Function is_installed 

pub fn is_installed(name: &str, cache: Option<&HashSet<String>>) -> bool

What: Check if a package is installed, using cache if provided or querying pacman directly.

Inputs:

• name: Package name to check.
• cache: Optional reference to a HashSet<String> containing installed package names.

Output:

• Returns true if the package is installed, false otherwise.

Details:

• If cache is provided, checks membership in the cache (O(1) lookup).
• If cache is None, queries pacman directly using pacman -Q.
• Gracefully degrades: returns false on error.

Example

use arch_toolkit::index::is_installed;
use std::collections::HashSet;

let cache = HashSet::from(["vim".to_string(), "git".to_string()]);
assert!(is_installed("vim", Some(&cache)));
assert!(!is_installed("nonexistent", Some(&cache)));