By Michal Forišek, Monika Steinová
There is an important distinction among designing a brand new set of rules, proving its correctness, and instructing it to an viewers. whilst educating algorithms, the teacher's major target may be to show the underlying principles and to aid the scholars shape right psychological types with regards to the set of rules. This technique can usually be facilitated through the use of appropriate metaphors. This paintings presents a collection of novel metaphors pointed out and built as compatible instruments for instructing some of the "classic textbook" algorithms taught in undergraduate classes around the globe. each one bankruptcy offers workouts and didactic notes for academics in response to the authors’ reports whilst utilizing the metaphor in a lecture room setting.
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This gives us a system of two linear equations in s and t. In the non-parallel case this system has a unique solution. The computed values s and t give us endpoints S and T of the shortest segment that connects the lines P0 P1 and Q 0 Q 1 . In order to compute the shortest distance between segments P0 P1 and Q 0 Q 1 , all that remains is to check whether S lies on the segment P0 P1 and whether T lies on Q 0 Q 1 . We already know how to do that. Another way of solving this case is given in [6] by using calculus: The square distance between the points P0 + su and Q 0 + tv is a quadratic function in both s and t.
The railroad car is already stuck at an endpoint of the segment. The rubber band tries to pull it further, but there are no more tracks for the car. In the optimal configuration each of the two cars is in one of the three above cases. By removing the impossible cases and using symmetry, we are left with four possible cases for the pair of cars: 1. The line segments share a common point, and both cars are at one such point. 2. Each car is at an endpoint of its segment. 3. One car is at an endpoint of its segment.
Práce mor. pˇrírodovˇed. spol. 3, 37–58 (1926) (in Czech) 5 Or, more precisely, is the decision version of this problem NP-complete? References ◦ 29 3. : Pˇríspˇevek k ˇrešení otázky ekonomické stavby elektrovodních sítí (Contribution to the solution of a problem of economical construction of electrical networks). Elektronický obzor 15, 153–154 (1926) (in Czech) 4. : On computing a longest path in a tree. Inf. Process. Lett. 81, 93–96 (2002) 5. : A theorem on trees. Q. J. Math. 23, 376–378 (1889) 6.