WordPress Walker menu for number of child posts

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I am looking to display the number of child posts for a hierarchical parent post in a wordpress menu. So, I will be adding the parent post to the menu. Obviously I will have to go with a custom Walker but I am unsure where to begin.

ie:

Menu Item (8)
Menu Item (15)
Menu Item (7)
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  1. WordPress stores the parent/child menu items relation via custom field called _menu_item_menu_item_parent. Therefore you can query for the sub-menu items in the following way: 

    class add_child_numbers_walker extends Walker_Nav_Menu {
    function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
        global $wp_query;
        $indent = ( $depth ) ? str_repeat( "t", $depth ) : '';

        $class_names = '';

        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $classes[] = 'menu-item-' . $item->ID;

        $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

        $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
        $id = $id ? ' id="' . esc_attr( $id ) . '"' : '';

        $output .= $indent . '<li' . $id . $class_names .'>';

        $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
        $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
        $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
        $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';

        $submenus = $depth == 0 ? get_posts( array( 'post_type' => 'nav_menu_item', 'numberposts' => -1, 'orderby' => 'menu_order', 'order' => 'ASC', 'meta_query' => array( array( 'key' => '_menu_item_menu_item_parent', 'value' => $item->ID ) ) ) ) : false;

        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        $item_output .= '</a>';
        $item_output .= $submenus ? ' <span class="submenus-count">(' . count( $submenus ) . ')</span>' : '';
        $item_output .= $args->after;

        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }
}

    This walker will add <span class="submenus-count">(X)</span> after all top-level links.

    You can call the menu like that:
    wp_nav_menu(array('theme_location' => 'theme-location', 'container' => '', 'walker' => new add_child_numbers_walker()));

    Since you said that you want to do a custom function to display your menus, here is a simple solution:

    function my_custom_nav( $post_type = 'page' ) {
    $current = is_singular() ? get_the_ID() : false;

    $posts = get_posts( array( 'post_type' => $post_type, 'numberposts' => -1, 'orderby' => 'menu_order', 'order' => 'ASC', 'child_of' => 0, 'post_parent' => 0 ) );
    if ( $posts ) {
        echo '<ul class="custom-nav ' . esc_attr( $post_type ) . '-nav">';
        foreach ($posts as $p) {
            $child_posts = get_posts( array( 'post_type' => $post_type, 'numberposts' => -1, 'orderby' => 'menu_order', 'order' => 'ASC', 'child_of' => $p->ID, 'post_parent' => $p->ID, 'fields' => 'ids' ) );
            $child = $child_posts ? ' <span class="submenus-count">(' . count( $child_posts ) . ')</span>' : '';
            $class = '';
            if ( $p->ID == $current ) {
                $class = 'current_page_item';
            } elseif ( $current && in_array( $current, $child_posts ) ) {
                $class = 'current_page_ancestor';
            }
            $class = '' != $class ? ' class="' . $class . '"' : '';
            echo '<li' . $class . '><a href="' . get_permalink( $p->ID ) . '">' . get_the_title( $p->ID ) . '</a>' . $child . '</li>';
        }
        echo '</ul>';
    }

}

    You can then display your menu like that: 

    <?php my_custom_nav( 'custom_post_type' ); ?>