Breadth-first search is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root, explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level, it uses the opposite strategy as depth-first search, which instead explores the node branch as far as possible before being forced to backtrack and expand other nodes. BFS and its application in finding connected components of graphs were invented in 1945 by Konrad Zuse, in his Ph. D. thesis on the Plankalkül programming language, but this was not published until 1972. It was reinvented in 1959 by Edward F. Moore, who used it to find the shortest path out of a maze, developed by C. Y. Lee into a wire routing algorithm. Input: A graph Graph and a starting vertex root of Graph Output: Goal state; the parent links trace the shortest path back to root 1 procedure BFS is 2 let Q be a queue 3 label start_v as discovered 4 Q.enqueue 5 while Q is not empty do 6 v:= Q.dequeue 7 if v is the goal 8 return v 9 for all edges from v to w in G.adjacentEdges do 10 if w is not labeled as discovered 11 label w as discovered 12 w.parent:= v 13 Q.enqueue This non-recursive implementation is similar to the non-recursive implementation of depth-first search, but differs from it in two ways: it uses a queue instead of a stack and it checks whether a vertex has been discovered before enqueueing the vertex rather than delaying this check until the vertex is dequeued from the queue.

The Q queue contains the frontier along which the algorithm is searching. Nodes can be labelled as discovered by storing them in a set, or by an attribute on each node, depending on the implementation. Note that the word node is interchangeable with the word vertex; the parent attribute of each node is useful for accessing the nodes in a shortest path, for example by backtracking from the destination node up to the starting node, once the BFS has been run, the predecessors nodes have been set. Breadth-first search produces a so-called breadth first tree. You can see; the following is an example of the breadth-first tree obtained by running a BFS on German cities starting from Frankfurt: The time complexity can be expressed as O, since every vertex and every edge will be explored in the worst case. | V | is the number of vertices and | E | is the number of edges in the graph. Note that O may vary between O and O, depending on how sparse the input graph is; when the number of vertices in the graph is known ahead of time, additional data structures are used to determine which vertices have been added to the queue, the space complexity can be expressed as O, where | V | is the cardinality of the set of vertices.

This is in addition to the space required for the graph itself, which may vary depending on the graph representation used by an implementation of the algorithm. When working with graphs that are too large to store explicitly, it is more practical to describe the complexity of breadth-first search in different terms: to find the nodes that are at distance d from the start node, BFS takes O time and memory, where b is the "branching factor" of the graph. In the analysis of algorithms, the input to breadth-first search is assumed to be a finite graph, represented explicitly as an adjacency list or similar representation. However, in the application of graph traversal methods in artificial intelligence the input may be an implicit representation of an infinite graph. In this context, a search method is described as being complete if it is guaranteed to find a goal state if one exists. Breadth-first search is complete; when applied to infinite graphs represented implicitly, breadth-first search will find the goal state, but depth-first search may get lost in parts of the graph that have no goal state and never return.

An enumeration of the vertices of a graph is said to be a BFS ordering if it is the possible output of the application of BFS to this graph. Let G = be a graph with n vertices. Recall that N is the set of neighbors of v. For σ = be a list of distinct elements of V, for v ∈ V ∖, let

The sources for Citizen Kane, the 1941 American motion picture that marked the feature film debut of Orson Welles, have been the subject of speculation and controversy since the project's inception. With a story spanning 60 years, the quasi-biographical film examines the life and legacy of Charles Foster Kane, played by Welles, a fictional character based in part upon the American newspaper magnate William Randolph Hearst and Chicago tycoons Samuel Insull and Harold McCormick. A rich incorporation of the experiences and knowledge of its authors, the film earned an Academy Award for Best Writing for Herman J. Mankiewicz and Welles. I wished to make a motion picture, not a narrative of action so much as an examination of character. For this, I desired a man of many aspects. Orson Welles never confirmed a principal source for the character of Charles Foster Kane. John Houseman, who worked with screenwriter Herman J. Mankiewicz on the early draft scripts, wrote that Kane is a synthesis of different personalities, with Hearst's life used as the main source.

"The truth is simple: for the basic concept of Charles Foster Kane and for the main lines and significant events of his public life, Mankiewicz used as his model the figure of William Randolph Hearst. To this were added incidents and details invented or derived from other sources." Houseman adds that they "grafted anecdotes from other giants of journalism, including Pulitzer and Mank's first boss, Herbert Bayard Swope."Welles said, "Mr. Hearst was quite a bit like Kane, although Kane isn't founded on Hearst in particular, many people sat for it so to speak", he acknowledged that aspects of Kane were drawn from the lives of two business tycoons familiar from his youth in Chicago — Samuel Insull and Harold Fowler McCormick. William Randolph Hearst was born rich, he was the pampered son of an adoring mother. That is the decisive fact about him. Charles Foster Kane was raised by a bank; the film is regarded as a fictionalized, unrelentingly hostile parody of William Randolph Hearst, in spite of Welles's statement that "Citizen Kane is the story of a wholly fictitious character."

Film historian Don Kilbourne has pointed out that much of the film's story is derived from aspects of Hearst's life, published and that "some of Kane's speeches are verbatim copies of Hearst's. When Welles denied that the film was about the still-influential publisher, he did not convince many people."The most identifiable anecdote from Hearst's life used in the film is his famous but certainly apocryphal exchange with illustrator Frederic Remington. In January 1897 Remington was sent to Cuba by Hearst's New York Journal, to provide illustrations to accompany Richard Harding Davis's reporting about an uprising against Spain's colonial rule. Remington purportedly cabled Hearst from Havana that he wished to return since everything was quiet and there would be no war. Hearst is supposed to have replied, "Please remain. You furnish the pictures, I'll furnish the war". Although Hearst denied the truth of the now legendary story, a milestone of yellow journalism, the ensuing Spanish–American War has been called "Mr. Hearst's War".

Hearst biographer David Nasaw described Kane as "a cartoon-like caricature of a man, hollowed out on the inside, defeated, solitary because he cannot command the total obedience, loyalty and love of those around him. Hearst, to the contrary, never regarded himself as a failure, never recognized defeat, never stopped loving Marion or his wife, he did not, at the end of his life, run away from the world to entomb himself in a vast, gloomy art-choked hermitage."Arguing for the release of Citizen Kane before the RKO board, Welles pointed out the irony that it was Hearst himself who had brought so much attention to the film being about him, that Hearst columnist Louella Parsons was doing the most to publicize Kane's identification with Hearst. Public denials aside, Welles held the view that Hearst was a public figure and that the facts of a public figure's life were available for writers to reshape and restructure into works of fiction. Welles's legal advisor, Arnold Weissberger, put the issue in the form of a rhetorical question: "Will a man be allowed in effect to copyright the story of his life?"Welles said that he had excised one scene from Mankiewicz's first draft, based on Hearst.

"In the original script we had a scene based on a notorious thing Hearst had done, which I still cannot repeat for publication. And I cut it out because I thought it wasn't in keeping with Kane's character. If I'd kept it in, I would have had no trouble with Hearst, he wouldn't have dared. In her 1971 essay, "Raising Kane", film critic Pauline Kael wrote that a vestige of this abandoned subplot survives in a remark made by Susan Alexander Kane to the reporter interviewing her: "Look, if you're smart, you'll get in touch with Raymond. He's the butler. You'll learn a lot from him, he knows where all the bodies are buried." Kael observed, "It's an cryptic speech. In the first draft, Raymond knew where the bodies were buried: Mankiewicz had dished up a nasty version of the scandal sometimes referred to as the Strange Death of Thomas Ince." Referring to the suspicious 1924 death of the American film mogul after being a guest on Hearst's yacht, noting that Kael's principal source was Houseman, film critic Jonathan Rosenbaum wrote that "it seems safe to conclude without her prodding, that some version of the story must have cropped up in Mankiewicz's first draft of the script, which Welles subsequently edited and added to."One particular aspect of the character, Kane's profligate collecting of possessions, was direct

Cecilia L. Ridgeway is an American sociologist and the Lucie Stern Professor of Social Sciences, Emerita in the Sociology Department at Stanford University, she is known for her research on gender and status processes on how large, societal-level gender and status inequalities are recreated in face-to-face interaction. Ridgeway served as president of the American Sociological Association in 2013, she edited Social Psychology Quarterly from 2001–2003. Ridgeway received her Bachelor's degree with Honors and distinction in Sociology from the University of Michigan in 1967, she went on to receive her Master's and PhD in Sociology and Social Psychology from Cornell University in 1969 and 1972 respectively. She taught at the University of Wisconsin-Milwaukee from 1972–1985, attaining the rank of associate professor in 1978, she went on to teach at the University of Iowa from 1985–1991, was instrumental in the development of their social psychology department. Her current position is at Stanford University.

Ridgeway's contributions to the field starts with her publications on status theory. Ridgeway has written on nonverbal dominance cues and expectation states theory, looking at how both connect to and can be viewed through a status theory lens. Ridgeway is known for her work on gender, how it is a social status category, her book, Framed by Gender: How Gender Inequality Persists in the Modern World, covers what gender inequality means in a modern context, how it is persisting in our society, possible ways to change these inequalities. Ridgeway's most significant contribution to the field of study has been her creation of and subsequent empirical tests of status construction theory. Status construction theory looks at one set of processes by which status beliefs are created and shared within society. Status beliefs refer to the conceptions that are held about groups based on status markers such as sex or ethnicity. Ridgeway's work has been used to further research on inequality and the creation/perpetuation of inequality based on ones perceived status within society.

Ridgeway received the Cooley-Mead Award from the American Sociological Association in 2005 for her career contributions to social psychology. In 2009, Ridgeway received the Jessie Bernard Award for her work on gender inequality and her mentorship of younger, female academics, she won the Distinguished Feminist Lecturer Award from the Sociologists for Women in Society due to her feminist scholarship in 2008. In 2012, her book, Framed by Gender: How Gender Inequality Persists in the Modern World, received the Outstanding Recent Contribution In Social Psychology Award from the Social Psychology Section of the American Sociological Association. Ridgeway, C. L.. Framed by gender: how gender inequality persists in the modern world. New York: Oxford University Press. Ridgeway, C. L.. The Social Construction of Status Value: Gender and Other Nominal Characteristics. Social Forces, 70, 367–386. Https://doi.org/10.1093/sf/70.2.367 Ridgeway, C. L.. Interaction and the Conservation of Gender Inequality: Considering Employment.

American Sociological Review, 62, 218–235. Https://www.jstor.org/stable/2657301 Ridgeway, C. L.. Why Status Matters for Inequality. American Sociological Review, 79, 1–16. Https://doi.org/10.1177/0003122413515997 Ridgeway, C. L. and Correll, S. J. Unpacking the Gender System: A Theoretical Perspective on Gender Beliefs and Social Relations. Gender & Society, 18, 510–531. Stanford Faculty Page