Question

1 Introduction Consider a perfectly square, infinite grid. Define the driving distance between two points with integer coordinates on the grid as the shortest path between the points when traveling along the gridlines. 2 Objective The goal of this activity is to develop an algorithm that computes the driving distance between two points with integer coordinates. Your solution will be expressed in the form of a flowchart along with a written description of how your algorithm works. 3 Example For points pı = (3,1) and p2 = (0,3), the driving distance is 5. 4 Additional Notes 1. The inputs for the algorithm will be two pairs of coordinates (x1, yı) and (22,y2). You can assume that they are provided as a list of 4 variables in whatever order you like. 2. Your algorithm may only make use of the basic operators we have discussed in class. You cannot assume that you have the absolute value function.

you have to show both algorithm and flowchart

you can just do the flow chart

Answer 1

Since the street is not one – way, we can easily find the distance.

Algorithm :

inputs : integer variables, p{11,41} and q{<2,42}.

begin :

di = distance between (21,71) and (12, y1); i.e, di = sqrt((:21 – 22))

da = distance between 12, y2) and (22, yı); i.e,dı = sqrt((y2 – yı))

d = di + d2:

return d:

$\textbf{end}$

Flowcharti

START inputs: P(X1,Y1) and q(X2,72) d1 = sqrt((x1-x2)2) d2 = sqrt((71-72)2) d = d1 + d2 return d END

Algorithm Explanation :

At first, we take two inputs P(x₁,y₁) and Q(x₂,y₂) which are the coordinates of the two points which is to be travelled by the car. As the gridlines are square shaped and these are the only way to drive, therefore the shortest distance between P and Q along the gridlines will the sum of distances from (x₁,y₁) and (x₂,y₁) AND (x₂,y₂) and (x₂,y₁).