search: cache remote tap formulae

Closes Homebrew/homebrew#40775.

Signed-off-by: Xu Cheng <xucheng@me.com>

Library/Homebrew/cmd/search.rb

@@ -108,11 +108,11 @@ module Homebrew
       return []
     end
 
-    results = []
+    @@remote_tap_formulae ||= Hash.new do |cache, key|
+      user, repo = key.split("/", 2)
       tree = {}
 
       GitHub.open "https://api.github.com/repos/#{user}/homebrew-#{repo}/git/trees/HEAD?recursive=1" do |json|
-      user = user.downcase if user == "Homebrew" # special handling for the Homebrew organization
         json["tree"].each do |object|
           next unless object["type"] == "blob"
 
@@ -126,18 +126,18 @@ module Homebrew
       end
 
       paths = tree["Formula"] || tree["HomebrewFormula"] || tree["Casks"] || tree["."] || []
-    paths.each do |path|
-      name = File.basename(path, ".rb")
-      results << "#{user}/#{repo}/#{name}" if rx === name
+      cache[key] = paths.map { |path| File.basename(path, ".rb") }
     end
+
+    names = @@remote_tap_formulae["#{user}/#{repo}"]
+    user = user.downcase if user == "Homebrew" # special handling for the Homebrew organization
+    names.select { |name| rx === name }.map { |name| "#{user}/#{repo}/#{name}" }
   rescue GitHub::HTTPNotFoundError => e
     opoo "Failed to search tap: #{user}/#{repo}. Please run `brew update`"
     []
   rescue GitHub::Error => e
     SEARCH_ERROR_QUEUE << e
     []
-  else
-    results
   end
 
   def search_formulae rx