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In common presentations of Dijkstra's algorithm, initially all nodes are entered into the priority queue. This is, however, not necessary: the algorithm can start with a priority queue that contains only one item, and insert new items as they are discovered (instead of doing a decrease-key, check whether the key is in the queue; if it is ...
Like heapsort, smoothsort organizes the input into a priority queue and then repeatedly extracts the maximum. Also like heapsort, the priority queue is an implicit heap data structure (a heap-ordered implicit binary tree), which occupies a prefix of the array. Each extraction shrinks the prefix and adds the extracted element to a growing sorted ...
Chen et al. [11] examined priority queues specifically for use with Dijkstra's algorithm and concluded that in normal cases using a d-ary heap without decrease-key (instead duplicating nodes on the heap and ignoring redundant instances) resulted in better performance, despite the inferior theoretical performance guarantees.
That is, if there is a sorting algorithm which can sort in O(S) time per key, where S is some function of n and word size, [22] then one can use the given procedure to create a priority queue where pulling the highest-priority element is O(1) time, and inserting new elements (and deleting elements) is O(S) time.
In Dijkstra's algorithm for the shortest path problem, vertices of a given weighted graph are extracted in increasing order by their distance from the starting vertex, and a priority queue is used to determine the closest remaining vertex to the starting vertex. Therefore, in this application, the priority queue operations are monotonic.
The d-ary heap consists of an array of n items, each of which has a priority associated with it. These items may be viewed as the nodes in a complete d-ary tree, listed in breadth first traversal order: the item at position 0 of the array (using zero-based numbering) forms the root of the tree, the items at positions 1 through d are its children, the next d 2 items are its grandchildren, etc.
The algorithm that is presented here does not need an explicit stack; instead, it uses recursive calls to implement the stack. The algorithm is not a pure operator-precedence parser like the Dijkstra shunting yard algorithm. It assumes that the primary nonterminal is parsed in a separate subroutine, like in a recursive descent parser.
In computer science, the shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation. It can produce either a postfix notation string, also known as reverse Polish notation (RPN), or an abstract syntax tree (AST). [ 1 ]