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function lookupByPositionIndex(i) node ← head i ← i + 1 # don't count the head as a step for level from top to bottom do while i ≥ node.width[level] do # if next step is not too far i ← i - node.width[level] # subtract the current width node ← node.next[level] # traverse forward at the current level repeat repeat return node.value end ...
This behavior can be axiomatized in various ways. For example, a common VDM (Vienna Development Method) description of a stack defines top (peek) and remove as atomic, where top returns the top value (without modifying the stack), and remove modifies the stack (without returning a value). [1] In this case pop is defined in terms of top and remove.
A similar function can be defined for popping and then inserting, which in Python is called "heapreplace": // Extract the root of the heap, and push a new item // heap : an array representing the heap, indexed at 1 // item : an element to insert // Returns the current root of heap Replace ( heap : List<T>, item : T) -> T: swap heap [1] and item ...
A singly-linked list structure, implementing a list with three integer elements. The term list is also used for several concrete data structures that can be used to implement abstract lists, especially linked lists and arrays. In some contexts, such as in Lisp programming, the term list may refer specifically to a linked list rather than an array.
Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
The dynamic array has performance similar to an array, with the addition of new operations to add and remove elements: Getting or setting the value at a particular index (constant time) Iterating over the elements in order (linear time, good cache performance) Inserting or deleting an element in the middle of the array (linear time)
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Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...