Find the area of the Orthogonal Polygon.

Question

Given an orthogonal polygon, calculate the area, and print it on screen. You will be given input as pairs of direction and length. Input will be provided in the form, direction indicator NEWS, followed by the distance indicator 1-99.

Sample 
Input => N5 E5 S5 W5. 
Output => 25 
Reason => This is a square of side 5, area is 25. 
Input => N10 E2 S8 E8 S2 W10 
Output => 36 
Reason => Depicts L shape. 
          This can be computed as Vertical Rectangle = 2x8, 
          Horizontal Rectangle = 2x8 and common square = 2x2.

Comments

You have given part of solution by yourself, since it is orthogonal hence all edges will be at orthogonal of each other. So we we divide the whole polygon into smaller rectangles (lets assume every square is an rectangle) and calculate the area separately and add.

So now the problem is to divide into rectangles.

Answer 1

Over and above Satish comment and help from Quora -

1. Segment N10, moving from (0, 0) to (0, 10). This increases y from 0 to 10, but because x is unchanged, the change in area is zero, because (Δx * y) = (0 * any number between 0 and 10) = 0.
2. Segment E2, moving from (0, 10) to (2, 10). The area is increased by (Δx * y) = (2 * 10) = 20.
3. Segment S8, moving from (2, 10) to (2, 2). This decreases y but does not change x. The area does not change (remains at 20).
4. Segment E8, moving from (2, 2) to (10, 2). The area is increased by (Δx * y) = (8 * 2) = 16. The total area is now (20 + 16) = 36.
5. Segment S2, moving from (10, 2) to (10, 0). This decreases y but does not change x. The total area does not change (remains at 36).

6. Segment W10, moving from (10, 0) to (0, 0). The area is changed by (Δx * y) = (-10 * 0), which happens to be zero.

   The total is, thus, (0 + 20 + 0 + 16 + 0 + 0) = 36.

Comments

good solution.... sir but i am not sure for all edge cases...if so..i will add those after checking them.

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Did not get you, what do you mean by all edges cases...