A-Z index list of category

How to make an alphabetical list of category??

i want someting like what

list of letter with link A

A category list

Art
Artist
Arc
Arm

B category list
C category list

i find this code but is for tags

<?php

     $list = '';
	$tags = get_terms('post_tag' );
	$groups = array();
	if( $tags && is_array( $tags ) ) {
		foreach( $tags as $tag ) {
			$first_letter = strtoupper( $tag->name[0] );
			$groups[ $first_letter ][] = $tag;
		}
			if( !empty( $groups ) ) {{
          	$index_row .='<ul class="topindex">';
         foreach ($groups as $letter => $tags) {
           	$index_row .= '<li><h4><a href="#' . $letter . '" title="' . $letter . '">' . apply_filters( 'the_title', $letter ) . '</a></h4></li>';
		}
				$index_row .='</ul><br class="clear" />';} 

				 $list .= '<ul class="index">';
			 foreach( $groups as $letter => $tags ) {
            $list .= '<li><a name="' . $letter . '"></a><h5><a href="#tags_top" title="back to top">' . apply_filters( 'the_title', $letter ) . '</a></h5>';
				$list .= '<ul class="links">';
				foreach( $tags as $tag ) {
               $url = attribute_escape( get_tag_link( $tag->term_id ) );
					$name = apply_filters( 'the_title', $tag->name );
               $list .= '<li><a title="' . $name . '" href="' . $url . '">' . $name . '</a></li>';

	} 		 $list .= '</ul></li>';
			} 	$list .= '</ul>';
		}
	}else $list .= '<p>Sorry, but no tags were found</p>';

	?>
<a name="tags_top"></a>
<?php print $index_row; ?>
<?php print $list; ?>

ul.topindex, .topindex li {display:inline;float:left;padding-right:5px}