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"Harold Samuel Kushner is a prominent American rabbi aligned with the progressive wing of Conservative Judaism and a popular author. Education Born in Brooklyn, Kushner graduated from Columbia University in 1955 and later obtained his rabbinical ordination from the Jewish Theological Seminary (JTS) in 1960. The same institution awarded him a doctoral degree in Bible in 1972. Kushner has also studied at the Hebrew University of Jerusalem, taught at Clark University and the Rabbinical School of the JTS, and received six honorary doctorates. Congregational Rabbi He served as the congregational rabbi of Temple Israel of Natick, in Natick, Massachusetts for 24 years and belongs to the Rabbinical Assembly. Author He is the author of a best selling book on the problem of evil, When Bad Things Happen to Good People. Written following the death of his son, Aaron, from the premature aging disease progeria, the book deals with questions about human suffering, God, omnipotence and theodicy. Aaron was born in 1963 and died in 1977; the book was published in 1981. Kushner has written a number of other popular theological books, such as How Good Do We Have to Be? (Dedicated to his grandson, Carl), To Life! and many others. In collaboration with the late Chaim Potok, Kushner co-edited Etz Hayim: A Torah Commentary, the new official Torah commentary of the Conservative movement, which was jointly published in 2001 by the Rabbinical Assembly and the Jewish Publication Society. His Living a Life That Matters became a best seller in the fall of 2001. Kushner's book, The Lord Is My Shepherd, was a meditation on the Twenty-Third Psalm released in 2003. Kushner also wrote a response to Simon Wiesenthal's question of forgiveness in the book The Sunflower: On the Possibilities and Limits of Forgiveness. List of publications * The Book of Job: When Bad Things Happened to a Good Person published in October 2012 * Conquering Fear: Living Boldly in an Uncertain World Published in 2009, is a theological piece that addresses fears of terrorism, natural disasters, rejection, growing old and offer suggestions on how best to cope, ultimately living with purpose and differentiating between God and nature. * Nine Essential Things I've Learned about Life * Faith & Family: Favorite Sermons of Rabbi Harold S. Kushner published in October 2007 * Practice Random Acts of Kindness: Bring More Peace, Love, And Compassion published in 2007 * Overcoming Life's Disappointments published in 2006 * The Lord Is My Shepherd: Healing Wisdom of the 23rd Psalm published in 2003 * Who Needs God published in 1989 * Living a Life That Matters: Resolving the Conflict Between Conscience and Success published in 2001 * How Good Do We Have to Be? A New Understanding of Guilt and Forgiveness published in 1997 * When Children Ask About God: A Guide for Parents Who Don't Always Have All the Answers published in 1995 * To Life: A Celebration of Jewish Being and Thinking published in 1994 * When All You've Ever Wanted Isn't Enough: The Search for a Life That Matters published in 1986 * When Bad Things Happen to Good People published in 1981 Miscellaneous * Kushner offered a reading from the Bible at the State Funeral of Ronald Reagan in the Washington National Cathedral on June 11, 2004. * In 2007 Rabbi Kushner was given the Lifetime Achievement Award by the Jewish Book Council. References External links * Rabbi Kushner's bio at Temple Israel * Rabbi Harold Kushner talks and gives stories in relation to his latest book Overcoming Life's Disappointments (video) 1935 births Living people American humanists Jewish humanists 20th- century rabbis 21st-century rabbis American Conservative rabbis Humanistic rabbis American Jewish theologians Process theologians Jewish American writers Jewish Theological Seminary of America semikhah recipients Columbia College (New York) alumni Hebrew University of Jerusalem alumni People from Brooklyn People from Greater Boston Erasmus Hall High School alumni "
"Hotspot or Hot spot may refer to: Places * Hot Spot, Kentucky, a community in the United States Arts, entertainment, and media=Fictional entities * Hot Spot (comics), a name for the DC Comics character Isaiah Crockett * Hot Spot (Transformers), any of several characters Films * Hot Spot (1941 film), later retitled I Wake Up Screaming * Hot Spot (1945 film), a Private Snafu film * The Hot Spot, a 1990 neo-noir film Other uses in arts, entertainment, and media * Hot Spot (board game), a 1979 board game published by Metagaming Concepts * "Hot Spot" (Burn Notice), a television episode * Hot Spot (musical), 1963 * "Hot Spot" (song), by Foxy Brown * Hotspot (album), a 2020 album by Pet Shop Boys * The Hot Spot (Podcast), a GameSpot podcast Computing * Hot spot (computer programming), a compute- intensive region of a program * Hot spot, an area which is customizable by users in software frameworks * Hotspot (Wi-Fi), a wireless network access point or area ** Connectify Hotspot, a software application for creating a wireless access point ** T-Mobile HotSpot, a service that allows mobile phone connections via a WiFi connection * HotSpot, a Java virtual machine * Screen hotspot, an area enabled for user interactivity on a display Science and healthcare * Hotspot (geology), an area of unusually high volcanic activity * Hot spot (veterinary medicine), an irritated skin lesion * Hot spot, a location with a high level of radioactive contamination * Biodiversity hotspot, a region of significant variety and variability of life * Hot spot effect in subatomic physics, regions of high energy density or temperature * Recombination hotspot, a region in a genome Other uses * Hot spot (casting), a metal casting defect * Hot Spot (cricket), an infrared tracking system * Airport hot spots, locations where aircraft collisions with ground equipment may occur * Hotspot camp, a refugee camp that serves as an initial reception point See also "
"binary max-heap with node keys being integers between 1 and 100 In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C.Black (ed.), Paul E. (2004-12-14). Entry for heap in Dictionary of Algorithms and Data Structures. Online version. U.S. National Institute of Standards and Technology, 14 December 2004. Retrieved on 2017-10-08 from https://xlinux.nist.gov/dads/HTML/heap.html. The node at the "top" of the heap (with no parents) is called the root node. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority. A common implementation of a heap is the binary heap, in which the tree is a binary tree (see figure). The heap data structure, specifically the binary heap, was introduced by J. W. J. Williams in 1964, as a data structure for the heapsort sorting algorithm. Heaps are also crucial in several efficient graph algorithms such as Dijkstra's algorithm. When a heap is a complete binary tree, it has a smallest possible height—a heap with N nodes and for each node a branches always has loga N height. Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an in-order traversal (as there would be in, e.g., a binary search tree). The heap relation mentioned above applies only between nodes and their parents, grandparents, etc. The maximum number of children each node can have depends on the type of heap. Operations The common operations involving heaps are: ;Basic * find-max (or find-min): find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. peek) * insert: adding a new key to the heap (a.k.a., pushThe Python Standard Library, 8.4. heapq — Heap queue algorithm, heapq.heappush) * extract-max (or extract-min): returns the node of maximum value from a max heap [or minimum value from a min heap] after removing it from the heap (a.k.a., popThe Python Standard Library, 8.4. heapq — Heap queue algorithm, heapq.heappop) * delete-max (or delete-min): removing the root node of a max heap (or min heap), respectively * replace: pop root and push a new key. More efficient than pop followed by push, since only need to balance once, not twice, and appropriate for fixed-size heaps.The Python Standard Library, 8.4. heapq — Heap queue algorithm, heapq.heapreplace ;Creation * create-heap: create an empty heap * heapify: create a heap out of given array of elements * merge (union): joining two heaps to form a valid new heap containing all the elements of both, preserving the original heaps. * meld: joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps. ;Inspection * size: return the number of items in the heap. * is-empty: return true if the heap is empty, false otherwise. ;Internal * increase-key or decrease-key: updating a key within a max- or min-heap, respectively * delete: delete an arbitrary node (followed by moving last node and sifting to maintain heap) * sift-up: move a node up in the tree, as long as needed; used to restore heap condition after insertion. Called "sift" because node moves up the tree until it reaches the correct level, as in a sieve. * sift-down: move a node down in the tree, similar to sift-up; used to restore heap condition after deletion or replacement. Implementation Heaps are usually implemented with an implicit heap data structure, which is an implicit data structure consisting of an array (fixed size or dynamic array) where each element represents a tree node whose parent/children relationship is defined implicitly by their index. After an element is inserted into or deleted from a heap, the heap property may be violated and the heap must be balanced by swapping elements within the array. Example of a complete binary max-heap with node keys being integers from 1 to 100 and how it would be stored in an array. In an implicit heap data structure, the first (or last) element will contain the root. The next two elements of the array contain its children. The next four contain the four children of the two child nodes, etc. Thus the children of the node at position n would be at positions 2n and 2n + 1 in a one-based array, or 2n + 1 and 2n + 2 in a zero-based array. Computing the index of the parent node of n-th element is also straightforward. For one- based arrays the parent of element n is located at position n/2. Similarly, for zero-based arrays, the parent is located at position (n-1)/2 (floored). This allows moving up or down the tree by doing simple index computations. Balancing a heap is done by sift-up or sift-down operations (swapping elements which are out of order). As we can build a heap from an array without requiring extra memory (for the nodes, for example), heapsort can be used to sort an array in-place. Different types of heaps implement the operations in different ways, but notably, insertion is often done by adding the new element at the end of the heap in the first available free space. This will generally violate the heap property, and so the elements are then shifted up until the heap property has been reestablished. Similarly, deleting the root is done by removing the root and then putting the last element in the root and sifting down to rebalance. Thus replacing is done by deleting the root and putting the new element in the root and sifting down, avoiding a sifting up step compared to pop (sift down of last element) followed by push (sift up of new element). Construction of a binary (or d-ary) heap out of a given array of elements may be performed in linear time using the classic Floyd algorithm, with the worst- case number of comparisons equal to 2N − 2s2(N) − e2(N) (for a binary heap), where s2(N) is the sum of all digits of the binary representation of N and e2(N) is the exponent of 2 in the prime factorization of N.. This is faster than a sequence of consecutive insertions into an originally empty heap, which is log-linear. Variants * 2–3 heap * B-heap * Beap * Binary heap * Binomial heap * Brodal queue * d-ary heap * Fibonacci heap * K-D Heap * Leaf heap * Leftist heap * Pairing heap * Radix heap * Randomized meldable heap * Skew heap * Soft heap * Ternary heap * Treap * Weak heap Comparison of theoretic bounds for variantsApplications The heap data structure has many applications. * Heapsort: One of the best sorting methods being in-place and with no quadratic worst-case scenarios. * Selection algorithms: A heap allows access to the min or max element in constant time, and other selections (such as median or kth-element) can be done in sub-linear time on data that is in a heap. * Graph algorithms: By using heaps as internal traversal data structures, run time will be reduced by polynomial order. Examples of such problems are Prim's minimal-spanning-tree algorithm and Dijkstra's shortest- path algorithm. *Priority Queue: A priority queue is an abstract concept like "a list" or "a map"; just as a list can be implemented with a linked list or an array, a priority queue can be implemented with a heap or a variety of other methods. *K-way merge: A heap data structure is useful to merge many already-sorted input streams into a single sorted output stream. Examples of the need for merging include external sorting and streaming results from distributed data such as a log structured merge tree. The inner loop is obtaining the min element, replacing with the next element for the corresponding input stream, then doing a sift-down heap operation. (Alternatively the replace function.) (Using extract-max and insert functions of a priority queue are much less efficient.) *Order statistics: The Heap data structure can be used to efficiently find the kth smallest (or largest) element in an array. Implementations * The C++ Standard Library provides the `make_heap`, `push_heap` and `pop_heap` algorithms for heaps (usually implemented as binary heaps), which operate on arbitrary random access iterators. It treats the iterators as a reference to an array, and uses the array-to-heap conversion. It also provides the container adaptor `priority_queue`, which wraps these facilities in a container-like class. However, there is no standard support for the replace, sift-up/sift-down, or decrease/increase-key operations. * The Boost C++ libraries include a heaps library. Unlike the STL, it supports decrease and increase operations, and supports additional types of heap: specifically, it supports d-ary, binomial, Fibonacci, pairing and skew heaps. * There is a generic heap implementation for C and C++ with D-ary heap and B-heap support. It provides an STL-like API. * The standard library of the D programming language includes `std.container.BinaryHeap`, which is implemented in terms of D's ranges. Instances can be constructed from any random-access range. `BinaryHeap` exposes an input range interface that allows iteration with D's built-in `foreach` statements and integration with the range-based API of the `std.algorithm` package. * The Java platform (since version 1.5) provides a binary heap implementation with the class in the Java Collections Framework. This class implements by default a min-heap; to implement a max-heap, programmer should write a custom comparator. There is no support for the replace, sift-up/sift-down, or decrease/increase-key operations. * Python has a `heapq` module that implements a priority queue using a binary heap. The library exposes a heapreplace function to support k-way merging. * PHP has both max-heap (`SplMaxHeap`) and min-heap (`SplMinHeap`) as of version 5.3 in the Standard PHP Library. * Perl has implementations of binary, binomial, and Fibonacci heaps in the `Heap` distribution available on CPAN. * The Go language contains a `heap` package with heap algorithms that operate on an arbitrary type that satisfies a given interface. That package does not support the replace, sift-up/sift-down, or decrease/increase-key operations. * Apple's Core Foundation library contains a `CFBinaryHeap` structure. * Pharo has an implementation of a heap in the Collections-Sequenceable package along with a set of test cases. A heap is used in the implementation of the timer event loop. * The Rust programming language has a binary max-heap implementation, `BinaryHeap`, in the `collections` module of its standard library. See also * Sorting algorithm * Search data structure * Stack (abstract data type) * Queue (abstract data type) * Tree (data structure) * Treap, a form of binary search tree based on heap-ordered trees ReferencesExternal links *Heap at Wolfram MathWorld *Explanation of how the basic heap algorithms work * "