Using a button or dropdown to separate the query by alphabet?

var _alphabetSearch = '';
 
$.fn.dataTable.ext.search.push( function ( settings, searchData ) {
    if ( ! _alphabetSearch ) {
        return true;
    }
 
    if ( searchData[0].charAt(0) === _alphabetSearch ) {
        return true;
    }
 
    return false;
} );
 
 
function bin ( data ) {
    var letter, bins = {};
 
    for ( var i=0, ien=data.length ; i<ien ; i++ ) {
        letter = data[i].charAt(0).toUpperCase();
 
        if ( bins[letter] ) {
            bins[letter]++;
        }
        else {
            bins[letter] = 1;
        }
    }
 
    return bins;
}
 
 
$(document).ready(function() {
    var table = $('#example').DataTable();
 
    var alphabet = $('<div class="alphabet"/>').append( 'Search: ' );
    var columnData = table.column(0).data();
    var bins = bin( columnData );
 
    $('<span class="clear active"/>')
        .data( 'letter', '' )
        .data( 'match-count', columnData.length )
        .html( 'None' )
        .appendTo( alphabet );
 
    for ( var i=0 ; i<26 ; i++ ) {
        var letter = String.fromCharCode( 65 + i );
 
        $('<span/>')
            .data( 'letter', letter )
            .data( 'match-count', bins[letter] || 0 )
            .addClass( ! bins[letter] ? 'empty' : '' )
            .html( letter )
            .appendTo( alphabet );
    }
 
    alphabet.insertBefore( table.table().container() );
 
    alphabet.on( 'click', 'span', function () {
        alphabet.find( '.active' ).removeClass( 'active' );
        $(this).addClass( 'active' );
 
        _alphabetSearch = $(this).data('letter');
        table.draw();
    } );
 
    var info = $('<div class="alphabetInfo"></div>')
        .appendTo( alphabet );
 
    alphabet
        .on( 'mouseenter', 'span', function () {
            info
                .css( {
                    opacity: 1,
                    left: $(this).position().left,
                    width: $(this).width()
                } )
                .html( $(this).data('match-count') );
        } )
        .on( 'mouseleave', 'span', function () {
            info.css('opacity', 0);
        } );
} );

div.alphabet {
    position: relative;
    display: table;
    width: 100%;
    margin-bottom: 1em;
}
 
div.alphabet span {
    display: table-cell;
    color: #3174c7;
    cursor: pointer;
    text-align: center;
    width: 3.5%
}
 
div.alphabet span:hover {
    text-decoration: underline;
}
 
div.alphabet span.active {
    color: black;
}
 
div.alphabet span.empty {
    color: red;
}
 
div.alphabetInfo {
    display: block;
    position: absolute;
    background-color: #111;
    border-radius: 3px;
    color: white;
    top: 2em;
    height: 1.8em;
    padding-top: 0.4em;
    text-align: center;
    z-index: 1;
}

<link href="https://cdn.datatables.net/1.10.16/css/jquery.dataTables.min.css" rel="stylesheet"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><scriptsrc="https://cdn.datatables.net/1.10.16/js/jquery.dataTables.min.js"></script>
<table id="example" class="display" style="width:100%">
        <thead>
            <tr>
                <th>Name</th>
                <th>Position</th>
                <th>Office</th>
                <th>Age</th>
                <th>Start date</th>
                <th>Salary</th>
            </tr>
        </thead>
        <tbody>
            <tr>
                <td>Tiger Nixon</td>
                <td>System Architect</td>
                <td>Edinburgh</td>
                <td>61</td>
                <td>2011/04/25</td>
                <td>$320,800</td>
            </tr>
            <tr>
                <td>Garrett Winters</td>
                <td>Accountant</td>
                <td>Tokyo</td>
                <td>63</td>
                <td>2011/07/25</td>
                <td>$170,750</td>
            </tr>
            <tr>
                <td>Ashton Cox</td>
                <td>Junior Technical Author</td>
                <td>San Francisco</td>
                <td>66</td>
                <td>2009/01/12</td>
                <td>$86,000</td>
            </tr>
            <tr>
                <td>Cedric Kelly</td>
                <td>Senior Javascript Developer</td>
                <td>Edinburgh</td>
                <td>22</td>
                <td>2012/03/29</td>
                <td>$433,060</td>
            </tr>
            <tr>
                <td>Airi Satou</td>
                <td>Accountant</td>
                <td>Tokyo</td>
                <td>33</td>
                <td>2008/11/28</td>
                <td>$162,700</td>
            </tr>
            <tr>
                <td>Brielle Williamson</td>
                <td>Integration Specialist</td>
                <td>New York</td>
                <td>61</td>
                <td>2012/12/02</td>
                <td>$372,000</td>
            </tr>
            <tr>
                <td>Herrod Chandler</td>
                <td>Sales Assistant</td>
                <td>San Francisco</td>
                <td>59</td>
                <td>2012/08/06</td>
                <td>$137,500</td>
            </tr>
            <tr>
                <td>Rhona Davidson</td>
                <td>Integration Specialist</td>
                <td>Tokyo</td>
                <td>55</td>
                <td>2010/10/14</td>
                <td>$327,900</td>
            </tr>
            <tr>
                <td>Colleen Hurst</td>
                <td>Javascript Developer</td>
                <td>San Francisco</td>
                <td>39</td>
                <td>2009/09/15</td>
                <td>$205,500</td>
            </tr>
            <tr>
                <td>Sonya Frost</td>
                <td>Software Engineer</td>
                <td>Edinburgh</td>
                <td>23</td>
                <td>2008/12/13</td>
                <td>$103,600</td>
            </tr>
            <tr>
                <td>Jena Gaines</td>
                <td>Office Manager</td>
                <td>London</td>
                <td>30</td>
                <td>2008/12/19</td>
                <td>$90,560</td>
            </tr>
            <tr>
                <td>Quinn Flynn</td>
                <td>Support Lead</td>
                <td>Edinburgh</td>
                <td>22</td>
                <td>2013/03/03</td>
                <td>$342,000</td>
            </tr>
            <tr>
                <td>Charde Marshall</td>
                <td>Regional Director</td>
                <td>San Francisco</td>
                <td>36</td>
                <td>2008/10/16</td>
                <td>$470,600</td>
            </tr>
            <tr>
                <td>Haley Kennedy</td>
                <td>Senior Marketing Designer</td>
                <td>London</td>
                <td>43</td>
                <td>2012/12/18</td>
                <td>$313,500</td>
            </tr>
            <tr>
                <td>Tatyana Fitzpatrick</td>
                <td>Regional Director</td>
                <td>London</td>
                <td>19</td>
                <td>2010/03/17</td>
                <td>$385,750</td>
            </tr>
            <tr>
                <td>Michael Silva</td>
                <td>Marketing Designer</td>
                <td>London</td>
                <td>66</td>
                <td>2012/11/27</td>
                <td>$198,500</td>
            </tr>
            <tr>
                <td>Paul Byrd</td>
                <td>Chief Financial Officer (CFO)</td>
                <td>New York</td>
                <td>64</td>
                <td>2010/06/09</td>
                <td>$725,000</td>
            </tr>
            <tr>
                <td>Gloria Little</td>
                <td>Systems Administrator</td>
                <td>New York</td>
                <td>59</td>
                <td>2009/04/10</td>
                <td>$237,500</td>
            </tr>
            <tr>
                <td>Bradley Greer</td>
                <td>Software Engineer</td>
                <td>London</td>
                <td>41</td>
                <td>2012/10/13</td>
                <td>$132,000</td>
            </tr>
            <tr>
                <td>Dai Rios</td>
                <td>Personnel Lead</td>
                <td>Edinburgh</td>
                <td>35</td>
                <td>2012/09/26</td>
                <td>$217,500</td>
            </tr>
            <tr>
                <td>Jenette Caldwell</td>
                <td>Development Lead</td>
                <td>New York</td>
                <td>30</td>
                <td>2011/09/03</td>
                <td>$345,000</td>
            </tr>
            <tr>
                <td>Yuri Berry</td>
                <td>Chief Marketing Officer (CMO)</td>
                <td>New York</td>
                <td>40</td>
                <td>2009/06/25</td>
                <td>$675,000</td>
            </tr>
            <tr>
                <td>Caesar Vance</td>
                <td>Pre-Sales Support</td>
                <td>New York</td>
                <td>21</td>
                <td>2011/12/12</td>
                <td>$106,450</td>
            </tr>
            <tr>
                <td>Doris Wilder</td>
                <td>Sales Assistant</td>
                <td>Sidney</td>
                <td>23</td>
                <td>2010/09/20</td>
                <td>$85,600</td>
            </tr>
            <tr>
                <td>Angelica Ramos</td>
                <td>Chief Executive Officer (CEO)</td>
                <td>London</td>
                <td>47</td>
                <td>2009/10/09</td>
                <td>$1,200,000</td>
            </tr>
            <tr>
                <td>Gavin Joyce</td>
                <td>Developer</td>
                <td>Edinburgh</td>
                <td>42</td>
                <td>2010/12/22</td>
                <td>$92,575</td>
            </tr>
            <tr>
                <td>Jennifer Chang</td>
                <td>Regional Director</td>
                <td>Singapore</td>
                <td>28</td>
                <td>2010/11/14</td>
                <td>$357,650</td>
            </tr>
            <tr>
                <td>Brenden Wagner</td>
                <td>Software Engineer</td>
                <td>San Francisco</td>
                <td>28</td>
                <td>2011/06/07</td>
                <td>$206,850</td>
            </tr>
            <tr>
                <td>Fiona Green</td>
                <td>Chief Operating Officer (COO)</td>
                <td>San Francisco</td>
                <td>48</td>
                <td>2010/03/11</td>
                <td>$850,000</td>
            </tr>
            <tr>
                <td>Shou Itou</td>
                <td>Regional Marketing</td>
                <td>Tokyo</td>
                <td>20</td>
                <td>2011/08/14</td>
                <td>$163,000</td>
            </tr>
            <tr>
                <td>Michelle House</td>
                <td>Integration Specialist</td>
                <td>Sidney</td>
                <td>37</td>
                <td>2011/06/02</td>
                <td>$95,400</td>
            </tr>
            <tr>
                <td>Suki Burks</td>
                <td>Developer</td>
                <td>London</td>
                <td>53</td>
                <td>2009/10/22</td>
                <td>$114,500</td>
            </tr>
            <tr>
                <td>Prescott Bartlett</td>
                <td>Technical Author</td>
                <td>London</td>
                <td>27</td>
                <td>2011/05/07</td>
                <td>$145,000</td>
            </tr>
            <tr>
                <td>Gavin Cortez</td>
                <td>Team Leader</td>
                <td>San Francisco</td>
                <td>22</td>
                <td>2008/10/26</td>
                <td>$235,500</td>
            </tr>
            <tr>
                <td>Martena Mccray</td>
                <td>Post-Sales support</td>
                <td>Edinburgh</td>
                <td>46</td>
                <td>2011/03/09</td>
                <td>$324,050</td>
            </tr>
            <tr>
                <td>Unity Butler</td>
                <td>Marketing Designer</td>
                <td>San Francisco</td>
                <td>47</td>
                <td>2009/12/09</td>
                <td>$85,675</td>
            </tr>
            <tr>
                <td>Howard Hatfield</td>
                <td>Office Manager</td>
                <td>San Francisco</td>
                <td>51</td>
                <td>2008/12/16</td>
                <td>$164,500</td>
            </tr>
            <tr>
                <td>Hope Fuentes</td>
                <td>Secretary</td>
                <td>San Francisco</td>
                <td>41</td>
                <td>2010/02/12</td>
                <td>$109,850</td>
            </tr>
            <tr>
                <td>Vivian Harrell</td>
                <td>Financial Controller</td>
                <td>San Francisco</td>
                <td>62</td>
                <td>2009/02/14</td>
                <td>$452,500</td>
            </tr>
            <tr>
                <td>Timothy Mooney</td>
                <td>Office Manager</td>
                <td>London</td>
                <td>37</td>
                <td>2008/12/11</td>
                <td>$136,200</td>
            </tr>
            <tr>
                <td>Jackson Bradshaw</td>
                <td>Director</td>
                <td>New York</td>
                <td>65</td>
                <td>2008/09/26</td>
                <td>$645,750</td>
            </tr>
            <tr>
                <td>Olivia Liang</td>
                <td>Support Engineer</td>
                <td>Singapore</td>
                <td>64</td>
                <td>2011/02/03</td>
                <td>$234,500</td>
            </tr>
            <tr>
                <td>Bruno Nash</td>
                <td>Software Engineer</td>
                <td>London</td>
                <td>38</td>
                <td>2011/05/03</td>
                <td>$163,500</td>
            </tr>
            <tr>
                <td>Sakura Yamamoto</td>
                <td>Support Engineer</td>
                <td>Tokyo</td>
                <td>37</td>
                <td>2009/08/19</td>
                <td>$139,575</td>
            </tr>
            <tr>
                <td>Thor Walton</td>
                <td>Developer</td>
                <td>New York</td>
                <td>61</td>
                <td>2013/08/11</td>
                <td>$98,540</td>
            </tr>
            <tr>
                <td>Finn Camacho</td>
                <td>Support Engineer</td>
                <td>San Francisco</td>
                <td>47</td>
                <td>2009/07/07</td>
                <td>$87,500</td>
            </tr>
            <tr>
                <td>Serge Baldwin</td>
                <td>Data Coordinator</td>
                <td>Singapore</td>
                <td>64</td>
                <td>2012/04/09</td>
                <td>$138,575</td>
            </tr>
            <tr>
                <td>Zenaida Frank</td>
                <td>Software Engineer</td>
                <td>New York</td>
                <td>63</td>
                <td>2010/01/04</td>
                <td>$125,250</td>
            </tr>
            <tr>
                <td>Zorita Serrano</td>
                <td>Software Engineer</td>
                <td>San Francisco</td>
                <td>56</td>
                <td>2012/06/01</td>
                <td>$115,000</td>
            </tr>
            <tr>
                <td>Jennifer Acosta</td>
                <td>Junior Javascript Developer</td>
                <td>Edinburgh</td>
                <td>43</td>
                <td>2013/02/01</td>
                <td>$75,650</td>
            </tr>
            <tr>
                <td>Cara Stevens</td>
                <td>Sales Assistant</td>
                <td>New York</td>
                <td>46</td>
                <td>2011/12/06</td>
                <td>$145,600</td>
            </tr>
            <tr>
                <td>Hermione Butler</td>
                <td>Regional Director</td>
                <td>London</td>
                <td>47</td>
                <td>2011/03/21</td>
                <td>$356,250</td>
            </tr>
            <tr>
                <td>Lael Greer</td>
                <td>Systems Administrator</td>
                <td>London</td>
                <td>21</td>
                <td>2009/02/27</td>
                <td>$103,500</td>
            </tr>
            <tr>
                <td>Jonas Alexander</td>
                <td>Developer</td>
                <td>San Francisco</td>
                <td>30</td>
                <td>2010/07/14</td>
                <td>$86,500</td>
            </tr>
            <tr>
                <td>Shad Decker</td>
                <td>Regional Director</td>
                <td>Edinburgh</td>
                <td>51</td>
                <td>2008/11/13</td>
                <td>$183,000</td>
            </tr>
            <tr>
                <td>Michael Bruce</td>
                <td>Javascript Developer</td>
                <td>Singapore</td>
                <td>29</td>
                <td>2011/06/27</td>
                <td>$183,000</td>
            </tr>
            <tr>
                <td>Donna Snider</td>
                <td>Customer Support</td>
                <td>New York</td>
                <td>27</td>
                <td>2011/01/25</td>
                <td>$112,000</td>
            </tr>
        </tbody>
        <tfoot>
            <tr>
                <th>Name</th>
                <th>Position</th>
                <th>Office</th>
                <th>Age</th>
                <th>Start date</th>
                <th>Salary</th>
            </tr>
        </tfoot>
    </table>