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NP$503470$ - Übersetzung nach deutsch
![P≠NP]], while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete)](https://commons.wikimedia.org/wiki/Special:FilePath/P np np-complete np-hard.svg?width=200 "P≠NP]], while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete)")
.jpg?width=200 "\"Our Founders\" bust at reception in Skukuza")
![[[Elephant]] family at an artificial water hole](https://commons.wikimedia.org/wiki/Special:FilePath/Kruger Park Elephants.jpg?width=200 "[[Elephant]] family at an artificial water hole")
![necking]]](https://commons.wikimedia.org/wiki/Special:FilePath/South African Giraffes, fighting.jpg?width=200 "necking]]")
![Two [[lion]]esses having a break after an unsuccessful hunt](https://commons.wikimedia.org/wiki/Special:FilePath/Two lions having a break after an unsuccessful hunt in Kruger National Park.jpg?width=200 "Two [[lion]]esses having a break after an unsuccessful hunt")
![A [[greater kudu]] bull](https://commons.wikimedia.org/wiki/Special:FilePath/Male greater kudu.jpg?width=200 "A [[greater kudu]] bull")
![[[Bridalveil Fall]] flows from a U-shaped hanging valley that was created by a tributary glacier.](https://commons.wikimedia.org/wiki/Special:FilePath/Bridalveil Fall and valley.JPG?width=200 "[[Bridalveil Fall]] flows from a U-shaped hanging valley that was created by a tributary glacier.")
![A view of the park and [[Vernal Fall]], photographed by photographer [[Eadweard Muybridge]] in 1872.](https://commons.wikimedia.org/wiki/Special:FilePath/Eadweard Muybridge - Pi-Wi-Ack (Shower of Stars), Vernal Fall, 400 Feet, Valley of Yosemite - Google Art Project.jpg?width=200 "A view of the park and [[Vernal Fall]], photographed by photographer [[Eadweard Muybridge]] in 1872.")
![Yosemite in [[autumn]]](https://commons.wikimedia.org/wiki/Special:FilePath/El Capitan at fall.jpg?width=200 "Yosemite in [[autumn]]")
![Glacially polished granite [[cirque]] in upper [[Tenaya Canyon]]](https://commons.wikimedia.org/wiki/Special:FilePath/Glacially polished granite.jpg?width=200 "Glacially polished granite [[cirque]] in upper [[Tenaya Canyon]]")
![domes]] including [[Half Dome]].](https://commons.wikimedia.org/wiki/Special:FilePath/Half Dome from Glacier Point, Yosemite NP - Diliff.jpg?width=200 "domes]] including [[Half Dome]].")
![Hikers line the [[Half Dome]] cables on a busy summer day in 2008](https://commons.wikimedia.org/wiki/Special:FilePath/Half dome cables big (cropped).jpg?width=200 "Hikers line the [[Half Dome]] cables on a busy summer day in 2008")
![USGS]] image)](https://commons.wikimedia.org/wiki/Special:FilePath/Map of Yosemite National Park.svg?width=200 "USGS]] image)")
![Marmot]] in [[Tuolumne Meadows]]](https://commons.wikimedia.org/wiki/Special:FilePath/Marmota flaviventris (Yellow Bellied Marmot), Yosemite NP - Diliff.jpg?width=200 "Marmot]] in [[Tuolumne Meadows]]")
![[[Mule deer]] in Yosemite Valley](https://commons.wikimedia.org/wiki/Special:FilePath/Mule deer in Yosemite Valley.jpg?width=200 "[[Mule deer]] in Yosemite Valley")
![O'Shaughnessy Dam]] in [[Hetch Hetchy]] Valley](https://commons.wikimedia.org/wiki/Special:FilePath/O'Shaughnessy Dam.jpg?width=200 "O'Shaughnessy Dam]] in [[Hetch Hetchy]] Valley")
![Cathedral Peak]]](https://commons.wikimedia.org/wiki/Special:FilePath/The spiny crown of Cathedral Peak, Yosemite National Park, California.jpg?width=200 "Cathedral Peak]]")
![Climbing the Narrows in [[Sentinel Rock]]](https://commons.wikimedia.org/wiki/Special:FilePath/Tom Frost - Ryan Frost in Narrows - 1996.jpg?width=200 "Climbing the Narrows in [[Sentinel Rock]]")
![The [[Merced River]] flowing through [[Yosemite Valley]], a [[U-shaped valley]]](https://commons.wikimedia.org/wiki/Special:FilePath/Valley View Yosemite August 2013 002.jpg?width=200 "The [[Merced River]] flowing through [[Yosemite Valley]], a [[U-shaped valley]]")
![yellow star thistle]] competes with Yosemite's native plants.<ref name = "exotic"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Yellow star thistle.jpg?width=200 "yellow star thistle]] competes with Yosemite's native plants.<ref name = \"exotic\"/>")
![black bear]] with an ear tag in Yosemite Valley](https://commons.wikimedia.org/wiki/Special:FilePath/YosemiteBlackBearTagged wb.jpg?width=200 "black bear]] with an ear tag in Yosemite Valley")
![The [[Meadow Fire]] burns in Little Yosemite Valley, 2014](https://commons.wikimedia.org/wiki/Special:FilePath/Yosemite Meadow fire, 9-7-2014.jpg?width=200 "The [[Meadow Fire]] burns in Little Yosemite Valley, 2014")
![bus service]]](https://commons.wikimedia.org/wiki/Special:FilePath/Yosemite Shuttle bus with Half Dome behind, May 2022.JPG?width=200 "bus service]]")
![[[El Capitan]], a granite monolith on Yosemite Valley's northern escarpment](https://commons.wikimedia.org/wiki/Special:FilePath/Yosemite Valley - El Capitan from Central Pillar of Frenzy - 2.JPG?width=200 "[[El Capitan]], a granite monolith on Yosemite Valley's northern escarpment")
![A ranger-guided [[snowshoe]] walk in the park](https://commons.wikimedia.org/wiki/Special:FilePath/Yosemite Winter Hiking.jpg?width=200 "A ranger-guided [[snowshoe]] walk in the park")
Definition
Wikipedia
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem.
A more precise specification is: a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, H's solution can be used to solve L in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists.
It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class.
