
      result = driver({0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0}, 8, 1)
      print(string.format("TEST-5...%s",result))
  
      result = driver({33}, 0, 0)
      print(string.format("TEST-6...%s",result))
  
      result = driver({76, 86, 46, -70, 92, 6, 70, -66, 64, 46, 86, -42, -46, -24, 8, 76, 4, -96, -86, 18, 70, -72, -56, -88, -96, 62, 22, 20, 42}, 21, 254)
      print(string.format("TEST-7...%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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 24, 0)
      print(string.format("TEST-8...%s",result))
  
      result = driver({25, 46, 41, 61, 93, 29, 65, 24, 10, 89, 22, 51, 18, 65, 70, 59, 87, 82, 97, 99, 15, 64, 20, 97, 12, 23, 76}, 20, 550)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.entry_cls_name: Solution
question_info.test_list: [{"idx": 0, "outputs": 301, "inputs": {"arr": [4, 5, 7, 12, 23, 31, 31, 45, 47, 60, 67, 70, 84, 85, 91, 96], "n": 11}}, {"idx": 1, "outputs": 102, "inputs": {"arr": [-88, -38, -50, -14, 36, -32, 0, -8, -12, -62, -46, 66, -46, -26, 6, -44, 14, -74, -84, 52, -28], "n": 18}}, {"idx": 2, "outputs": 1, "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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 39}}, {"idx": 3, "outputs": 396, "inputs": {"arr": [85, 42, 7, 35, 35, 21, 97, 59, 88, 50, 12, 44, 85, 22, 38, 23, 42, 61, 44, 63, 23, 69, 28, 17, 73, 20, 71, 80, 15, 42, 28, 10, 56, 77, 43], "n": 26}}, {"idx": 4, "outputs": 582, "inputs": {"arr": [-92, -82, -82, -74, -72, -68, -68, -66, -60, -54, -42, -38, -36, -32, -30, -16, -14, -12, -10, 14, 24, 28, 34, 34, 38, 42, 44, 52, 70, 72, 80, 84, 86, 94], "n": 32}}, {"idx": 5, "outputs": 1, "inputs": {"arr": [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0], "n": 8}}, {"idx": 6, "outputs": 0, "inputs": {"arr": [33], "n": 0}}, {"idx": 7, "outputs": 254, "inputs": {"arr": [76, 86, 46, -70, 92, 6, 70, -66, 64, 46, 86, -42, -46, -24, 8, 76, 4, -96, -86, 18, 70, -72, -56, -88, -96, 62, 22, 20, 42], "n": 21}}, {"idx": 8, "outputs": 0, "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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 24}}, {"idx": 9, "outputs": 550, "inputs": {"arr": [25, 46, 41, 61, 93, 29, 65, 24, 10, 89, 22, 51, 18, 65, 70, 59, 87, 82, 97, 99, 15, 64, 20, 97, 12, 23, 76], "n": 20}}]
question_info.extension: lua
question_info.entry_fn_name: dynamic_programming_set_14_maximum_sum_increasing_subsequence
question_info.test_case_ids: 0 1 2 3 4 5 6 7 8 9
question_info.commands: lua __FILENAME__