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{"payload":{"allShortcutsEnabled":false,"path":"Priority Queue","repo":{"id":324936366,"defaultBranch":"master","name":"swift-algorithm-club","ownerLogin":"vaquarkhan","currentUserCanPush":false,"isFork":true,"isEmpty":false,"createdAt":"2020-12-28T06:59:09.000Z","ownerAvatar":"https://avatars.githubusercontent.com/u/3491908?v=4","public":true,"private":false,"isOrgOwned":false},"currentUser":null,"refInfo":{"name":"master","listCacheKey":"v0:1616426006.916799","canEdit":false,"refType":"branch","currentOid":"2fdd8b8be1b3fcd17ad0394053e672f2bd1d3076"},"tree":{"items":[{"name":"Tests","path":"Priority Queue/Tests","contentType":"directory"},{"name":"PriorityQueue.swift","path":"Priority Queue/PriorityQueue.swift","contentType":"file"},{"name":"README.markdown","path":"Priority Queue/README.markdown","contentType":"file"}],"templateDirectorySuggestionUrl":null,"readme":{"displayName":"README.markdown","richText":"\u003carticle class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePriority Queue\u003c/h1\u003e\u003ca id=\"user-content-priority-queue\" class=\"anchor\" aria-label=\"Permalink: Priority Queue\" href=\"#priority-queue\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eA priority queue is a \u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Queue\"\u003equeue\u003c/a\u003e where the most important element is always at the front.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe queue can be a \u003cem\u003emax-priority\u003c/em\u003e queue (largest element first) or a \u003cem\u003emin-priority\u003c/em\u003e queue (smallest element first).\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWhy use a priority queue?\u003c/h2\u003e\u003ca id=\"user-content-why-use-a-priority-queue\" class=\"anchor\" aria-label=\"Permalink: Why use a priority queue?\" href=\"#why-use-a-priority-queue\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePriority queues are useful for algorithms that need to process a (large) number of items and where you repeatedly need to identify which one is now the biggest or smallest -- or however you define \"most important\".\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExamples of algorithms that can benefit from a priority queue:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eEvent-driven simulations. Each event is given a timestamp and you want events to be performed in order of their timestamps. The priority queue makes it easy to find the next event that needs to be simulated.\u003c/li\u003e\n\u003cli\u003eDijkstra's algorithm for graph searching uses a priority queue to calculate the minimum cost.\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Huffman%20Coding\"\u003eHuffman coding\u003c/a\u003e for data compression. This algorithm builds up a compression tree. It repeatedly needs to find the two nodes with the smallest frequencies that do not have a parent node yet.\u003c/li\u003e\n\u003cli\u003eA* pathfinding for artificial intelligence.\u003c/li\u003e\n\u003cli\u003eLots of other places!\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eWith a regular queue or plain old array you'd need to scan the entire sequence over and over to find the next largest item. A priority queue is optimized for this sort of thing.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWhat can you do with a priority queue?\u003c/h2\u003e\u003ca id=\"user-content-what-can-you-do-with-a-priority-queue\" class=\"anchor\" aria-label=\"Permalink: What can you do with a priority queue?\" href=\"#what-can-you-do-with-a-priority-queue\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCommon operations on a priority queue:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cstrong\u003eEnqueue\u003c/strong\u003e: inserts a new element into the queue.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDequeue\u003c/strong\u003e: removes and returns the queue's most important element.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eFind Minimum\u003c/strong\u003e or \u003cstrong\u003eFind Maximum\u003c/strong\u003e: returns the most important element but does not remove it.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eChange Priority\u003c/strong\u003e: for when your algorithm decides that an element has become more important while it's already in the queue.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eHow to implement a priority queue\u003c/h2\u003e\u003ca id=\"user-content-how-to-implement-a-priority-queue\" class=\"anchor\" aria-label=\"Permalink: How to implement a priority queue\" href=\"#how-to-implement-a-priority-queue\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThere are different ways to implement priority queues:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eAs a \u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Ordered%20Array\"\u003esorted array\u003c/a\u003e. The most important item is at the end of the array. Downside: inserting new items is slow because they must be inserted in sorted order.\u003c/li\u003e\n\u003cli\u003eAs a balanced \u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Binary%20Search%20Tree\"\u003ebinary search tree\u003c/a\u003e. This is great for making a double-ended priority queue because it implements both \"find minimum\" and \"find maximum\" efficiently.\u003c/li\u003e\n\u003cli\u003eAs a \u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Heap\"\u003eheap\u003c/a\u003e. The heap is a natural data structure for a priority queue. In fact, the two terms are often used as synonyms. A heap is more efficient than a sorted array because a heap only has to be partially sorted. All heap operations are \u003cstrong\u003eO(log n)\u003c/strong\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eHere's a Swift priority queue based on a heap:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-swift notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public struct PriorityQueue\u0026lt;T\u0026gt; {\n fileprivate var heap: Heap\u0026lt;T\u0026gt;\n\n public init(sort: (T, T) -\u0026gt; Bool) {\n heap = Heap(sort: sort)\n }\n\n public var isEmpty: Bool {\n return heap.isEmpty\n }\n\n public var count: Int {\n return heap.count\n }\n\n public func peek() -\u0026gt; T? {\n return heap.peek()\n }\n\n public mutating func enqueue(element: T) {\n heap.insert(element)\n }\n\n public mutating func dequeue() -\u0026gt; T? {\n return heap.remove()\n }\n\n public mutating func changePriority(index i: Int, value: T) {\n return heap.replace(index: i, value: value)\n }\n}\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003estruct\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePriorityQueue\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e\u0026lt;\u003c/span\u003eT\u003cspan class=\"pl-c1\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003efileprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003evar\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003e\u003cspan class=\"pl-c1\"\u003eheap\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eHeap\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e\u0026gt;\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-v\"\u003einit\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003esort\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003e\u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e,\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u0026gt;\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eBool\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n heap \u003cspan class=\"pl-c1\"\u003e=\u003c/span\u003e \u003cspan class=\"pl-en\"\u003eHeap\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003esort\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e sort\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003evar\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003e\u003cspan class=\"pl-c1\"\u003eisEmpty\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eBool\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003eisEmpty\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003evar\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003e\u003cspan class=\"pl-c1\"\u003ecount\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eInt\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003ecount\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-en\"\u003efunc\u003c/span\u003e peek\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u0026gt;\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e\u003cspan class=\"pl-c1\"\u003e?\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003e\u003cspan class=\"pl-en\"\u003epeek\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003emutating\u003c/span\u003e \u003cspan class=\"pl-en\"\u003efunc\u003c/span\u003e enqueue\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003eelement\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003e\u003cspan class=\"pl-en\"\u003einsert\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003eelement\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003emutating\u003c/span\u003e \u003cspan class=\"pl-en\"\u003efunc\u003c/span\u003e dequeue\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-c1\"\u003e-\u0026gt;\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003e\u003cspan class=\"pl-c1\"\u003e?\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003e\u003cspan class=\"pl-en\"\u003eremove\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003emutating\u003c/span\u003e \u003cspan class=\"pl-en\"\u003efunc\u003c/span\u003e changePriority\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003eindex i\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eInt\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e,\u003c/span\u003e value\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eT\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e \u003cspan class=\"pl-kos\"\u003e{\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e heap\u003cspan class=\"pl-kos\"\u003e.\u003c/span\u003e\u003cspan class=\"pl-en\"\u003ereplace\u003c/span\u003e\u003cspan class=\"pl-kos\"\u003e(\u003c/span\u003eindex\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e i\u003cspan class=\"pl-kos\"\u003e,\u003c/span\u003e value\u003cspan class=\"pl-kos\"\u003e:\u003c/span\u003e value\u003cspan class=\"pl-kos\"\u003e)\u003c/span\u003e\n \u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\n\u003cspan class=\"pl-kos\"\u003e}\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAs you can see, there's nothing much to it. Making a priority queue is easy if you have a \u003ca href=\"/vaquarkhan/swift-algorithm-club/blob/master/Heap\"\u003eheap\u003c/a\u003e because a heap \u003cem\u003eis\u003c/em\u003e pretty much a priority queue.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSee also\u003c/h2\u003e\u003ca id=\"user-content-see-also\" class=\"anchor\" aria-label=\"Permalink: See also\" href=\"#see-also\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Priority_queue\" rel=\"nofollow\"\u003ePriority Queue on Wikipedia\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cem\u003eWritten for Swift Algorithm Club by Matthijs Hollemans\u003c/em\u003e\u003c/p\u003e\n\u003c/article\u003e","errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Priority Queue","anchor":"priority-queue","htmlText":"Priority Queue"},{"level":2,"text":"Why use a priority queue?","anchor":"why-use-a-priority-queue","htmlText":"Why use a priority queue?"},{"level":2,"text":"What can you do with a priority queue?","anchor":"what-can-you-do-with-a-priority-queue","htmlText":"What can you do with a priority queue?"},{"level":2,"text":"How to implement a 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