title: Ways Transforming One String Removing 0 Characters
signature: function ways_transforming_one_string_removing_0_characters(a, b)
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, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(a, b) 
      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("abcccdf", "abccdf", 3)
      print(string.format("TEST-0...%s",result))
  
      result = driver("aabba", "ab", 4)
      print(string.format("TEST-1...%s",result))
  
      result = driver("aabsdfljk", "aa", 1)
      print(string.format("TEST-2...%s",result))
  
      result = driver("IONiqV", "XKbBiGZ", 0)
      print(string.format("TEST-3...%s",result))
  
      result = driver("9667771256770", "50915176", 0)
      print(string.format("TEST-4...%s",result))
  
      result = driver("10001011", "01", 11)
      print(string.format("TEST-5...%s",result))
  
      result = driver("fczbDtMDT", "FbX", 0)
      print(string.format("TEST-6...%s",result))
  
      result = driver("298746088", "29888", 1)
      print(string.format("TEST-7...%s",result))
  
      result = driver("01100011000", "0", 7)
      print(string.format("TEST-8...%s",result))
  
      result = driver("Qk", "", 1)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def ways_transforming_one_string_removing_0_characters(a, b):
      n = len(a)
      m = len(b)
      if (m == 0):
          return 1
      dp = [([0] * (n + 1)) for _ in range((m + 1))]
      for i in range(m):
          for j in range(i, n):
              if (i == 0):
                  if (j == 0):
                      if (a[j] == b[i]):
                          dp[i][j] = 1
                      else:
                          dp[i][j] = 0
                  elif (a[j] == b[i]):
                      dp[i][j] = (dp[i][(j - 1)] + 1)
                  else:
                      dp[i][j] = dp[i][(j - 1)]
              elif (a[j] == b[i]):
                  dp[i][j] = (dp[i][(j - 1)] + dp[(i - 1)][(j - 1)])
              else:
                  dp[i][j] = dp[i][(j - 1)]
      return dp[(m - 1)][(n - 1)]
source_cpp: int ways_transforming_one_string_removing_0_characters(string a, string b) {
    int n = a . size ( ), m = b . size ( );
    if ( m == 0 ) return 1;
    int dp [ m + 1 ] [ n + 1 ];
    memset ( dp, 0, sizeof ( dp ) );
    for ( int i = 0;
    i < m;
    i ++ ) {
      for ( int j = i;
      j < n;
      j ++ ) {
        if ( i == 0 ) {
          if ( j == 0 ) dp [ i ] [ j ] = ( a [ j ] == b [ i ] ) ? 1 : 0;
          else if ( a [ j ] == b [ i ] ) dp [ i ] [ j ] = dp [ i ] [ j - 1 ] + 1;
          else dp [ i ] [ j ] = dp [ i ] [ j - 1 ];
        }
        else {
          if ( a [ j ] == b [ i ] ) dp [ i ] [ j ] = dp [ i ] [ j - 1 ] + dp [ i - 1 ] [ j - 1 ];
          else dp [ i ] [ j ] = dp [ i ] [ j - 1 ];
        }
      }
    }
    return dp [ m - 1 ] [ n - 1 ];
  }