How to restrict WooCommerce cart item quantity to one for specific item

In my custom Woocommerce template I want to restrict the quantity of a product to 1.

I'm working from Empty cart upon page load allowing add to cart in WooCommerce answer to my previous question.

This is what I have:

 <?php 
$current_product_id = 5; // The product ID 
$cart               = WC()->cart; // The WC_Cart Object
       $quantity = $cart_item['quantity'];//the quantity
// When cart is not empty 
if ( ! $cart->is_empty() ) {
    // Loop through cart items
    foreach( $cart->get_cart() as $cart_item_key => $cart_item ) {
        // If the cart item is not the current defined product ID
        if( $current_product_id != $cart_item['product_id'] ) {
            $cart->remove_cart_item( $cart_item_key ); // remove it from cart
        }
}
 if( $quantity >=1) {
    $cart->remove_cart_item( $cart_item_key ); // remove it from cart
 } }}
?>

It kind'a works. But I want checkout on the same page, and with this code checkout does not update when product is added to cart.

To restrict the quantity to 1 you will use the WC_cart set_quantity() method this way:

<?php 
$current_product_id = 5; // The product ID 
$cart               = WC()->cart; // The WC_Cart Object

// When cart is not empty 
if ( ! $cart->is_empty() ) {
    // Loop through cart items
    foreach( $cart->get_cart() as $cart_item_key => $cart_item ) {
        // If the cart item is not the current defined product ID
        if( $current_product_id != $cart_item['product_id'] ) {
            $cart->remove_cart_item( $cart_item_key ); // remove it from cart
        } 
        // If the cart item is the current defined product ID and quantity is more than 1
        elseif( $cart_item['quantity'] > 1 ) {
            $cart->set_quantity( $cart_item_key, 1 ); // Set the quantity to 1
        }
    }
}
?>

It should work.