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Dijkstra's algorithm ( / ˈdaɪkstrəz / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. [4] [5] [6]
Moreover, for each number of cities there is an assignment of distances between the cities for which the nearest neighbor heuristic produces the unique worst possible tour. (If the algorithm is applied on every vertex as the starting vertex, the best path found will be better than at least N/2-1 other tours, where N is the number of vertices.)
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle . It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the ...
50 states and Washington, D.C. This table lists the 336 incorporated places in the United States, excluding the U.S. territories, with a population of at least 100,000 as of July 1, 2023, as estimated by the U.S. Census Bureau. Five states have no cities with populations exceeding 100,000. They are: Delaware, Maine, Vermont, West Virginia, and ...
There are no international passenger trains between the United States and Mexico, nor to Canada outside of Ontario, Montreal, and Vancouver. Cities lacking inter-city rail service [ edit ] For purposes of this list, a city is considered served if it is within 35 miles (56 km) of an Amtrak or other inter-city passenger rail station.
The Bay Area consists of nine counties ( Alameda, Contra Costa, Marin, Napa, San Francisco, San Mateo, Santa Clara, Solano, and Sonoma) and 101 municipalities. [5] One, San Francisco, is a consolidated city–county. California law makes no distinction between "city" and "town", and municipalities may use either term in their official names. [6]
Pennsylvania is a state located in the Northeastern United States. As of the 2020 U.S. census, Pennsylvania is the fifth-most populous state with 13,002,700 inhabitants [1] and the 32nd-largest by land area spanning 44,742.70 square miles (115,883.1 km 2) of land. [2] Pennsylvania is divided into 67 counties and contains 2,560 municipalities.
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