Initial data commit

Task/Shoelace-formula-for-polygonal-area/Java/shoelace-formula-for-polygonal-area.java

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+import java.util.List;
+
+public class ShoelaceFormula {
+    private static class Point {
+        int x, y;
+
+        Point(int x, int y) {
+            this.x = x;
+            this.y = y;
+        }
+
+        @Override
+        public String toString() {
+            return String.format("(%d, %d)", x, y);
+        }
+    }
+
+    private static double shoelaceArea(List<Point> v) {
+        int n = v.size();
+        double a = 0.0;
+        for (int i = 0; i < n - 1; i++) {
+            a += v.get(i).x * v.get(i + 1).y - v.get(i + 1).x * v.get(i).y;
+        }
+        return Math.abs(a + v.get(n - 1).x * v.get(0).y - v.get(0).x * v.get(n - 1).y) / 2.0;
+    }
+
+    public static void main(String[] args) {
+        List<Point> v = List.of(
+            new Point(3, 4),
+            new Point(5, 11),
+            new Point(12, 8),
+            new Point(9, 5),
+            new Point(5, 6)
+        );
+        double area = shoelaceArea(v);
+        System.out.printf("Given a polygon with vertices %s,%n", v);
+        System.out.printf("its area is %f,%n", area);
+    }
+}