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Discussion

Carlos, Dave and Yolanda were fascinated by the discussion on complexity. Zori was less enthusiastic but even she sensed that the question of which problems could be solved quickly had practical implications.

Discussion

Carlos, Dave and Yolanda were fascinated by the discussion on complexity. Zori was less enthusiastic but even she sensed that the question of which problems could be solved quickly had practical implications. She could even predict that people could earn a nice income solving problems faster and more accurately than their competition.

Bob remarked, I'm not sure I understand what's being talked about here. I don't see why it can't be the case that all problems can be solved. Maybe we just don't know how to do it. Xing said, Any finite problem can be solved. There is always a way to list all the possibilities, compare them one by one and take the best one as the answer. Alice joined in, Well, a problem might take a long time just because it is big. For example, suppose you are given two DVD's, each completely full with the data for a large integer. How are you possibly going to multiply them together, even with a large computer and fancy software. Carlos then offered, But I think there are really hard problems that any algorithm will take a long time to solve and not just because the input size is large. At this point, I don't know how to formulate such a problem but I suspect that they exist.

Manje Akukho kalkuli yokuxazulula le nto, kodwa amaphuzu ayo anga kalkuli. Zama enye ngezansi, noma ubhale yakho.

Qhubeka usebenza

I-akhawunti emahhala ifaka iziphawulo kulesifundo ngasinye, irekhodi lokuthi yini oqedile, izinkinga zakho ezixazululiwe endaweni eyodwa, nodokotela owaziyo ongabuza mayelana nalekhasi. I-matematics ivulekile kubo bonke, noma ngabe babhalise noma cha.

Bhala Ngena

Amaphawu asetshenziswa lapha

Chofoza noma yiluphi uphawu lwesibonakaliso ukuze uthole ukuchaza okuphelele, isithombe, kanye nokuthi iyiphi inhlamvu ekhona ekhuluma ngaso.

Imibuzo abantu bebuza

Permutation or combination?

Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).

What is a graph in this sense?

Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.

Amangxenye wale khasi aguqulwe kusuka Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). I-condensed futhi iphinde icaciswe lapha; amaphutha awusizo.

Okuningi Combinatorics & Graph Theory

The counting principlesPigeonhole principle and inclusion, exclusionBinomial coefficients and Pascal's triangleRecurrences and generating functionsGraphs: vertices, edges, degreesPaths, cycles, trees, Euler and HamiltonColouring and planar graphs