var Component=(()=>{var d=Object.create;var l=Object.defineProperty;var u=Object.getOwnPropertyDescriptor;var m=Object.getOwnPropertyNames;var h=Object.getPrototypeOf,N=Object.prototype.hasOwnProperty;var k=(a,n)=>()=>(n||a((n={exports:{}}).exports,n),n.exports),b=(a,n)=>{for(var s in n)l(a,s,{get:n[s],enumerable:!0})},t=(a,n,s,i)=>{if(n&&typeof n=="object"||typeof n=="function")for(let c of m(n))!N.call(a,c)&&c!==s&&l(a,c,{get:()=>n[c],enumerable:!(i=u(n,c))||i.enumerable});return a};var y=(a,n,s)=>(s=a!=null?d(h(a)):{},t(n||!a||!a.__esModule?l(s,"default",{value:a,enumerable:!0}):s,a)),f=a=>t(l({},"__esModule",{value:!0}),a);var r=k((P,o)=>{o.exports=_jsx_runtime});var x={};b(x,{default:()=>q,frontmatter:()=>w});var e=y(r()),w={title:"Priority Queue",slug:"priority-queue",description:"This article dives into the fundamentals of Priority Queues exploring their key operations, use cases, and detailed implementations in Python, Java, C++, Go, and Rust, with a focus on efficiency and real-world applications.",image:"https://cdn.procoding.org/datastructures/heap/priority-queue.png",publishedAt:"2024-08-31",updatedAt:"2024-08-31",isPublished:!0,category:"Data Structures",metadescription:"This article dives into the fundamentals of Priority Queues, exploring their key operations, use cases, and detailed implementations in Python, Java, C++, Go, and Rust, with a focus on efficiency and real-world applications.",keywords:"heap,priorityqueue,datastructures",subcategory:"heap",tags:["heap","priorityqueue","datastructures"],author:"abhishek",id:"f3181129-0bd3-4ebe-92bf-6e9b725efec0"};function p(a){let n=Object.assign({p:"p",img:"img",h2:"h2",ol:"ol",li:"li",strong:"strong",ul:"ul",code:"code",h3:"h3",blockquote:"blockquote",pre:"pre",span:"span"},a.components);return(0,e.jsxs)(e.Fragment,{children:[(0,e.jsx)(n.p,{children:(0,e.jsx)(n.img,{src:"https://cdn.procoding.org/datastructures/heap/priority-queue.png",alt:"Priority Queue",title:"Priority Queue"})}),` `,(0,e.jsx)(n.p,{children:"A priority queue is a specialized type of data structure where each element is associated with a priority, and the element with the highest priority is served before other elements. Unlike regular queues, where elements are served in a first-come, first-served (FIFO) manner, priority queues order elements based on their priority."}),` `,(0,e.jsx)(n.h2,{children:"Key Concepts of Priority Queues"}),` `,(0,e.jsxs)(n.ol,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Priority"}),": Each element in a priority queue has a priority level. Elements with higher priorities are dequeued before elements with lower priorities."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Order of Insertion"}),": When two elements have the same priority, the order of insertion is maintained. The element that was inserted first will be dequeued first (this is called a stable priority queue)."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Underlying Data Structure"}),": Priority queues can be implemented using different data structures, but heaps (particularly binary heaps) are the most common due to their efficient insertion and deletion operations."]}),` `]}),` `,(0,e.jsx)(n.h2,{children:"Types of Priority Queues"}),` `,(0,e.jsxs)(n.ol,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Min-Priority Queue"}),": In a min-priority queue, the element with the lowest priority is dequeued first. This is often implemented using a min-heap."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Max-Priority Queue"}),": In a max-priority queue, the element with the highest priority is dequeued first. This can be implemented using a max-heap or by negating the priorities in a min-heap."]}),` `]}),` `,(0,e.jsx)(n.h2,{children:"Operations on a Priority Queue"}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsxs)(n.strong,{children:["Insertion (",(0,e.jsx)(n.code,{children:"enqueue"}),")"]}),": Adding a new element to the priority queue. The element is placed in the correct position based on its priority."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsxs)(n.strong,{children:["Deletion (",(0,e.jsx)(n.code,{children:"dequeue"}),")"]}),": Removing the element with the highest (or lowest in a min-priority queue) priority from the queue."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Peek"}),": Viewing the element with the highest priority without removing it from the queue."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Is Empty"}),": Checking if the priority queue is empty."]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Size"}),": Returning the number of elements currently in the priority queue."]}),` `]}),` `,(0,e.jsx)(n.h2,{children:"Which data structure to use for Priority Queue?"}),` `,(0,e.jsx)(n.p,{children:"To implement a priority queue, several data structures can be used, each with its own trade-offs in terms of time complexity and ease of implementation. The most common data structures for implementing a priority queue are:"}),` `,(0,e.jsxs)(n.h3,{children:["1. ",(0,e.jsx)(n.strong,{children:"Binary Heap"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": Binary Tree"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Variants"}),": Min-Heap, Max-Heap"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(log n)"}),` `,(0,e.jsx)(n.li,{children:"Deletion (Extract-Min/Extract-Max): O(log n)"}),` `,(0,e.jsx)(n.li,{children:"Peek (Get-Min/Get-Max): O(1)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Efficient for implementing a priority queue due to logarithmic time complexity for insertion and deletion operations."}),` `,(0,e.jsx)(n.li,{children:"Heaps are relatively simple to implement."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Not ideal for dynamic or highly variable data where you need to frequently change priorities (e.g., decrease-key operations)."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.h3,{children:["2. ",(0,e.jsx)(n.strong,{children:"Binary Search Tree (BST)"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": Tree"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Variants"}),": Self-balancing BSTs like AVL Tree, Red-Black Tree"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(log n) (for balanced trees)"}),` `,(0,e.jsx)(n.li,{children:"Deletion: O(log n) (for balanced trees)"}),` `,(0,e.jsx)(n.li,{children:"Peek (Find-Min/Find-Max): O(log n) (for balanced trees)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Allows for all priority queue operations with logarithmic time complexity."}),` `,(0,e.jsx)(n.li,{children:"Provides sorted order traversal, which might be useful in some applications."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"More complex to implement than heaps."}),` `,(0,e.jsx)(n.li,{children:"Insertions and deletions are more computationally expensive due to the need to maintain balance."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.h3,{children:["3. ",(0,e.jsx)(n.strong,{children:"Fibonacci Heap"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": Heap"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(1)"}),` `,(0,e.jsx)(n.li,{children:"Deletion (Extract-Min): O(log n)"}),` `,(0,e.jsx)(n.li,{children:"Decrease-Key: O(1)"}),` `,(0,e.jsx)(n.li,{children:"Peek: O(1)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Very efficient for algorithms like Dijkstra's shortest path, where the decrease-key operation is frequent."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"More complex to implement compared to binary heaps."}),` `,(0,e.jsx)(n.li,{children:"Higher constant factors can make it less efficient in practice for some scenarios."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.h3,{children:["4. ",(0,e.jsx)(n.strong,{children:"Unordered List"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": List/Array"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(1)"}),` `,(0,e.jsx)(n.li,{children:"Deletion (Extract-Min/Extract-Max): O(n) (requires linear search)"}),` `,(0,e.jsx)(n.li,{children:"Peek: O(n)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Very easy to implement."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Inefficient for priority queue operations, especially for large datasets."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.h3,{children:["5. ",(0,e.jsx)(n.strong,{children:"Ordered List"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": List/Array"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(n) (requires shifting elements to maintain order)"}),` `,(0,e.jsx)(n.li,{children:"Deletion (Extract-Min/Extract-Max): O(1)"}),` `,(0,e.jsx)(n.li,{children:"Peek: O(1)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Provides quick access to the element with the highest priority."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion is inefficient due to the need to maintain order."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.h3,{children:["6. ",(0,e.jsx)(n.strong,{children:"Pairing Heap"})]}),` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Type"}),": Heap"]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Time Complexity"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Insertion: O(1)"}),` `,(0,e.jsx)(n.li,{children:"Deletion (Extract-Min): O(log n)"}),` `,(0,e.jsx)(n.li,{children:"Decrease-Key: Amortized O(1)"}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Pros"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Simpler than Fibonacci heaps with similar time complexity."}),` `]}),` `]}),` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"Cons"}),":",` `,(0,e.jsxs)(n.ul,{children:[` `,(0,e.jsx)(n.li,{children:"Less known and understood than binary heaps or Fibonacci heaps."}),` `]}),` `]}),` `]}),` `,(0,e.jsxs)(n.blockquote,{children:[` `,(0,e.jsxs)(n.p,{children:[(0,e.jsx)(n.strong,{children:"Binary Heap"})," is the most common and practical choice for implementing a priority queue due to its balanced performance across operations and relatively simple implementation."]}),` `,(0,e.jsxs)(n.p,{children:[(0,e.jsx)(n.strong,{children:"Fibonacci Heaps"})," are theoretically more efficient for certain operations but are complex to implement."]}),` `,(0,e.jsxs)(n.p,{children:[(0,e.jsx)(n.strong,{children:"Binary Search Trees"})," can be used when you need additional operations like range queries or ordered traversal."]}),` `,(0,e.jsxs)(n.p,{children:[(0,e.jsx)(n.strong,{children:"Unordered or Ordered Lists"})," are simple but generally inefficient for large datasets."]}),` `]}),` `,(0,e.jsxs)(n.p,{children:["In most cases, ",(0,e.jsx)(n.strong,{children:"binary heaps"})," (either as a min-heap or max-heap) are recommended for implementing priority queues because they provide a good balance between performance and ease of implementation."]}),` `,(0,e.jsx)(n.h2,{children:"Priority Queue Implementation"}),` `,(0,e.jsx)(n.p,{children:"We will be implementing Max-Priority Queue using max-heap. 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`,(0,e.jsx)(n.h2,{children:"Applications of Priority Queues"}),` `,(0,e.jsxs)(n.ol,{children:[` `,(0,e.jsxs)(n.li,{children:[(0,e.jsx)(n.strong,{children:"CPU Scheduling"}),": Operating systems use priority queues to manage processes based on their priority. 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Tag: priorityqueue

Priority Queue