Wordpress search optimization: limit search result (not post_per_page) - wordpress

Question

I have searched stackoverflow. none of them apply to my question. Most of the answer just about limit per page (how many posts to show per page, not how many result to search)
I'm trying to speed up wordpress search.
For example I have 10millions post to search. and user type "a". It will take very long to search all of that because wordpress is using SQL_CALC_FOUND_ROWS.
The fact is that there is no need to search milions of rows (posts) and the answer "1000+" is enough for users. So we need to stop search after we found 1000 results.
The only way i can think of is to use:
'no_found_rows' => true
But then we dont have pagination functionality.
Or maybe we can use a separate query to get the result and to count how many posts found (with limiter)?
I dont understand how can wordpress doesnt have this functionality. Even big site like amazon limit the search result. So if you search "a" or "usb", it will return just the first 20 pages.

Answer 1

Try this code, its works on my wordpress with 1M posts
If you use search for custom post type, change
post_type = 'post'
to your post type name
add_filter('pre_get_posts', 'fix_search_pagination_with_nfr', 1000);
function fix_search_pagination_with_nfr() {
global $wp_query, $wpdb;
if ( ! is_admin() && $wp_query->is_main_query() && $wp_query->is_search() ) {
$wp_query->query_vars['no_found_rows'] = 1;
$wp_query->found_posts = $wpdb->get_var( "SELECT COUNT(*) FROM wp_posts WHERE 1=1 AND wp_posts.post_type = 'post' AND (wp_posts.post_status = 'publish' OR wp_posts.post_status = 'private')" );
$wp_query->found_posts = apply_filters_ref_array( 'found_posts', array( $wp_query->found_posts, &$wp_query ) );
if($wp_query->query_vars['posts_per_page'] > 0) {
$wp_query->max_num_pages = ceil($wp_query->found_posts / $wp_query->query_vars['posts_per_page']);
} else {
$wp_query->max_num_pages = 0;
}
}
return $wp_query;
}