How can database queries be optimized to avoid unnecessary calls within recursive functions in PHP?

To optimize database queries within recursive functions in PHP, you can implement a technique called memoization. Memoization involves storing the results of expensive function calls in memory so that they can be quickly retrieved if the same function is called again with the same input parameters. This can help avoid unnecessary database queries within recursive functions by reusing previously calculated results.

// Implementing memoization to optimize database queries within recursive functions
function fibonacci($n, $cache = []) {
    if (array_key_exists($n, $cache)) {
        return $cache[$n];
    }
    
    if ($n <= 1) {
        return $n;
    }
    
    $result = fibonacci($n - 1, $cache) + fibonacci($n - 2, $cache);
    $cache[$n] = $result;
    
    return $result;
}

// Example usage
echo fibonacci(10);