I added a smart search table on my sample site surprisingly on the first try: https://databasetable-net.000webhostapp.com/

The table is fully responsive on a computer when you make the screen smaller. However, the table pushes left on a smart phone.

This article solution of adding the css: #smart_table{ margin: 0 auto; } did not work.
https://datatables.net/forums/discussion/45913/table-not-centered
Removing the boostrap contrainer also did not work (as that could conflict with datatables CDN). Adding a col-xs-10 container also did not seem to have an impact.

Here is my full code if needed:

<!--========= ADVANCED SEARCH ===============-->

 <center><div class="container-fluid"><h4>Advanced Multi-Search Option (see below)</h4>  <br>

<table class="table table-striped table-bordered table-hover table-condensed" cellpadding="3" cellspacing="0" border="0" style="width: 70%; margin: 0 auto 2em auto;" id="smart_table">
        <thead>
            <tr>
                <th>Target</th>
                <th>Search text</th>
                <th>Treat as regex</th>
                <th>Use smart search</th>
            </tr>
        </thead>
        <tbody>
            <tr id="filter_global">
                <td>Global search</td>
                <td align="center"><input type="text" class="global_filter" id="global_filter"></td>
                <td align="center"><input type="checkbox" class="global_filter" id="global_regex"></td>
                <td align="center"><input type="checkbox" class="global_filter" id="global_smart" checked="checked"></td>
            </tr>
            <tr id="filter_col1" data-column="0">
                <td>Column - ID</td>
                <td align="center"><input type="text" class="column_filter" id="col0_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col0_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col0_smart" checked="checked"></td>
            </tr>
            <tr id="filter_col2" data-column="1">
                <td>Column - First Name</td>
                <td align="center"><input type="text" class="column_filter" id="col1_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col1_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col1_smart" checked="checked"></td>
            </tr>
            <tr id="filter_col3" data-column="2">
                <td>Column - Last Name</td>
                <td align="center"><input type="text" class="column_filter" id="col2_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col2_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col2_smart" checked="checked"></td>
            </tr>
            <tr id="filter_col4" data-column="3">
                <td>Column - Zip</td>
                <td align="center"><input type="text" class="column_filter" id="col3_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col3_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col3_smart" checked="checked"></td>
            </tr>
            <tr id="filter_col5" data-column="4">
                <td>Column - Date</td>
                <td align="center"><input type="text" class="column_filter" id="col4_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col4_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col4_smart" checked="checked"></td>
                 <tr id="filter_col5" data-column="4">
                <td>Column - Updated</td>
                <td align="center"><input type="text" class="column_filter" id="col4_filter"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col4_regex"></td>
                <td align="center"><input type="checkbox" class="column_filter" id="col4_smart" checked="checked"></td>
            </tr>

        </tbody>
    </table> 
    </div> </center>
    <br>
     <center><div class="container-fluid"><h5>Smart search built-in filtering is "smart" in that it breaks the user's input into individual words and then matches those words in any position and in any order in the table (rather than simple doing a simple string compare). <a href="https://datatables.net/reference/option/search.smart" target="_blank">Click here for more info!</a></h5> </div> </center> <br>
</body>
  </html>

  <script type="text/javascript"> 
  $(document).ready(function() {
function filterGlobal () {
    $('#example').DataTable().search(
        $('#global_filter').val(),
        $('#global_regex').prop('checked'),
        $('#global_smart').prop('checked')
    ).draw();
}

function filterColumn ( i ) {
    $('#example').DataTable().column( i ).search(
        $('#col'+i+'_filter').val(),
        $('#col'+i+'_regex').prop('checked'),
        $('#col'+i+'_smart').prop('checked')
    ).draw();
}

$(document).ready(function() {
    $('#example').DataTable();

    $('input.global_filter').on( 'keyup click', function () {
        filterGlobal();
    } );

    $('input.column_filter').on( 'keyup click', function () {
        filterColumn( $(this).parents('tr').attr('data-column') );
    } );
} );
} ); //end
</script>