Shandong University-Algorithm Analysis and Design Final Exam 2020-12-18

This course has not been a water course since 2019. Except for some basic proofs, the original questions are basically not tested. They are all adapted questions, but the principles have been learned, and the amount of questions is large. You must study hard! ! !
1.
(1) An English question is an adaptation of the safe edge theorem
(2) Pseudo-code with strong connected components, time complexity, and correctness proof
(3) Variation of maximum flow <= minimum cut
2.
(1) Change 3SAT problem is reduced to the Indenpent problem (independent set problem)
(2) Prove that the flow obtained after augmentation is still a legal flow (capacity limitation and flow conservation)
3. Dynamic programming longest path adaptation
4. The shortest between all pairs of vertices Path-basic idea, filling in the form (Ford-wall algorithm)
5. Adaptation of the backpack problem (the minimum weight that can reach a certain value-roughly this is what it means)
is really difficult
to do a good thing, I hope the algorithm results can give me back.