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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
51542e57c510707936e723bb0bc4659eb2755229	all together, an iterative deepening search from depth	all together, an iterative deepening search from depth 1 {\displaystyle 1} all the way down to depth d {\displaystyle d} expands only about 11 % {\displaystyle 11\%} more nodes than a single breadth-first or depth-limited search to depth d {\displaystyle d}, when b = 10 {\displaystyle b=10}.	wikipedia
ab2d1630636236103b5484d2a0c8890f95e31552	since (1 − x) − 2 {\displaystyle (1-x)^{-2}}	since (1 − x) − 2 {\displaystyle (1-x)^{-2}} or (1 − 1 b) − 2 {\displaystyle \left(1-{\frac {1}{b}}\right)^{-2}} is a constant independent of d {\displaystyle d} (the depth), if b > 1 {\displaystyle b>1} (i.e., if the branching factor is greater than 1), the running time of the depth-first iterative deepening search is...	wikipedia
d231946381a16cbd418818532ad6ba03ffbb1a6f	b d (1 + 2 x + 3	b d (1 + 2 x + 3 x 2 + ⋯ + (d − 1) x d − 2 + d x d − 1 + (d + 1) x d) ≤ b d (1 − x) − 2 {\displaystyle b^{d}(1+2x+3x^{2}+\cdots +(d-1)x^{d-2}+dx^{d-1}+(d+1)x^{d})\leq b^{d}(1-x)^{-2}}, for a b s (x) < 1 {\displaystyle abs(x)<1}	wikipedia
165f7694f9c9bbae8cf5538467660256837a3551	where b d {\displaystyle b^{d}} is the number	where b d {\displaystyle b^{d}} is the number of expansions at depth d {\displaystyle d}, 2 b d − 1 {\displaystyle 2b^{d-1}} is the number of expansions at depth d − 1 {\displaystyle d-1}, and so on. factoring out b d {\displaystyle b^{d}} gives	wikipedia
ab25e556db2f1bd25a6aa7a44cff9bf0c0e2eb36	in an iterative deepening search, the nodes at	in an iterative deepening search, the nodes at depth d {\displaystyle d} are expanded once, those at depth d − 1 {\displaystyle d-1} are expanded twice, and so on up to the root of the search tree, which isexpanded d + 1 {\displaystyle d+1} times. so the total number of expansions in an iterative deepening search is	wikipedia
674ad00b36cc928d121cace8a8f63ad7f20465cc	the time complexity of iddfs in a (well-balanced)	the time complexity of iddfs in a (well-balanced) tree works out to be the same as breadth-first search, i.e. o (b d) {\displaystyle o(b^{d})}, where b {\displaystyle b} is the branching factor and d {\displaystyle d} is the depth of the goal.	wikipedia
43861d2f0790bc4f7a437abec7335ef8e10f1041	a second advantage is the responsiveness of the	a second advantage is the responsiveness of the algorithm. because early iterations use small values for d {\displaystyle d}, they execute extremely quickly. this allows the algorithm to supply early indications of the result almost immediately, followed by refinements as d {\displaystyle d} increases. when used in an ...	wikipedia
3356d5b32ced6f3bde42c3390c15a93fa6a7f9d3	the main advantage of iddfs in game tree	the main advantage of iddfs in game tree searching is that the earlier searches tend to improve the commonly used heuristics, such as the killer heuristic and alpha–beta pruning, so that a more accurate estimate of the score of various nodes at the final depth search can occur, and the search completes more quickly sin...	wikipedia
b6ba871ebe81521db016db0e2f3f01626ba2f3d6	iterative deepening visits states multiple times, and it	iterative deepening visits states multiple times, and it may seem wasteful. however, if iddfs explores a search tree to depth d {\displaystyle d}, most of the total effort is in exploring the states at depth d {\displaystyle d}. relative to the number of states at depth d {\displaystyle d}, the cost of repeatedly visit...	wikipedia
354aaebd4d921c0b7171cdc8f73efdfe43302dae	in computer science, iterative deepening search or more	in computer science, iterative deepening search or more specifically iterative deepening depth-first search (ids or iddfs) is a state space /graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found. iddfs is optimal, meaning that...	wikipedia
b1532fdbcceb92ddcd657affb13f374dc355c908	shuto tanabe (田邉秀斗, tanabe shuto, born 5	shuto tanabe (田邉秀斗, tanabe shuto, born 5 may 2002) is a japanese footballer who plays as a right-back for j1 league club, kawasaki frontale.	wikipedia
38e4d94766a23ff9eed72677bb7a647c3abeeda1	pray iv reign is the fourth studio album	pray iv reign is the fourth studio album by american hip hop rapper jim jones, released on march 24, 2009, under e1, columbia and sony music entertainment. the album, his first not to be released under diplomat records, also serves as his first under a major record label. the album includes production from ron browz, c...	wikipedia
570f6cbb09313891a0676f00965ae4f006b4825a	jim jones released a mixtape, titled pray iv	jim jones released a mixtape, titled pray iv reign: the mixtape, on march 3, 2009 to promote the album. most of the songs on the mixtape are tracks that failed to make the album's final track listing.	wikipedia
43fb9c13a10e515fde000bac4381cfd62154e23a	alex thornton of hophopdx liked the songs "how	alex thornton of hophopdx liked the songs "how to be a boss" with ludacris saying it stole the show, "precious" with ryan leslie and "my my my". he also liked the lead single " pop champagne " but like most critics he hated the second single " na na nana na na "	wikipedia
0bc4863c9f1bdaefd7300e9f638ceb5768fe5066	xxl gave the album a 4/5, stating that	xxl gave the album a 4/5, stating that the album is an extreme improvement with many heartfelt tracks, but many disappointments. xxl complimented the lead single, " pop champagne ", "my my my", and the promo singles "precious" and "frenemies", but disliked the second single " na na nana na na ", "pop off" and "this is ...	wikipedia
d97763ca8284c645aea23d7a0fcc835ffcf7666f	jones partnered with itunes, which had a "countdown	jones partnered with itunes, which had a "countdown to jim jones pray iv reign". on february 17, they released the second single " na na nana na na ". on march 3, they released "precious" featuring vocals and production from ryan leslie, on march 17, the song titled "frenemies" was released, and on march 24, the entire...	wikipedia
92d1a95df567b3aee512e7896fcc6b44ba0856a9	on january 1, 2009 a song titled "	on january 1, 2009 a song titled " na na nana na na " was premiered and on february 17, was released to itunes. it serves as the album's second single and features up-and-coming singer brittney taylor aka bree-beauty. jim jones also teamed up with bet, to promote the album as well. on march 2, 2009, jim jones appeared ...	wikipedia
dbf24b28e4b546414b2c45887fb45cae3afa32ef	to promote the album, jones worked with damon	to promote the album, jones worked with damon dash and director j. kyle manzay to stage the play hip-hop monologues: inside the life and mind of jim jones. the “hip-hop monologues” is a musical theatrical experience, co-written by jim jones, using the music from pray iv reign, as the platform. an ensemble of profession...	wikipedia
bcbbbc87d92c9f4f86d2004804ecdc189394804c	in october 2008, jim jones released a promotional	in october 2008, jim jones released a promotional video for the album, rapping his verse on his remix to kid cudi 's " day 'n' nite ". jim jones initially wanted to release the album on december 9, which was coincidentally the same date jay-z was going to release the blueprint 3 and 50 cent was going to release before ...	wikipedia
0ac0c977265da8030e54f7c59f1999f755353b18	" pop champagne ", a song jones recorded	" pop champagne ", a song jones recorded with ron browz and dipset cohort juelz santana, was leaked online in the summer of 2008. it quickly became a club banger and hit single, peaking at #22 on the billboard hot 100. the song was released as the album's lead single on september 4, 2008. the song proved to be jones' s...	wikipedia
c254b16aea943ce6690f66a67fe40dec7dbee541	on july 8, 2008, jones' released a song	on july 8, 2008, jones' released a song titled "the good shit", featuring production from ron browz and a guest appearance from fellow byrdgang member noe. it was intended to be the album's first single when it was titled back 2 back, but was instead used for promotional purposes.	wikipedia
62f8bdbb7359b48a1f2f001c7c8f59258af2a3e5	they did a show up in washington heights,	they did a show up in washington heights, the initial conversation was just that it was an honor to meet them, i think they're kinna cool. and from there it led into me saying, it'd be crazy if i remixed "electric feel". they were like, yeah, that would be crazy. so i said, let me get the beats and shit.	wikipedia
4d711bbc5cadfbfa7d17eb66587a115714545a3f	in a 2008 listening session, a few tracks	in a 2008 listening session, a few tracks were revealed. the "intro" was originally titled "across 110th street" and "how to be a boss" was originally titled "follow this blueprint". on the sixth track, titled "frienemies", jones' addresses his strained relationships with cam'ron and max b. "my my my" is a song he reco...	wikipedia
930d35fd568348be4c9844256932a5b91871c6c1	the album, originally titled back 2 back, was	the album, originally titled back 2 back, was his first album with columbia records. the album cover was photographed by thi chien. there are several different album covers. the first version is the original cover, the second, third and fourth are all the original cover, but with different colored backgrounds, such as ...	wikipedia
38e4d94766a23ff9eed72677bb7a647c3abeeda1	pray iv reign is the fourth studio album	pray iv reign is the fourth studio album by american hip hop rapper jim jones, released on march 24, 2009, under e1, columbia and sony music entertainment. the album, his first not to be released under diplomat records, also serves as his first under a major record label. the album includes production from ron browz, c...	wikipedia
913f4ec7ef29ba2d6bb2b07c8a91b09099d08a20	mathematics during the golden age of islam, especially	mathematics during the golden age of islam, especially during the 9th and 10th centuries, was built upon syntheses of greek mathematics and indian mathematics. important developments of the period include extension of the place-value system to include decimal fractions, the systematised study of algebra and advances in...	wikipedia
9f48d0012522657b88f443d94e19ee135c42e9db	the medieval arab-islamic world played a crucial role	the medieval arab-islamic world played a crucial role in shaping the trajectory of mathematics, with al-khwārizmī 's algebraic innovations serving as a cornerstone. the dissemination of arabic mathematics to the west during the islamic golden age, facilitated by cultural exchanges and translations, left a lasting impac...	wikipedia
c19ef746fef96b885ef2aedd114bc5815924fc34	in 18th century germany and france, the prevailing	in 18th century germany and france, the prevailing orientalist view was "east and west oppose each other not as geographical but as historical positivities", which labeled " rationalism " as the essence of the west, while the "call of the orient " movement emerged in the 19th century was interpreted as "against rationa...	wikipedia
54072f72f86a40bfd1838f2c7ffce38333c9a906	despite the fundamental works arabic mathematicians have done	despite the fundamental works arabic mathematicians have done on the development of algebra and algebraic geometry, western historians in the 18th and early 19th century still regarded it as a fact that classical science and math were unique phenomena of the west. even though some math contributions from arab mathemati...	wikipedia
cc69495a01296a3f6b16707a4c0d1b3bb0e761e6	despite the fundamental works arabic mathematicians have done	words: "to justify the exclusion of science written in arabic from the history of science, one invokes its absence of rigor, its calculatory appearance and its practical aims. furthermore, strictly dependent on greek science and, lastly, incapable of introducing experimental norms, scientists of that time were relegat...	wikipedia
cab68e1c72b837b52515edb2bf18d716044f781e	abū kāmil (arabic: أبو كامل شجاع بن أسلم	abū kāmil (arabic: أبو كامل شجاع بن أسلم بن محمد بن شجاع, also known as al-ḥāsib al-miṣrī—lit. "the egyptian calculator") (c. 850 – c. 930), was studied algebra following the author of algebra, al-khwārizmī. his book of algebra (kitāb fī al-jabr wa al-muqābala) is "essentially a commentary on and elaboration of al-khwā...	wikipedia
707ef8962e9ebf43dab3b52e8ba707a56ccfd393	al-khayyām (1048–1131) was a persian mathematician, astronomer, and	al-khayyām (1048–1131) was a persian mathematician, astronomer, and poet, known for his work on algebra and geometry, particularly his investigations into the solutions of cubic equations. he was "the first in history to elaborate a geometrical theory of equations with degrees ≤ 3", and has great influence on the work ...	wikipedia
bc49ba81c5bacf1155e1c532120e9c75d9dceda7	al-battānī is one of the islamic mathematicians who	al-battānī is one of the islamic mathematicians who made great contributions to the development of trigonometry. he "innovated new trigonometric functions, created a table of cotangents, and made some formulas in spherical trigonometry." these discoveries, together with his astronomical works which are praised for thei...	wikipedia
b3360bcda2de16cc5129f16bb9fc777872113761	the influence of medieval arab-islamic mathematics to the	the influence of medieval arab-islamic mathematics to the rest of the world is wide and profound, in both the realm of science and mathematics. the knowledge of the arabs went into the western world through spain and sicily during the translation movement. "the moors (western mohammedans from that part of north africa ...	wikipedia
d633279a465b2ae7d9384d187164f7ccd5c342b0	between the 9th and 10th centuries, the egyptian	between the 9th and 10th centuries, the egyptian mathematician abu kamil wrote a now-lost treatise on the use of double false position, known as the book of the two errors (kitāb al-khaṭāʾayn). the oldest surviving writing on double false position from the middle east is that of qusta ibn luqa (10th century), an arab m...	wikipedia
027639d18d5d1c8534726a157449a2cdd1bdd829	the product of a negative number— al-nāqiṣ —by	the product of a negative number— al-nāqiṣ —by a positive number— al-zāʾid —is negative, and by a negative number is positive. if we subtract a negative number from a higher negative number, the remainder is their negative difference. the difference remains positive if we subtract a negative number from a lower negativ...	wikipedia
2c2782ed3d59c9ec2db718abdd627c6a1fbe160e	in the 9th century, islamic mathematicians were familiar	in the 9th century, islamic mathematicians were familiar with negative numbers from the works of indian mathematicians, but the recognition and use of negative numbers during this period remained timid. al-khwarizmi did not use negative numbers or negative coefficients. but within fifty years, abu kamil illustrated the...	wikipedia
0c37922e33cc30661e11b9480fe0c85f5918ab87	the spherical law of sines was discovered in	the spherical law of sines was discovered in the 10th century: it has been attributed variously to abu-mahmud khojandi, nasir al-din al-tusi and abu nasr mansur, with abu al-wafa' buzjani as a contributor. ibn muʿādh al-jayyānī 's the book of unknown arcs of a sphere in the 11th century introduced the general law of si...	wikipedia
faf52845b3fb9dce7e1789f1f506cb24bc25a57d	in the twelfth century, latin translations of al-khwarizmi	in the twelfth century, latin translations of al-khwarizmi 's arithmetic on the indian numerals introduced the decimal positional number system to the western world. his compendious book on calculation by completion and balancing presented the first systematic solution of linear and quadratic equations. in renaissance ...	wikipedia
455a6eeaa1ce33e86ad11f1a87c7eb59294ae528	the greeks had discovered irrational numbers, but were	the greeks had discovered irrational numbers, but were not happy with them and only able to cope by drawing a distinction between magnitude and number. in the greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete. hence, irrationals could only be ...	wikipedia