text:
Intestinal villus
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Intestinal ville
Micrograph of the small intestine mucosa showing villi - top half of image. H&E stain
Section of duodenum of cat. X 60.
Details
Identifiers
Latin
villi intestinales
TA
A05.6.01.011
FMA
76464
Anatomical terminology
[edit on Wikidata]
Intestinal villi (singular: villus) are small, finger-like projections that extend into the lumen of the small intestine. Each villus is approximately 0.5–1.6 mm in length (in humans), and has many microvilli projecting from the enterocytes of its epithelium which collectively form the striated or brush border. Each of these microvilli are much smaller than a single villus. The intestinal villi are much smaller than any of the circular folds in the intestine.
Villi increase the internal surface area of the intestinal walls making available a greater surface area for absorption. An increased absorptive area is useful because digested nutrients (including monosaccharide and amino acids) pass into the semipermeable villi through diffusion, which is effective only at short distances. In other words, increased surface area (in contact with the fluid in the lumen) decreases the average distance travelled by nutrient molecules, so effectiveness of diffusion increases. The villi are connected to the blood vessels so the circulating blood then carries these nutrients away.
Contents
[hide]
1 Structure
1.1 Histology
2 Function
3 Additional images
4 References
Structure[edit]
Histology[edit]
Vertical section of a villus from the dog's small intestine. X 80. (Simple columnar epithelium labeled at right, third from top.)
Enterocytes, along with goblet cells, represent the principal cell types of the epithelium of the villi in the small intestine.[1]
Function[edit]
There, the villi and the microvilli increase intestinal absorptive surface area approximately 30-fold and 600-fold, respectively, providing exceptionally efficient absorption of nutrients in the lumen.[2]
There are also enzymes (enterocyte digestive enzyme) on the surface for digestion. Villus capillaries collect amino acids and simple sugars taken up by the villi into the blood stream. Villus lacteals (lymph capillary) collect absorbed chylomicrons, which are lipoproteins composed of triglycerides, cholesterol and amphipathic proteins, and are taken to the rest of the body through the lymph fluid.
Villi are specialised for absorption in the small intestine as they have a thin wall, one cell thick, which enables a shorter diffusion path. They have a large surface area so there will be more efficient absorption of fatty acids and glycerol into the blood stream. They have a rich blood supply to keep a concentration gradient.[3] Please see the following publication about the vascular supply of the human intestinal villus :
C.W. Chan, Y.K. Leung and K.W. Chan -- Microscopic anatomy of the vasculature of the human intestinal villus - a study with review -- Eur J Anat, 18 (4): 291-301 (2014)
Additional images[edit]
Different stages of coeliac disease
Structure of a villus (see reference quoted in text)
Microvilli (shaggy hair) show electron dense plaques (open arrow) at their apices.
References[edit]
Jump up ^ http://www.copewithcytokines.org/cope.cgi?key=Paneth%20cells
Jump up ^ "Oral Delivery of Macromolecular Drugs - Barriers, - Andreas Bernkop-Schnürch - Springer".
Jump up ^ "Digestion: Digestive System, Enzymes, Absorption in the Small Intestine".
[hide]
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Authority control
NDL: 00575812
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Family Guy (season 16)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Family Guy (season 16)
Country of origin
United States
Release
Original network
Fox
Original release
October 1, 2017 (2017-10-01) – present
Season chronology
← Previous
Season 15
List of Family Guy episodes
Family Guy's sixteenth season premiered on Fox in the United States on October 1, 2017.[1]
The series follows the dysfunctional Griffin family, consisting of father Peter, mother Lois, daughter Meg, son Chris, baby Stewie and the family dog Brian, who reside in their hometown of Quahog. The executive producers for the sixteenth production season are Seth MacFarlane, Richard Appel, Alec Sulkin, Steve Callaghan, Danny Smith and Kara Vallow. Sulkin returns after a two-season absence as the new showrunner for the series, replacing previous showrunner Callaghan. Appel will continue to serve as showrunner alongside Sulkin.
The season will feature guest appearances from Danny Trejo, Ian McKellen, Kristen Bell, Louis C.K., Bill Maher, and Modern Family cast members Ty Burrell, Julie Bowen and Sofía Vergara.[2][3]
The season will also mark the final appearances of Adam West and Carrie Fisher following their deaths, as well as the show's 300th episode.[4] During this season, Brian is kicked out of the Griffin house in a three-episode story arc after he posts a tweet that angers Quahog. Also, Brian and Stewie solve a mystery in a Sherlock Holmes parody and Meg comes out as a lesbian.[5]
Contents
[hide]
1 Episodes
2 Unscheduled episodes
3 References
4 External links
Episodes[edit]
See also: List of Family Guy episodes
No.
overall
No. in
season
Title
Directed by
Written by
Original air date
Prod.
code
U.S. viewers
(millions)
290
1 "Emmy-Winning Episode" James Purdum
Dominic Bianchi
Peter Shin Aaron Lee October 1, 2017 (2017-10-01) FACX06 2.80[6]
Peter goes out of his way to earn an Emmy win after getting fed up with not being nominated. He tries to make Family Guy more like several Emmy-nominated television shows, including Modern Family and Transparent.
291
2 "Foxx in the Men House" Brian Iles Andrew Goldberg October 8, 2017 (2017-10-08) EACX20 3.05[7]
Peter meets a paramedic named Striker after being knocked unconscious. He later dumps Quagmire, Cleveland and Joe as friends, due to his friendship with Striker giving him inflated self-esteem. Later on, Peter comes to realize he does not have the strength to do the physical activities that Striker wants to do.
292
3 "Nanny Goats" Steve Robertson Tom Devanney October 15, 2017 (2017-10-15) FACX02 2.54[8]
Lois' mother, Barbara, hires a nanny for the Griffin family when she gets displeased with recent living arrangements for the kids. This enables Peter and Lois to reconnect with their love.
293
4 "Follow the Money" Mike Kim Kevin Biggins October 22, 2017 (2017-10-22) EACX15 2.69[9]
Chris receives a dollar for his birthday from Carter and loses it at the same time, only to realize it is a rare dollar. Chris and Carter begin an adventure to find the dollar, as it's being passed by every citizen of Quahog.
294
5 "Three Directors" Joe Vaux Travis Bowe November 5, 2017 (2017-11-05) EACX18 2.31[10]
The story of Peter's firing from the brewery, as told in the directorial styles of Quentin Tarantino, Wes Anderson, and Michael Bay.
295
6 "The D in Apartment 23" Julius Wu Artie Johann November 12, 2017 (2017-11-12) FACX03 3.11[11]
After Brian posts a tweet on Twitter that is deemed racist, it goes viral and the Griffins become social pariahs, prompting them to move Brian out of the house.
296
7 "Petey IV" Mike Kim Anthony Blasucci November 19, 2017 (2017-11-19) FACX04 2.08[12]
Vladimir Putin visits Quahog after Peter writes an email to him about the ending to a Russian bootleg version of Rocky IV. Meanwhile, Brian gets a job at a suicide hotline center, where he falls for his co-worker, Martha.
297
8 "Crimes and Meg's Demeanor" Greg Colton Mike Desilets December 3, 2017 (2017-12-03) FACX05 2.59[13]
Meg takes up drinking at a high school party, which both concerns and delights Peter. Meanwhile, Brian believes that Principal Shepherd has committed a crime.
298
9 "Don't Be a Dickens at Christmas" Jerry Langford Danny Smith December 10, 2017 (2017-12-10) FACX07 2.98[14]
In a play on Charles Dickens' A Christmas Carol, Peter takes a journey around Quahog with the ghost of Patrick Swayze after he loses his Christmas spirit.
299
10 "Boy (Dog) Meets Girl (Dog)"[15] TBA TBA January 7, 2018 (2018-01-07) FACX09 TBD
Brian falls in love with Ellie, a female show dog. Meanwhile, Peter and Lois attempt to convince Chris that the book author "Arthur Valentine" is not real.
300
11 "Dog Bites Bear"[16] TBA TBA January 14, 2018 (2018-01-14) FACX01 TBD
Unscheduled episodes[edit]
Production code
Title
Reference
FACX10 "Send in Stewie, Please" [17]
FACX15 "HTTPete" [18]
FACX?? "Doc Brown" [19]
FACX?? "V is for Mystery" [20]
FACX?? "Veteran Guy" [21]
FACX?? "Family Guy Through the Years" [22]
FACX?? "The Woof of Wall Street" [23]
FACX?? "Switch the Flip" [24]
FACX?? "Are You There God? It's Me, Peter" [25]
FACX?? "The Unkindest Cut" [26]
References[edit]
Jump up ^ Andreeva, Nellie (June 22, 2017). "Fox Sets Fall 2017 Premiere Dates: 'Empire', 'The Gifted' & 'Orville'". Deadline. Retrieved September 1, 2017.
Jump up ^ Dan Snierson (July 19, 2017). "Ian McKellen to guest on Family Guy". Ew.com. Retrieved August 25, 2017.
Jump up ^ Dan Snierson (August 13, 2017). "Kristen Bell, Louis C.K. to guest on Family Guy". Ew.com. Retrieved August 25, 2017.
Jump up ^ Snierson, Dan (2017-09-28). "Family Guy season 15 preview: Peter loses his job, Quagmire loses his penis". EW.com. Retrieved 2017-11-30.
Jump up ^ Hugar, John (November 14, 2016). "Talking to Showrunner Alec Sulkin About Working to Revitalize 'Family Guy'". Split Sider. Retrieved November 19, 2017.
Jump up ^ Porter, Rick (October 3, 2017). "'NCIS: LA' and '60 Minutes' adjust up, 'Wisdom of the Crowd' and 'Ten Days in the Valley' down: Sunday final ratings". TV by the Numbers. Retrieved October 3, 2017.
Jump up ^ Porter, Rick (October 10, 2017). "NFL adjusts up, all others unchanged: Sunday final ratings". TV by the Numbers. Retrieved October 10, 2017.
Jump up ^ Porter, Rick (October 17, 2017). "'Madam Secretary' and 'Wisdom of the Crowd' adjust down, '60 Minutes, 'AFV' and NFL up: Sunday final ratings". TV by the Numbers. Retrieved October 17, 2017.
Jump up ^ Porter, Rick (October 24, 2017). "'NCIS: LA' and 'Shark Tank' adjust up, 'Madam Secretary' adjusts down: Sunday final ratings". TV by the Numbers. Retrieved October 24, 2017.
Jump up ^ Porter, Rick (November 7, 2017). "'Family Guy,' '60 Minutes' adjust up, 'Bob's Burgers' and 'Madam Secretary' adjust down: Sunday final ratings". TV by the Numbers. Retrieved November 7, 2017.
Jump up ^ Porter, Rick (November 14, 2017). "'Wisdom of the Crowd' adjusts down: Sunday final ratings". TV by the Numbers. Retrieved November 14, 2017.
Jump up ^ Porter, Rick (November 21, 2017). "'Sunday Night Football' adjusts up, '60 Minutes' and 'Madam Secretary' adjust down: Sunday final ratings". TV by the Numbers. Retrieved November 21, 2017.
Jump up ^ Porter, Rick (December 5, 2017). "'Sunday Night Football' adjusts up: Sunday final ratings". TV by the Numbers. Retrieved December 5, 2017.
Jump up ^ Porter, Rick (December 12, 2017). "'Bob's Burgers,' 'The Simpsons' and '60 Minutes' adjust down: Sunday final ratings". TV by the Numbers. Retrieved December 12, 2017.
Jump up ^ "Family Guy on FOX - "Boy (Dog) Meets Girl (Dog)"". The Futon Critic. Retrieved December 13, 2017.
Jump up ^ "Family Guy on FOX". The Futon Critic. Retrieved December 13, 2017.
Jump up ^ Reg. # PAu003851061 at U.S. Copyright Records database.
Jump up ^ "Instagram". Instagram. December 14, 2016. Retrieved December 31, 2016.
Jump up ^ Reg. # PAu003803650 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003848125 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003852729 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003852731 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003852736 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003859910 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003864137 at U.S. Copyright Records database.
Jump up ^ Reg. # PAu003864165 at U.S. Copyright Records database.
External links[edit]
[show]
v
t
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Family Guy episodes
Seasons
1
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3
4
5
6
7
8
9
10
11
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13
14
15
16
Season 16
"Emmy-Winning Episode"
"Foxx in the Men House"
"Nanny Goats"
"Follow the Money"
"Three Directors"
"The D in Apartment 23"
"Petey IV"
"Crimes and Meg's Demeanor"
"Don't Be a Dickens on Christmas"
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Family Guy Online (2012)
Back to the Multiverse (2012)
Family Guy: The Quest for Stuff (2014)
Family Guy: Another Freakin' Mobile Game (2017)
See also
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Night of the Hurricane
The Cleveland Show
American Dad!
Animation Domination
"Cartoon Wars Part I"
"Cartoon Wars Part II"
Book
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Monongahela River
From Wikipedia, the free encyclopedia
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For other uses, see Monongahela (disambiguation).
Monongahela River
The Monongahela River in Pittsburgh passing the South Side on the right and Uptown/The Bluff on the left just before entering Downtown Pittsburgh
Country
United States
States
Pennsylvania, West Virginia
Counties
Marion WV, Monongalia WV, Greene PA, Fayette PA, Washington PA, Westmoreland PA, Allegheny PA
Tributaries
- left Peters Creek, Streets Run, Becks Run
- right Cheat River, Youghiogheny River, Turtle Creek
Source
Tygart Valley River
- location Pocahontas County, West Virginia
- elevation 4,540 ft (1,384 m) [1]
- coordinates 38°28′06″N 79°58′51″W / 38.46833°N 79.98083°W / 38.46833; -79.98083 [2]
Secondary source
West Fork River
- location Upshur County, West Virginia
- elevation 1,309 ft (399 m) [3]
- coordinates 38°51′08″N 80°21′32″W / 38.85222°N 80.35889°W / 38.85222; -80.35889 [4]
Source confluence
- location Fairmont, West Virginia
- elevation 863 ft (263 m) [4]
- coordinates 39°27′53″N 80°09′10″W / 39.46472°N 80.15278°W / 39.46472; -80.15278 [5]
Mouth
Ohio River
- location Pittsburgh, Pennsylvania
- elevation 709 ft (216 m) [5]
- coordinates 40°26′30″N 80°00′58″W / 40.44167°N 80.01611°W / 40.44167; -80.01611Coordinates: 40°26′30″N 80°00′58″W / 40.44167°N 80.01611°W / 40.44167; -80.01611 [5]
Length
130 mi (209 km) [6]
Basin
7,340 sq mi (19,011 km2) [7]
Discharge
for Braddock, PA
- average 12,650 cu ft/s (358 m3/s) [8]
- max 81,100 cu ft/s (2,296 m3/s)
- min 2,900 cu ft/s (82 m3/s)
Discharge elsewhere (average)
- Masontown, PA 8,433 cu ft/s (239 m3/s) [9]
Map of the Monongahela River basin, with the Monongahela River highlighted
The Monongahela River (/məˌnɒŋɡəˈhiːlə/ mə-NONG-gə-HEE-lə, /-ˈheɪ-/ -HAY-)[10] — often referred to locally as the Mon (/mɒn/) — is a 130-mile-long (210 km)[6] river on the Allegheny Plateau in north-central West Virginia and southwestern Pennsylvania, which flows from south to north. The Monongahela joins the Allegheny River to form the Ohio River at Pittsburgh.
Contents
[hide]
1 Etymology
1.1 Variant names
2 Geography
3 History
3.1 Ice Age Events
3.2 18th and 19th centuries
3.3 20th century
4 Gallery
5 See also
6 Notes and references
7 Bibliography
8 External links
Etymology[edit]
The Unami word Monongahela means "falling banks", in reference to the geological instability of the river's banks. Moravian missionary David Zeisberger (1721–1808) gave this account of the naming: "In the Indian tongue the name of this river was Mechmenawungihilla (alternatively spelled Menawngihella), which signifies a high bank, which is ever washed out and therefore collapses."[11]
The Lenape Language Project renders the word as Mënaonkihëla (pronounced [mənaoŋɡihəla]), translated "where banks cave in or erode",[12] from the verbs mënaonkihële "the dirt caves off" (such as the bank of a river or creek, or in a landslide)[13] and mënaonke (pronounced [mənaoŋɡe]), "it has a loose bank" (where one might fall in).[14]
Monongalia County and the town of Monongah, both in West Virginia, are named for the river, as is the city of Monongahela in Pennsylvania. (The name "Monongalia" is either a Latinized adaptation of "Monongahela" or simply a variant spelling.)
Variant names[edit]
According to the Geographic Names Information System, the Monongahela River has also been known historically as:[5]
Malangueulé[15]
Manaungahela River
Me-nan-gi-hil-li
Meh-non-au-au-ge-hel-al
Mehmannaunringgehlau
Mehmannauwinggehla
Mo-hon-ga-ly River
Mo-hon-galy River
Mo-hon-gey-e-la River
Mo-hong-gey-e-la River
Mohungahala River
Mohunghala River
Monaung River
Monaungahela River
Monna River
Monnyahela River
Monona River
Mononga River
Monongahalia River
Monongahaly River
Monongaheley River
Monongahelia River
Monongalia River
Monongalo River
Mononguhela River
Mononyahela River
Muddy River
Geography[edit]
The Monongahela is formed by the confluence of the West Fork River and its "East Fork"—the Tygart Valley River—at Fairmont, West Virginia. The river is navigable its entire length with a series of locks and dams that maintain a minimum depth of 9 feet (2.7 m) to accommodate coal-laden barges. In southwestern Pennsylvania, the Monongahela is met by two major tributaries: the Cheat River, which joins at Point Marion, and the Youghiogheny River, which joins at McKeesport.
The upper drainage area of the river basin is renowned for its water sports/hobbies of whitewater kayaking (and in some cases whitewater rafting) opportunities. The land here is of a very rugged plateau type which allows streams to gather sufficient water volume before they fall off the plateau and create challenging rapids. Some of the best known specific stream locations for this include:
Youghiogheny River at Ohiopyle, Pennsylvania[16]
Youghiogheny River at Friendsville, Maryland[17]
Cheat River at Albright, West Virginia[18][19]
Tygart River at Belington, West Virginia[20][21][22]
History[edit]
Ice Age Events[edit]
Prior to early Pleistocene regional glaciation, more than 780,000 years ago, the ancestral Monongahela River (a.k.a. the Pittsburgh River) flowed northward from present-day north-central West Virginia, across western Pennsylvania and northwestern Ohio, and into the Saint Lawrence River watershed. One (or more) extensive ice sheet advance dammed the old north-flowing drainage and created a vast lake—known as Lake Monongahela—stretching from an unknown point north of present-day Beaver, Pennsylvania for ~200 miles (320 km) south to Weston, West Virginia. A river-lake with many narrow bays, its maximum water surface rose to 1,100 feet (340 m) above sea level. Over 200 feet (61 m) deep in places, its southwestward overflow gradually incised old drainage divides and contributed to the geological development of the present-day upper Ohio River Valley.[23] [24]
18th and 19th centuries[edit]
The Monongahela River valley was the site of a famous battle that was one of the first in the French and Indian War—the Braddock Expedition (May–July 1755). It resulted in a sharp defeat for two thousand British and Colonial forces against those of the French and their Native American allies.
In 1817, the Pennsylvania legislature authorized the Monongahela Navigation Company to build 16 dams with bypass locks to create a river transportation system between Pittsburgh and the area that would later become West Virginia.[25] Originally planned to run as far south as the Cheat River, the system was extended to Fairmont, and bituminous coal from West Virginia was the chief product transported downstream. After a canal tunnel through Grant's Hill in Pittsburgh was completed in 1832, boats could travel between the Monongahela River and the Western Division Canal of Pennsylvania's principal east-west canal and railroad system, the Main Line of Public Works. In 1897, the federal government took possession of the Monongahela Navigation through condemnation proceedings. Later, the dam-lock combinations were increased in size and reduced in number.[26] In 2006, the navigation system, operated by the U.S. Army Corps of Engineers, had nine dam-locks along 128.7 miles (207.1 km) of waterway.[27] The locks overcame a change in elevation of about 147 feet (44.8 m).[26]
Briefly linked to the Monongahela Navigation was the Youghiogheny Navigation, a slack water system of 18.5 miles (29.8 km) between McKeesport and West Newton. It had two dam-locks overcoming a change in elevation of about 27 feet (8.2 m). Opening in 1850, it was destroyed by a flood in 1865.[26]
During the 19th century, the Monongahela was heavily used by industry, and several U.S. Steel plants, including the Homestead Works, site of the Homestead Strike of 1892, were built along its banks. Following the killing of several workers in the course of the strike, anarchist Emma Goldman wrote: "Words had lost their meaning in the face of the innocent blood spilled on the banks of the Monongahela."
20th century[edit]
Three ships in the United States Navy have been named Monongahela after the river. In the 1930s, severe drought caused the river to run dry.
The river was the site of a famous airplane crash that has become the subject of numerous urban legends and conspiracy theories. Early in the morning of January 31, 1956, a B-25 bomber en route from Nellis Air Force Base in Nevada to Olmsted Air Force Base in Pennsylvania crashed into the river near the Glenwood Bridge in Homestead, Pennsylvania. All six crewmen survived the crash, but two later succumbed to exposure and drowned. Despite the relative shallowness of the water, the aircraft was never recovered.[28][29] The Pittsburgh Post-Gazette published a graphical representation of the flight path and flight details in 1999.[30][31]
Gallery[edit]
The South Tenth Street Bridge over the Monongahela River in Pittsburgh in 2005
The Monongahela River in Fairmont, West Virginia in 2006
Monongahela River Scene, 1857[32]
Opekiska Lock and Dam on the Monongahela River near Fairmont, West Virginia at river mile 115 (185 km)
See also[edit]
Pittsburgh portal
West Virginia portal
List of crossings of the Monongahela River
List of rivers of Pennsylvania
List of rivers of West Virginia
Geography of Pennsylvania
Notes and references[edit]
Jump up ^ Google Earth elevation for GNIS source coordinates. Retrieved on March 12, 2007.
Jump up ^ Geographic Names Information System. "Geographic Names Information System entry for Tygart Valley River (Feature ID #1553309)". Retrieved 2007-03-12.
Jump up ^ Geographic Names Information System. "Geographic Names Information System entry for Straight Fork (headwaters tributary of West Fork River) (Feature ID #1547564)". Retrieved 2007-03-12.
^ Jump up to: a b Geographic Names Information System. "Geographic Names Information System entry for West Fork River (Feature ID #1548931)". Retrieved 2007-03-12.
^ Jump up to: a b c d Geographic Names Information System. "Geographic Names Information System entry for Monongahela River (Feature ID #1209053)". Retrieved 2007-03-12.
^ Jump up to: a b U.S. Geological Survey. National Hydrography Dataset high-resolution flowline data. The National Map, accessed August 15, 2011
Jump up ^ Gillespie, William H. (2006). "Monongahela River". In Ken Sullivan (ed.). The West Virginia Encyclopedia. Charleston, W.Va.: West Virginia Humanities Council. p. 492. ISBN 0-9778498-0-5. CS1 maint: Extra text: editors list (link)
Jump up ^ United States Geological Survey; USGS 03085000 Monongahela River at Braddock, PA; retrieved Sep 29, 2010.
Jump up ^ United States Geological Survey; USGS 03072655 Monongahela River near Masontown, PA; retrieved September 29, 2010.
Jump up ^ There are several ways to pronounce this word that are acceptable. From "Geographical Names" of Merriam-Webster's Collegiate Dictionary, Eleventh Edition (2009): /məˌnɒnɡəˈhiːlə/, /məˌnɒɡəˈhiːlə/ or /məˌnɒŋɡəˈheɪlə/.
Jump up ^ Zeisberger, David, David Zeisberger's History of the Northern American Indians in 18th Century Ohio, New York and Pennsylvania, pg 43; Wennawoods Publishing, 1999, ISBN 1-889037-17-6
Jump up ^ "Lenape Talking Dictionary". Retrieved 2010-12-10.
Jump up ^ "Lenape Talking Dictionary". Retrieved 2010-12-10.
Jump up ^ "Lenape Talking Dictionary". Retrieved 2010-12-10.
Jump up ^ John Gilmary Shea. Relations diverses sur la bataille du Malangueulé : gagné le 9 juillet, 1755, par les François sous M. de Beaujeu, commandant du fort du Quesne sur les Anglois sous M. Braddock, général en chef des troupes angloises. Nouvelle York : De la Presse Cramoisy, 1860. OCLC 15760312.
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/1687/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/753/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/2346/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/2347/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/2451/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/2452/
Jump up ^ https://www.americanwhitewater.org/content/River/detail/id/2453/
Jump up ^ Garton, E. Ray (2012). "Fauna of the Ice Age". Wonderful West Virginia. p. 11 (January issue).
Jump up ^ Jacobson, Robert B., Elston, Donald P., and Heaton, John W., 1988, Stratigraphy and magnetic polarity of the high terrace remnants in the upper Ohio and Monongahela rivers in West Virginia, Pennsylvania, and Ohio: Quaternary Research, v. 29, p. 216-232.
Jump up ^ Monongahela Navigation Company Copybook, 1840-1897, DAR.1937.41, The Darlington Collection, Special Collections Department, University of Pittsburgh
^ Jump up to: a b c Shank, William H. (1986). The Amazing Pennsylvania Canals, 150th Anniversary Edition. York, Pennsylvania: American Canal and Transportation Center. p. 76. ISBN 0-933788-37-1.
Jump up ^ "Navigation". U.S. Army Corps of Engineers. 2006. Archived from the original on 2007-11-25. Retrieved 2007-11-27.
Jump up ^ Powell, Albrecht. "The Pittsburgh B-25 Ghost Bomber Mystery (1956)". About.com. Retrieved 2016-02-13.
Jump up ^ Ove, Torsten (4 April 1999). "Searchers say 'Ghost Bomber' can be found in the Mon". Retrieved 2016-02-13.
Jump up ^ James Hilston, Post-Gazette Staff Artist. "PG Graphic: One of the Mysteries of Pittsburgh: The B-25 in the Mon". Retrieved 2016-02-13.
Jump up ^ "Let's learn from the past: B-25 'Ghost Bomber'". Pittsburgh Post-Gazette. Retrieved 2016-02-13.
Jump up ^ Ballou's Pictorial, issue of 21 Feb 1857
Bibliography[edit]
Bissell, Richard (1952), The Monongahela, Rinehart & Co.
Callahan, James Morton and Bernard Lee Butcher (1912), Genealogical and Personal History of the Upper Monongahela Valley, West Virginia, New York: Lewis Historical Publishing Company.
Core, Earl L. (1984), "The Monongalia River," in: Bartlett, Richard A. (ed), Rolling Rivers: An Encyclopedia of America's Rivers. New York: McGraw-Hill. ISBN 0-07-003910-0. pp 149–52.
Core, Earl L. (1974–84), The Monongalia Story: A Bicentennial History, Parsons, W.Va.: McClain Printing Co., 5 volumes; an extensive, well-documented natural & human history of the Monongahela River basin.
Volume I: Prelude (1974)
Volume II: The Pioneers (1976)
Volume III: Discord (1979)
Volume IV: Industrialization (1984)
Volume V: Sophistication (1984)
External links[edit]
Wikimedia Commons has media related to Monongahela River.
U.S. Geological Survey: PA stream gaging stations
Beach, Chandler B., ed. (1914). "Monongahela". The New Student's Reference Work. Chicago: F. E. Compton and Co.
Authority control
WorldCat Identities
GND: 4629706-6
LCCN: sh85086954
NARA: 10043802
VIAF: 248283758
Retrieved from "https://en.wikipedia.org/w/index.php?title=Monongahela_River&oldid=848676145"
Categories:
Monongahela River
Tributaries of the Ohio River
Rivers of Pennsylvania
Rivers of West Virginia
Rivers of Allegheny County, Pennsylvania
Rivers of Washington County, Pennsylvania
Rivers of Westmoreland County, Pennsylvania
Rivers of Fayette County, Pennsylvania
Rivers of Greene County, Pennsylvania
Rivers of Monongalia County, West Virginia
Rivers of Marion County, West Virginia
Water transportation in Pennsylvania
Water transportation in West Virginia
Allegheny Plateau
Hidden categories:
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Cop Car (Keith Urban song)
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"Cop Car"
Single by Keith Urban
from the album Fuse
Released
13 January 2014 (2014-01-13)
Format
Digital download
Genre
Country pop
Length
4:16
Label
Hit Red
Capitol Nashville
Songwriter(s)
Zach Crowell
Sam Hunt
Matt Jenkins
Producer(s)
Zach Crowell[1]
Keith Urban
Keith Urban singles chronology
"We Were Us"
(2013) "Cop Car"
(2014) "Somewhere in My Car"
(2014)
"We Were Us"
(2013) "Cop Car"
(2014) "Somewhere in My Car"
(2014)
"Cop Car" is a song written by Zach Crowell, Sam Hunt, and Matt Jenkins and recorded by New Zealand-born Australian country music singer Keith Urban. It was released in January 2014 as the third international single and fourth overall from his eighth studio album Fuse (2013).
Contents
[hide]
1 Content
2 Critical reception
3 Personnel
4 Music video
5 Chart performance
5.1 Year-end charts
6 Certifications
7 Sam Hunt version
7.1 Chart performance
8 References
Content[edit]
The song is a mid-tempo ballad about two young lovers who are arrested when trespassing together, and "f[a]ll in love in the back of a cop car".[2]
Critical reception[edit]
Joseph Hudak of Country Weekly gave the single a "B+", saying that "It's a clever concept, elevated to near greatness by its sheer originality." He praised Urban's "earnest" vocals, and said that "the production is slick and alive—though not necessarily squarely 'country'."[2] Kevin John Coyne of Country Universe gave it an identical rating, saying that he did not believe its storyline, but said that "Keith Urban’s heartfelt delivery and careful choice of what lines to emphasize keep the proceedings grounded. He’s so effective at capturing the feeling of falling in love that the specifics of the event surrounding the moment are appropriately secondary to the emotions at play."[3] Thom Jurek of AllMusic wrote that "The muted drum loop that fuels the shimmering 'Cop Car,' is layered in atmospherics worthy of Achtung Baby, but the melody is pure country."[4]
The song was nominated for Best Country Solo Performance at the 57th Grammy Awards but lost to Carrie Underwood's "Something in the Water".
Personnel[edit]
Compiled from liner notes.[1]
Zach Crowell — programming, electric guitar, acoustic guitar, bass guitar, piano, percussion, synthesizer, background vocals
John Fields — bass guitar
Devin Malone — dobro, pedal steel guitar, electric guitar
Chris McHugh — drums
Russell Terrell — background vocals
Keith Urban — all vocals, electric guitar, EBow
Music video[edit]
The music video was directed by John Urbano and premiered in January 2014.[5]
Chart performance[edit]
"Cop Car" peaked at number eight on the Billboard Country Airplay chart in May 2014, making it his lowest-peaking single on that chart since 1999. The song has sold 772,000 copies in the U.S. as of June 2014.[6]
Chart (2014)
Peak
position
Canada (Canadian Hot 100)[7] 38
Canada Country (Billboard)[8] 5
US Billboard Hot 100[9] 41
US Country Airplay (Billboard)[10] 8
US Hot Country Songs (Billboard)[11] 4
Year-end charts[edit]
Chart (2014)
Position
US Country Airplay (Billboard)[12] 52
US Hot Country Songs (Billboard)[13] 27
Certifications[edit]
Region
Certification
Certified units/Sales
United States (RIAA)[14]
Platinum 1,000,000^
*sales figures based on certification alone
^shipments figures based on certification alone
Sam Hunt version[edit]
"Cop Car"
Song by Sam Hunt
from the album Montevallo
Released
October 27, 2014
Format
Digital download
Genre
Country pop
Length
4:13
Label
MCA Nashville
Songwriter(s)
Zach Crowell
Sam Hunt
Matt Jenkins
Producer(s)
Zach Crowell
Shane McAnally
Montevallo track listing
"Make You Miss Me"
(7) "Cop Car"
(8) "Raised on It"
(9)
Sam Hunt—who co-wrote the song originally—recorded his version of it on his debut studio album Montevallo, which was released on October 27, 2014.
Hunt explains that the reason he included the song on his album is because "After writing the songs on the record, it was like a movie, and "Cop Car" was a pivotal scene in that movie. Even though Keith Urban had recorded it, I felt it still had a place on the record."[15]
Chart performance[edit]
Chart (2014)
Peak
position
US Country Digital Songs[16] 48
References[edit]
^ Jump up to: a b Fuse (Deluxe Edition) (CD booklet). Keith Urban. Capitol Records Nashville/Hit Red Records. 2013. B0019113-02.
^ Jump up to: a b Hudak, Joseph (27 January 2014). "Singles: Keith Urban — 'Cop Car'". Country Weekly. 21 (4): 50.
Jump up ^ Coyne, Kevin John (16 January 2014). "'Cop Car' review". Country Universe. Retrieved 21 January 2014.
Jump up ^ Jurek, Thom. "Fuse review". Allmusic. Retrieved 21 January 2014.
Jump up ^ Wyland, Sarah (28 January 2014). "Watch Keith Urban's "Cop Car" Music Video". Great American Country. Retrieved 30 January 2014.
Jump up ^ Bjorke, Matt (June 19, 2014). "Country Chart News: The Top 30 Digital Singles For June 19, 2014". Roughstock. Archived from the original on July 14, 2014.
Jump up ^ "Keith Urban Chart History (Canadian Hot 100)" Billboard.
Jump up ^ "Keith Urban Chart History (Canada Country)" Billboard.
Jump up ^ "Keith Urban Chart History (Hot 100)" Billboard.
Jump up ^ "Keith Urban Chart History (Country Airplay)" Billboard.
Jump up ^ "Keith Urban Chart History (Hot Country Songs)" Billboard.
Jump up ^ "Best of 2014: Country Airplay". Billboard. Prometheus Global Media. 2014. Retrieved December 9, 2014.
Jump up ^ "Best of 2014: Hot Country Songs". Billboard. Prometheus Global Media. 2014. Retrieved December 9, 2014.
Jump up ^ "American single certifications – Keith Urban – Cop Car". Recording Industry Association of America. Retrieved August 10, 2014. If necessary, click Advanced, then click Format, then select Single, then click SEARCH
Jump up ^ Mansfield, Brian (October 13, 2014). "On the Verge: Sam Hunt's 'Night' shines bright". USA Today. Retrieved October 27, 2014.
Jump up ^ "Sam Hunt Album & Song Chart History - Country Digital Songs". Billboard. Prometheus Global Media. Retrieved July 11, 2016.
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Merge sort
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Merge sort
An example of merge sort. First divide the list into the smallest unit (1 element), then compare each element with the adjacent list to sort and merge the two adjacent lists. Finally all the elements are sorted and merged.
Class
Sorting algorithm
Data structure
Array
Worst-case performance
O(n log n)
Best-case performance
O(n log n) typical,
O(n) natural variant
Average performance
O(n log n)
Worst-case space complexity
О(n) total, O(n) auxiliary
In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Mergesort is a divide and conquer algorithm that was invented by John von Neumann in 1945.[1] A detailed description and analysis of bottom-up mergesort appeared in a report by Goldstine and Neumann as early as 1948.[2]
Contents
[hide]
1 Algorithm
1.1 Top-down implementation
1.2 Bottom-up implementation
1.3 Top-down implementation using lists
1.4 Bottom-up implementation using lists
2 Natural merge sort
3 Analysis
4 Variants
5 Use with tape drives
6 Optimizing merge sort
7 Parallel merge sort
8 Comparison with other sort algorithms
9 Notes
10 References
11 External links
Algorithm[edit]
Merge sort animation. The elements to sort are represented by dots.
Conceptually, a merge sort works as follows:
Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.
Top-down implementation[edit]
Example C-like code using indices for top down merge sort algorithm that recursively splits the list (called runs in this example) into sublists until sublist size is 1, then merges those sublists to produce a sorted list. The copy back step is avoided with alternating the direction of the merge with each level of recursion.
// Array A[] has the items to sort; array B[] is a work array. TopDownMergeSort(A[], B[], n) { CopyArray(A, 0, n, B); // duplicate array A[] into B[] TopDownSplitMerge(B, 0, n, A); // sort data from B[] into A[] } // Sort the given run of array A[] using array B[] as a source. // iBegin is inclusive; iEnd is exclusive (A[iEnd] is not in the set). TopDownSplitMerge(B[], iBegin, iEnd, A[]) { if(iEnd - iBegin < 2) // if run size == 1 return; // consider it sorted // split the run longer than 1 item into halves iMiddle = (iEnd + iBegin) / 2; // iMiddle = mid point // recursively sort both runs from array A[] into B[] TopDownSplitMerge(A, iBegin, iMiddle, B); // sort the left run TopDownSplitMerge(A, iMiddle, iEnd, B); // sort the right run // merge the resulting runs from array B[] into A[] TopDownMerge(B, iBegin, iMiddle, iEnd, A); } // Left source half is A[ iBegin:iMiddle-1]. // Right source half is A[iMiddle:iEnd-1 ]. // Result is B[ iBegin:iEnd-1 ]. TopDownMerge(A[], iBegin, iMiddle, iEnd, B[]) { i = iBegin, j = iMiddle; // While there are elements in the left or right runs... for (k = iBegin; k < iEnd; k++) { // If left run head exists and is <= existing right run head. if (i < iMiddle && (j >= iEnd || A[i] <= A[j])) { B[k] = A[i]; i = i + 1; } else { B[k] = A[j]; j = j + 1; } } } CopyArray(A[], iBegin, iEnd, B[]) { for(k = iBegin; k < iEnd; k++) B[k] = A[k]; }
Bottom-up implementation[edit]
Example C-like code using indices for bottom up merge sort algorithm which treats the list as an array of n sublists (called runs in this example) of size 1, and iteratively merges sub-lists back and forth between two buffers:
// array A[] has the items to sort; array B[] is a work array void BottomUpMergeSort(A[], B[], n) { // Each 1-element run in A is already "sorted". // Make successively longer sorted runs of length 2, 4, 8, 16... until whole array is sorted. for (width = 1; width < n; width = 2 * width) { // Array A is full of runs of length width. for (i = 0; i < n; i = i + 2 * width) { // Merge two runs: A[i:i+width-1] and A[i+width:i+2*width-1] to B[] // or copy A[i:n-1] to B[] ( if(i+width >= n) ) BottomUpMerge(A, i, min(i+width, n), min(i+2*width, n), B); } // Now work array B is full of runs of length 2*width. // Copy array B to array A for next iteration. // A more efficient implementation would swap the roles of A and B. CopyArray(B, A, n); // Now array A is full of runs of length 2*width. } } // Left run is A[iLeft :iRight-1]. // Right run is A[iRight:iEnd-1 ]. void BottomUpMerge(A[], iLeft, iRight, iEnd, B[]) { i = iLeft, j = iRight; // While there are elements in the left or right runs... for (k = iLeft; k < iEnd; k++) { // If left run head exists and is <= existing right run head. if (i < iRight && (j >= iEnd || A[i] <= A[j])) { B[k] = A[i]; i = i + 1; } else { B[k] = A[j]; j = j + 1; } } } void CopyArray(B[], A[], n) { for(i = 0; i < n; i++) A[i] = B[i]; }
Top-down implementation using lists[edit]
Pseudocode for top down merge sort algorithm which recursively divides the input list into smaller sublists until the sublists are trivially sorted, and then merges the sublists while returning up the call chain.
function merge_sort(list m) // Base case. A list of zero or one elements is sorted, by definition. if length of m ≤ 1 then return m // Recursive case. First, divide the list into equal-sized sublists // consisting of the first half and second half of the list. // This assumes lists start at index 0. var left := empty list var right := empty list for each x with index i in m do if i < (length of m)/2 then add x to left else add x to right // Recursively sort both sublists. left := merge_sort(left) right := merge_sort(right) // Then merge the now-sorted sublists. return merge(left, right)

In this example, the merge function merges the left and right sublists.
function merge(left, right) var result := empty list while left is not empty and right is not empty do if first(left) ≤ first(right) then append first(left) to result left := rest(left) else append first(right) to result right := rest(right) // Either left or right may have elements left; consume them. // (Only one of the following loops will actually be entered.) while left is not empty do append first(left) to result left := rest(left) while right is not empty do append first(right) to result right := rest(right) return result

Bottom-up implementation using lists[edit]
Pseudocode for bottom up merge sort algorithm which uses a small fixed size array of references to nodes, where array[i] is either a reference to a list of size 2 i or 0. node is a reference or pointer to a node. The merge() function would be similar to the one shown in the top down merge lists example, it merges two already sorted lists, and handles empty lists. In this case, merge() would use node for its input parameters and return value.
function merge_sort(node head) // return if empty list if (head == nil) return nil var node array[32]; initially all nil var node result var node next var int i result = head // merge nodes into array while (result != nil) next = result.next; result.next = nil for(i = 0; (i < 32) && (array[i] != nil); i += 1) result = merge(array[i], result) array[i] = nil // do not go past end of array if (i == 32) i -= 1 array[i] = result result = next // merge array into single list result = nil for (i = 0; i < 32; i += 1) result = merge(array[i], result) return result

Natural merge sort[edit]
A natural merge sort is similar to a bottom up merge sort except that any naturally occurring runs (sorted sequences) in the input are exploited. Both monotonic and bitonic (alternating up/down) runs may be exploited, with lists (or equivalently tapes or files) being convenient data structures (used as FIFO queues or LIFO stacks).[3] In the bottom up merge sort, the starting point assumes each run is one item long. In practice, random input data will have many short runs that just happen to be sorted. In the typical case, the natural merge sort may not need as many passes because there are fewer runs to merge. In the best case, the input is already sorted (i.e., is one run), so the natural merge sort need only make one pass through the data. In many practical cases, long natural runs are present, and for that reason natural merge sort is exploited as the key component of Timsort. Example:
Start       : 3--4--2--1--7--5--8--9--0--6
Select runs : 3--4  2  1--7  5--8--9  0--6
Merge       : 2--3--4  1--5--7--8--9  0--6
Merge       : 1--2--3--4--5--7--8--9  0--6
Merge       : 0--1--2--3--4--5--6--7--8--9

Tournament replacement selection sorts are used to gather the initial runs for external sorting algorithms.
Analysis[edit]
A recursive merge sort algorithm used to sort an array of 7 integer values. These are the steps a human would take to emulate merge sort (top-down).
In sorting n objects, merge sort has an average and worst-case performance of O(n log n). If the running time of merge sort for a list of length n is T(n), then the recurrence T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists). The closed form follows from the master theorem for divide-and-conquer recurrences.
In the worst case, the number of comparisons merge sort makes is equal to or slightly smaller than (n ⌈lg n⌉ - 2⌈lg n⌉ + 1), which is between (n lg n - n + 1) and (n lg n + n + O(lg n)).[4]
For large n and a randomly ordered input list, merge sort's expected (average) number of comparisons approaches α·n fewer than the worst case where α = − 1 + ∑ k = 0 ∞ 1 2 k + 1 ≈ 0.2645. {\displaystyle \alpha =-1+\sum _{k=0}^{\infty }{\frac {1}{2^{k}+1}}\approx 0.2645.}
In the worst case, merge sort does about 39% fewer comparisons than quicksort does in the average case. In terms of moves, merge sort's worst case complexity is O(n log n)—the same complexity as quicksort's best case, and merge sort's best case takes about half as many iterations as the worst case.[citation needed]
Merge sort is more efficient than quicksort for some types of lists if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common. Unlike some (efficient) implementations of quicksort, merge sort is a stable sort.
Merge sort's most common implementation does not sort in place;[5] therefore, the memory size of the input must be allocated for the sorted output to be stored in (see below for versions that need only n/2 extra spaces).
Variants[edit]
Variants of merge sort are primarily concerned with reducing the space complexity and the cost of copying.
A simple alternative for reducing the space overhead to n/2 is to maintain left and right as a combined structure, copy only the left part of m into temporary space, and to direct the merge routine to place the merged output into m. With this version it is better to allocate the temporary space outside the merge routine, so that only one allocation is needed. The excessive copying mentioned previously is also mitigated, since the last pair of lines before the return result statement (function merge in the pseudo code above) become superfluous.
One drawback of merge sort, when implemented on arrays, is its O(n) working memory requirement. Several in-place variants have been suggested:
Katajainen et al. present an algorithm that requires a constant amount of working memory: enough storage space to hold one element of the input array, and additional space to hold O(1) pointers into the input array. They achieve an O(n log n) time bound with small constants, but their algorithm is not stable.[6]
Several attempts have been made at producing an in-place merge algorithm that can be combined with a standard (top-down or bottom-up) merge sort to produce an in-place merge sort. In this case, the notion of "in-place" can be relaxed to mean "taking logarithmic stack space", because standard merge sort requires that amount of space for its own stack usage. It was shown by Geffert et al. that in-place, stable merging is possible in O(n log n) time using a constant amount of scratch space, but their algorithm is complicated and has high constant factors: merging arrays of length n and m can take 5n + 12m + o(m) moves.[7] This high constant factor and complicated in-place algorithm was made simpler and easier to understand. Bing-Chao Huang and Michael A. Langston[8] presented a straightforward linear time algorithm practical in-place merge to merge a sorted list using fixed amount of additional space. They both have used the work of Kronrod and others. It merges in linear time and constant extra space. The algorithm takes little more average time than standard merge sort algorithms, free to exploit O(n) temporary extra memory cells, by less than a factor of two. Though the algorithm is much faster in practical way but it is unstable also for some list. But using similar concept they have been able to solve this problem. Other in-place algorithms include SymMerge, which takes O((n + m) log (n + m)) time in total and is stable.[9] Plugging such an algorithm into merge sort increases its complexity to the non-linearithmic, but still quasilinear, O(n (log n)2).
An alternative to reduce the copying into multiple lists is to associate a new field of information with each key (the elements in m are called keys). This field will be used to link the keys and any associated information together in a sorted list (a key and its related information is called a record). Then the merging of the sorted lists proceeds by changing the link values; no records need to be moved at all. A field which contains only a link will generally be smaller than an entire record so less space will also be used. This is a standard sorting technique, not restricted to merge sort.
Use with tape drives[edit]
Merge sort type algorithms allowed large data sets to be sorted on early computers that had small random access memories by modern standards. Records were stored on magnetic tape and processed on banks of magnetic tape drives, such as these IBM 729s.
An external merge sort is practical to run using disk or tape drives when the data to be sorted is too large to fit into memory. External sorting explains how merge sort is implemented with disk drives. A typical tape drive sort uses four tape drives. All I/O is sequential (except for rewinds at the end of each pass). A minimal implementation can get by with just 2 record buffers and a few program variables.
Naming the four tape drives as A, B, C, D, with the original data on A, and using only 2 record buffers, the algorithm is similar to Bottom-up implementation, using pairs of tape drives instead of arrays in memory. The basic algorithm can be described as follows:
Merge pairs of records from A; writing two-record sublists alternately to C and D.
Merge two-record sublists from C and D into four-record sublists; writing these alternately to A and B.
Merge four-record sublists from A and B into eight-record sublists; writing these alternately to C and D
Repeat until you have one list containing all the data, sorted—in log2(n) passes.
Instead of starting with very short runs, usually a hybrid algorithm is used, where the initial pass will read many records into memory, do an internal sort to create a long run, and then distribute those long runs onto the output set. The step avoids many early passes. For example, an internal sort of 1024 records will save 9 passes. The internal sort is often large because it has such a benefit. In fact, there are techniques that can make the initial runs longer than the available internal memory.[10]
A more sophisticated merge sort that optimizes tape (and disk) drive usage is the polyphase merge sort.
Optimizing merge sort[edit]
On modern computers, locality of reference can be of paramount importance in software optimization, because multilevel memory hierarchies are used. Cache-aware versions of the merge sort algorithm, whose operations have been specifically chosen to minimize the movement of pages in and out of a machine's memory cache, have been proposed. For example, the tiled merge sort algorithm stops partitioning subarrays when subarrays of size S are reached, where S is the number of data items fitting into a CPU's cache. Each of these subarrays is sorted with an in-place sorting algorithm such as insertion sort, to discourage memory swaps, and normal merge sort is then completed in the standard recursive fashion. This algorithm has demonstrated better performance[examples needed] on machines that benefit from cache optimization. (LaMarca & Ladner 1997)
Kronrod (1969) suggested an alternative version of merge sort that uses constant additional space. This algorithm was later refined. (Katajainen, Pasanen & Teuhola 1996)
Also, many applications of external sorting use a form of merge sorting where the input get split up to a higher number of sublists, ideally to a number for which merging them still makes the currently processed set of pages fit into main memory.
Parallel merge sort[edit]
Merge sort parallelizes well due to use of the divide-and-conquer method. Several parallel variants are discussed in the third edition of Cormen, Leiserson, Rivest, and Stein's Introduction to Algorithms.[11] The first of these can be very easily expressed in a pseudocode with fork and join keywords:
// Sort elements lo through hi (exclusive) of array A. algorithm mergesort(A, lo, hi) is if lo+1 < hi then // Two or more elements. mid = ⌊(lo + hi) / 2⌋ fork mergesort(A, lo, mid) mergesort(A, mid, hi) join merge(A, lo, mid, hi)

This algorithm is a trivial modification from the serial version, and its speedup is not impressive: when executed on an infinite number of processors, it runs in Θ(n) time, which is only a Θ(log n) improvement on the serial version. A better result can be obtained by using a parallelized merge algorithm, which gives parallelism Θ(n / (log n)2), meaning that this type of parallel merge sort runs in
Θ ( ( n log  n ) ⋅ ( log  n ) 2 n ) = Θ ( ( log  n ) 3 ) {\displaystyle \Theta \left((n\log n)\cdot {\frac {(\log n)^{2}}{n}}\right)=\Theta ((\log n)^{3})}
time if enough processors are available.[11] Such a sort can perform well in practice when combined with a fast stable sequential sort, such as insertion sort, and a fast sequential merge as a base case for merging small arrays.[12]
Merge sort was one of the first sorting algorithms where optimal speed up was achieved, with Richard Cole using a clever subsampling algorithm to ensure O(1) merge.[13] Other sophisticated parallel sorting algorithms can achieve the same or better time bounds with a lower constant. For example, in 1991 David Powers described a parallelized quicksort (and a related radix sort) that can operate in O(log n) time on a CRCW parallel random-access machine (PRAM) with n processors by performing partitioning implicitly.[14] Powers[15] further shows that a pipelined version of Batcher's Bitonic Mergesort at O((log n)2) time on a butterfly sorting network is in practice actually faster than his O(log n) sorts on a PRAM, and he provides detailed discussion of the hidden overheads in comparison, radix and parallel sorting.
Comparison with other sort algorithms[edit]
Although heapsort has the same time bounds as merge sort, it requires only Θ(1) auxiliary space instead of merge sort's Θ(n). On typical modern architectures, efficient quicksort implementations generally outperform mergesort for sorting RAM-based arrays.[citation needed] On the other hand, merge sort is a stable sort and is more efficient at handling slow-to-access sequential media. Merge sort is often the best choice for sorting a linked list: in this situation it is relatively easy to implement a merge sort in such a way that it requires only Θ(1) extra space, and the slow random-access performance of a linked list makes some other algorithms (such as quicksort) perform poorly, and others (such as heapsort) completely impossible.
As of Perl 5.8, merge sort is its default sorting algorithm (it was quicksort in previous versions of Perl). In Java, the Arrays.sort() methods use merge sort or a tuned quicksort depending on the datatypes and for implementation efficiency switch to insertion sort when fewer than seven array elements are being sorted.[16] The Linux kernel uses merge sort for its linked lists.[17] Python uses Timsort, another tuned hybrid of merge sort and insertion sort, that has become the standard sort algorithm in Java SE 7 (for arrays of non-primitive types),[18] on the Android platform,[19] and in GNU Octave.[20]
Notes[edit]
Jump up ^ Knuth (1998, p. 158)
Jump up ^ Jyrki Katajainen and Jesper Larsson Träff (1997). "A meticulous analysis of mergesort programs".
Jump up ^ Powers, David M. W. and McMahon Graham B. (1983), "A compendium of interesting prolog programs", DCS Technical Report 8313, Department of Computer Science, University of New South Wales.
Jump up ^ The worst case number given here does not agree with that given in Knuth's Art of Computer Programming, Vol 3. The discrepancy is due to Knuth analyzing a variant implementation of merge sort that is slightly sub-optimal
Jump up ^ Cormen; Leiserson; Rivest; Stein. Introduction to Algorithms. p. 151. ISBN 978-0-262-03384-8. |access-date= requires |url= (help)
Jump up ^ Katajainen, Jyrki; Pasanen, Tomi; Teuhola, Jukka (1996). "Practical in-place mergesort". Nordic J. Computing. 3 (1): 27–40. CiteSeerX 10.1.1.22.8523  .
Jump up ^ Geffert, Viliam; Katajainen, Jyrki; Pasanen, Tomi (2000). "Asymptotically efficient in-place merging". Theoretical Computer Science. 237: 159–181. doi:10.1016/S0304-3975(98)00162-5.
Jump up ^ Huang, Bing-Chao; Langston, Michael A. (March 1988). "Practical In-Place Merging". Communications of the ACM. 31 (3): 348–352. doi:10.1145/42392.42403.
Jump up ^ Kim, Pok-Son; Kutzner, Arne (2004). Stable Minimum Storage Merging by Symmetric Comparisons. European Symp. Algorithms. Lecture Notes in Computer Science. 3221. pp. 714–723. CiteSeerX 10.1.1.102.4612  . doi:10.1007/978-3-540-30140-0_63. ISBN 978-3-540-23025-0.
Jump up ^ Selection sort. Knuth's snowplow. Natural merge.
^ Jump up to: a b Cormen et al. 2009, pp. 797–805
Jump up ^ V. J. Duvanenko, "Parallel Merge Sort", Dr. Dobb's Journal, March 2011
Jump up ^ Cole, Richard (August 1988). "Parallel merge sort". SIAM J. Comput. 17 (4): 770–785. CiteSeerX 10.1.1.464.7118  . doi:10.1137/0217049
Jump up ^ Powers, David M. W. Parallelized Quicksort and Radixsort with Optimal Speedup, Proceedings of International Conference on Parallel Computing Technologies. Novosibirsk. 1991.
Jump up ^ David M. W. Powers, Parallel Unification: Practical Complexity, Australasian Computer Architecture Workshop, Flinders University, January 1995
Jump up ^ OpenJDK Subversion
Jump up ^ linux kernel /lib/list_sort.c
Jump up ^ jjb. "Commit 6804124: Replace "modified mergesort" in java.util.Arrays.sort with timsort". Java Development Kit 7 Hg repo. Retrieved 24 Feb 2011.
Jump up ^ "Class: java.util.TimSort<T>". Android JDK Documentation. Archived from the original on January 20, 2015. Retrieved 19 Jan 2015.
Jump up ^ "liboctave/util/oct-sort.cc". Mercurial repository of Octave source code. Lines 23-25 of the initial comment block. Retrieved 18 Feb 2013. Code stolen in large part from Python's, listobject.c, which itself had no license header. However, thanks to Tim Peters for the parts of the code I ripped-off.
References[edit]
Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009) [1990]. Introduction to Algorithms (3rd ed.). MIT Press and McGraw-Hill. ISBN 0-262-03384-4.
Katajainen, Jyrki; Pasanen, Tomi; Teuhola, Jukka (1996). "Practical in-place mergesort". Nordic Journal of Computing. 3. pp. 27–40. ISSN 1236-6064. Retrieved 2009-04-04. . Also Practical In-Place Mergesort. Also [1]
Knuth, Donald (1998). "Section 5.2.4: Sorting by Merging". Sorting and Searching. The Art of Computer Programming. 3 (2nd ed.). Addison-Wesley. pp. 158–168. ISBN 0-201-89685-0.
Kronrod, M. A. (1969). "Optimal ordering algorithm without operational field". Soviet Mathematics - Doklady. 10. p. 744.
LaMarca, A.; Ladner, R. E. (1997). "The influence of caches on the performance of sorting". Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms (SODA97): 370–379. CiteSeerX 10.1.1.31.1153  .
Sun Microsystems. "Arrays API". Retrieved 2007-11-19.
Sun Microsystems. "java.util.Arrays.java". Retrieved 2007-11-19.
External links[edit]
The Wikibook Algorithm implementation has a page on the topic of: Merge sort
Animated Sorting Algorithms: Merge Sort at the Wayback Machine (archived 6 March 2015) – graphical demonstration
Dictionary of Algorithms and Data Structures: Merge sort
Mergesort applet with "level-order" recursive calls to help improve algorithm analysis
Open Data Structures - Section 11.1.1 - Merge Sort
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