title: Find Maximum Dot Product Two Arrays Insertion 0S
signature: function find_maximum_dot_product_two_arrays_insertion_0s(a, b, m, n)
source_py: def find_maximum_dot_product_two_arrays_insertion_0s(A, B, m, n):
      dp = [[0 for i in range((m + 1))] for j in range((n + 1))]
      for i in range(1, (n + 1), 1):
          for j in range(i, (m + 1), 1):
              dp[i][j] = max((dp[(i - 1)][(j - 1)] + (A[(j - 1)] * B[(i - 1)])), dp[i][(j - 1)])
      return dp[n][m]
source_cpp: long long int find_maximum_dot_product_two_arrays_insertion_0s(vector<int> A, vector<int> B, int m, int n) {
    long long int dp [ n + 1 ] [ m + 1 ];
    memset ( dp, 0, sizeof ( dp ) );
    for ( int i = 1;
    i <= n;
    i ++ ) for ( int j = i;
    j <= m;
    j ++ ) dp [ i ] [ j ] = max ( ( dp [ i - 1 ] [ j - 1 ] + ( A [ j - 1 ] * B [ i - 1 ] ) ), dp [ i ] [ j - 1 ] );
    return dp [ n ] [ m ];
  }
question_info.entry_fn_name: find_maximum_dot_product_two_arrays_insertion_0s
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(a, b, m, n, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(a, b, m, 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({7, 9, 22, 68}, {14, 22, 54, 58}, 3, 2, 610)
      print(string.format("TEST-0...%s",result))
  
      result = driver({24, 40, 98, 58, -24, 24, 76, 48, -92, -16, -46, -48, -70, 88, 66, 2, 44, 36, 34, 34, 46, 90, -80, -24, -58, 68, 72, -20, -62, -40}, {30, -88, 6, -26, -76, 14, -80, -30, -58, 76, 40, -28, -54, 38, -60, -60, 88, -80, -22, 90, 50, -48, 68, -26, 26, -2, 68, -16, 88, -72}, 22, 22, 7952)
      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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {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}, 22, 19, 0)
      print(string.format("TEST-2...%s",result))
  
      result = driver({32, 15, 41, 41, 4, 42, 22, 33, 33, 11, 68, 5, 41, 80, 39, 15, 36, 75, 41, 11, 25, 40, 50, 19, 39, 12, 75, 28, 52, 20, 63, 5, 27, 53, 19, 62, 98, 72, 10, 90, 74, 93, 52, 81, 91, 65, 90, 93}, {80, 18, 9, 29, 62, 89, 4, 40, 47, 15, 35, 82, 22, 97, 63, 54, 7, 58, 64, 73, 54, 79, 21, 21, 20, 19, 56, 42, 6, 97, 7, 34, 55, 35, 57, 86, 73, 88, 20, 29, 48, 52, 8, 77, 2, 12, 6, 47}, 30, 25, 50904)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-94, -76, -68, -50, -28, -20, 18, 24, 30, 54, 74, 84, 98}, {-88, -80, -78, -68, -44, -38, 42, 50, 62, 68, 70, 80, 92}, 11, 8, 31016)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0}, {1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1}, 21, 33, 0)
      print(string.format("TEST-5...%s",result))
  
      result = driver({14, 27, 43, 49}, {51, 59, 76, 83}, 2, 2, 2307)
      print(string.format("TEST-6...%s",result))
  
      result = driver({78, -26, -12, 38, -90}, {14, 50, -6, -38, 80}, 3, 2, 492)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 1, 1, 1}, {0, 0, 0, 1}, 3, 2, 0)
      print(string.format("TEST-8...%s",result))
  
      result = driver({12, 69, 57, 7, 52, 14, 15, 83, 67, 57, 15, 86, 81, 43, 1, 64, 45, 68, 30, 23, 14, 70, 13, 51, 23, 33, 98, 68, 24, 43, 12, 82, 46}, {12, 48, 57, 40, 47, 36, 22, 50, 68, 98, 77, 78, 39, 55, 87, 75, 65, 27, 33, 27, 70, 34, 67, 71, 84, 33, 7, 61, 3, 9, 67, 92, 60}, 17, 32, 0)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.test_list: [{"idx": 0, "outputs": 610, "inputs": {"a": [7, 9, 22, 68], "b": [14, 22, 54, 58], "m": 3, "n": 2}}, {"idx": 1, "outputs": 7952, "inputs": {"a": [24, 40, 98, 58, -24, 24, 76, 48, -92, -16, -46, -48, -70, 88, 66, 2, 44, 36, 34, 34, 46, 90, -80, -24, -58, 68, 72, -20, -62, -40], "b": [30, -88, 6, -26, -76, 14, -80, -30, -58, 76, 40, -28, -54, 38, -60, -60, 88, -80, -22, 90, 50, -48, 68, -26, 26, -2, 68, -16, 88, -72], "m": 22, "n": 22}}, {"idx": 2, "outputs": 0, "inputs": {"a": [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], "b": [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], "m": 22, "n": 19}}, {"idx": 3, "outputs": 50904, "inputs": {"a": [32, 15, 41, 41, 4, 42, 22, 33, 33, 11, 68, 5, 41, 80, 39, 15, 36, 75, 41, 11, 25, 40, 50, 19, 39, 12, 75, 28, 52, 20, 63, 5, 27, 53, 19, 62, 98, 72, 10, 90, 74, 93, 52, 81, 91, 65, 90, 93], "b": [80, 18, 9, 29, 62, 89, 4, 40, 47, 15, 35, 82, 22, 97, 63, 54, 7, 58, 64, 73, 54, 79, 21, 21, 20, 19, 56, 42, 6, 97, 7, 34, 55, 35, 57, 86, 73, 88, 20, 29, 48, 52, 8, 77, 2, 12, 6, 47], "m": 30, "n": 25}}, {"idx": 4, "outputs": 31016, "inputs": {"a": [-94, -76, -68, -50, -28, -20, 18, 24, 30, 54, 74, 84, 98], "b": [-88, -80, -78, -68, -44, -38, 42, 50, 62, 68, 70, 80, 92], "m": 11, "n": 8}}, {"idx": 5, "outputs": 0, "inputs": {"a": [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0], "b": [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1], "m": 21, "n": 33}}, {"idx": 6, "outputs": 2307, "inputs": {"a": [14, 27, 43, 49], "b": [51, 59, 76, 83], "m": 2, "n": 2}}, {"idx": 7, "outputs": 492, "inputs": {"a": [78, -26, -12, 38, -90], "b": [14, 50, -6, -38, 80], "m": 3, "n": 2}}, {"idx": 8, "outputs": 0, "inputs": {"a": [0, 1, 1, 1], "b": [0, 0, 0, 1], "m": 3, "n": 2}}, {"idx": 9, "outputs": 0, "inputs": {"a": [12, 69, 57, 7, 52, 14, 15, 83, 67, 57, 15, 86, 81, 43, 1, 64, 45, 68, 30, 23, 14, 70, 13, 51, 23, 33, 98, 68, 24, 43, 12, 82, 46], "b": [12, 48, 57, 40, 47, 36, 22, 50, 68, 98, 77, 78, 39, 55, 87, 75, 65, 27, 33, 27, 70, 34, 67, 71, 84, 33, 7, 61, 3, 9, 67, 92, 60], "m": 17, "n": 32}}]