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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 ...
Several programming languages and libraries provide functions for fast and vectorized clamping. In Python, the pandas library offers the Series.clip [1] and DataFrame.clip [2] methods. The NumPy library offers the clip [3] function. In the Wolfram Language, it is implemented as Clip [x, {minimum, maximum}]. [4]
The procedure for deleting the root from the heap (effectively extracting the maximum element in a max-heap or the minimum element in a min-heap) while retaining the heap property is as follows: Replace the root of the heap with the last element on the last level. Compare the new root with its children; if they are in the correct order, stop.
Example of Min-max heap. Each node in a min-max heap has a data member (usually called key) whose value is used to determine the order of the node in the min-max heap. The root element is the smallest element in the min-max heap. One of the two elements in the second level, which is a max (or odd) level, is the greatest element in the min-max heap
The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
Python's standard library includes heapq.nsmallest and heapq.nlargest functions for returning the smallest or largest elements from a collection, in sorted order. The implementation maintains a binary heap, limited to holding elements, and initialized to the first elements in the collection. Then, each subsequent item of the collection may ...