WP_Query Multiple Category Parameters not working - php

Question

Situation:
I cannot successfully a category parameter within WP_Query that searches within two categories mixing both OR and AND relationships.
Explanation:
I've got a search/filter that sorts by region, month, and year and it works great! When using the category_name parameter, it will successfully search for a region.
<?php // These grab data from the URL which are submitted by the form
$p_topi = $_GET['topic'];
$p_reg = $_GET['region'];
$p_mon = $_GET['mon'];
$p_year = (int) $_GET['yr'];
?>
<?php
$archive_args = array(
'post_type' => 'thought_leadership',
'category_name' => $p_reg, // Pay attention to this
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
$archive_query = new WP_Query($archive_args);
if ($archive_query->have_posts()) : while ($archive_query->have_posts()) : $archive_query->the_post(); ?>
I was asked to add sorting by topic. I tested it by replacing the variable used with category_name and that worked well.
$archive_args = array(
'post_type' => 'thought_leadership',
'category_name' => $p_topi, // Changed the variable to topic
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
I then tried combining the two variables and it sort of worked. Specifically, it worked as an OR operator, filtering by region or topic. It will not filter by both.
$archive_args = array(
'post_type' => 'thought_leadership',
'category_name' => "$p_topi, $p_reg", // Combined the variables
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
I then tried using the + symbol to make the parameter accept both variables at the same time. It worked, but now it won't work as an OR operator. In other words, I have to select a topic and region, or the search won't find any results.
$archive_args = array(
'post_type' => 'thought_leadership',
'category_name' => "$p_topi+$p_reg", // + makes it an AND operator
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
I researched WP_Query and found this excellent reference: https://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters
I tried category__and but it returns with no posts matching that criteria.
$archive_args = array(
'post_type' => 'thought_leadership',
'category__and' => array( 12, 5 ), // 12 = ID for topic, 5 = ID for region
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
I also tested category__in but found that it will not display children of a category. That's a problem because both topic and region have children. Like category__and it returns with no posts matching that criteria.
$archive_args = array(
'post_type' => 'thought_leadership',
'category__in' => array( 12, 5 ),
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
);
As suggested by #Muhammad tayyab, I tried using tax_query. I got it work on an && basis.
$archive_args = array(
'post_type' => 'thought_leadership',
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
'tax_query' => array(
'relation' => 'AND',
array(
'taxonomy' => 'category', // correct
'field' => 'slug', // correct
'terms' => $p_reg,
),
array(
'taxonomy' => 'category', // correct
'field' => 'slug', // correct
'terms' => $p_topi,
)
,)
);
But I couldn't successfully get the OR operator to work with nested arrays.
$archive_args = array(
'post_type' => 'thought_leadership',
'year' => $p_year,
'monthnum'=> $p_mon,
'posts_per_page' => 100,
'tax_query' => array(
'relation' => 'OR',
array(
'taxonomy' => 'category',
'field' => 'slug',
'terms' => $p_reg,
),
array(
'relation' => 'AND',
array(
'taxonomy' => 'category',
'field' => 'slug',
'terms' => $p_reg,
),
array(
'taxonomy' => 'category',
'field' => 'slug',
'terms' => $p_topi,
),
),
),
);
Primary Question:
Do you know of any way to create a search which will accept 0, 1 or 2 parameters? Said differently, I need to set it up so my users can search for region and/or topic or none at all.

Answer 1

Your question is vague but this might help:
$args = array(
'post_type' => 'post',
'tax_query' => array(
'relation' => 'AND',
array(
'taxonomy' => 'movie_genre',
'field' => 'slug',
'terms' => array( 'action', 'comedy' ),
),
array(
'taxonomy' => 'actor',
'field' => 'term_id',
'terms' => array( 103, 115, 206 ),
'operator' => 'NOT IN',
),
),
);
$query = new WP_Query( $args );
You can search by multiple taxonomies this way. You can use in relation to specify and or not relationship.