Consider all scenarios in which we have a city on a flat plane in which all roads are straight lines; the points at which two (or more) roads meet are called junctions; and we have two points A and B that are accessible from each other by road.In this question you have to determine whether the following statement is true or false.Among all possible routes between A and B, the shortest route goes through the fewest number of junctions.The following points may be helpful:Consider using a pen and paper to draw a few maps when thinking about this problem.The statement is about all possible scenarios, not just a particular city map that you may happen to draw. The statement is about all maps imaginable (with the above-mentioned properties). Obviously you cannot draw all possible maps, so you need to reason about this problem.The statement is true if you can convince yourself that it holds in all possible maps for all possible pairs of locations A and B. The statement is false if you can draw a map in which the statement does not hold.You can assume all distances are finite.Is the statement true or false?

Which of the following is not an assumption of a shortest path problem?A) The lines connecting certain pairs of nodes always allow travel in either direction.B) Associated with each link or arc is a nonnegative number called its length.C) A path through the network must be chosen going from the origin to the destination.D) The objective is to find a shortest path from the origin to the destination.E) None of the choices is correct

find the number of paths that you could take to travel from A and B if you are only allowed to move to the right or down through the grid. You cannot travel a path if the path is not drawn in .

Determine the number of pathways that we can take to go from point A to point B, if we can only travel along the intersected points and can only go South or East.

There are 101 towns in a country. Some pairs of towns are connected by one-way roads, and there are exactly 40 roads going into and 40 roads leaving each town. Can you reach each town from any other, driving along at most three roads?⚡aYesbNocMay be

State Government wants to connect the state road to the national highway from a town. There are 3 possible locations in the town A,B and C to connect to the National Highway whose locations are given by coordinates (3,8)(3,8),(5,7)(5,7),(6,9)(6,9) . The National Highway connects the 2 points (2,1)(2,1),(10,7)(10,7) and You, being the contractor, have the freedom to select any one of the 3 possible locations in the town.Hint   Always select the shortest path to construct the road.Note: 1 unit = 100 meterWhat is the minimum length of road in meter required to construct to connect to the National Highway?