Calculate area of Rectilinear Polygon in C

Question

I have to develop a C program for a given set of input values, where we describe the rectanged figure by its boundary by specifying a starting point and a series of movements in four basic directions – as if we were going around the formation along its boundary.
We enter each movement in the direction (WESN) and length – "W 3" means moving from the current position three steps west (left).

The figure in Figure 1 could be described — starting from the upper-right corner — as:

"W 6, S 2, W 3, S 2, E 1, S 2, E 2, N 1, E 2, N 1, E 2, N 1, W 2, N 1, E 3, S 3, E 1, N 5".

My problem is:

1. What is such a shape called in geometry?
2. How can I calculate the area of such a shape? I have lengths of all the sides as W6, S4 etc.

Thanks.

Answer 1

The shape is called polyomino. It's special case of polygon.

The problem of finding the area can be solved by starting at point (0,0) with a polygon of area 0. Next, extending the area by rectangle while moving horizontally.

Assume that the current point is (x,y). Moving to east by d unit means adding a rectangle at points (x,0) -> (x,y) -> (x + d, y) -> (x + d, 0). Rectangle's area is d * y. When moving west one needs to subtract the rectangle.

The final area is positive if the walk is clockwise or negative if the path was counter-clockwise.

This approach results in a very simple program:

#include <stdio.h>

int main() {
    int x = 0, y = 0, A = 0, d;
    int c;
    while ((c = getchar()) != EOF) { 
        if        (c == 'W' && scanf(" %d", &d) == 1) {
            x += d;
            A += d * y;
        } else if (c == 'E' && scanf(" %d", &d) == 1) {
            x -= d;
            A -= d * y;
        } else if (c == 'N' && scanf(" %d", &d) == 1) {
            y += d;
        } else if (c == 'S' && scanf(" %d", &d) == 1) {
            y -= d;
        }
    }
    if (A < 0) A = -A;
    printf("%d\n", A);
    return 0;
}

For input from the question is gives the expected answer of 33.