feat(math, rectangle-area): compute area

Author: BrianLusina

pymath/rectangle_area/README.md

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+# Rectangle Area
+
+You are given the coordinates of two axis-aligned rectangles in a 2D plane. Your task is to calculate the total area 
+covered by both rectangles.
+
+The first rectangle is specified by the coordinates of its bottom-left corner (ax1, ay1) and top-right corner (ay1, ay2).
+
+Similarly, the second rectangle is defined by its bottom-left corner (bx1, by1) and top-right corner (bx2, by2).
+
+> Note: The rectangles may overlap.
+
+## Constraints
+
+1. -10^4 ≤ ax1 ≤ ax2 ≤ 10^4
+2. −10^4 ≤ ay1 ≤ ay2 ≤ 10^4
+3. −10^4 ≤ bx1 ≤ bx2 ≤10^4
+4. −10^4 ≤ by1 ≤ by2 ≤ 10^4
+
+## Examples
+
+![Example 1](./images/examples/rectangle_area_example_1.png)
+![Example 2](./images/examples/rectangle_area_example_2.png)
+![Example 3](./images/examples/rectangle_area_example_3.png)
+![Example 4](./images/examples/rectangle_area_example_4.png)

pymath/rectangle_area/__init__.py

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+def compute_area(
+    ax1: int, ay1: int, ax2: int, ay2: int, bx1: int, by1: int, bx2: int, by2: int
+):
+    # 1. Calculate the area of each individual rectangle
+    area_a = (ax2 - ax1) * (ay2 - ay1)
+    area_b = (bx2 - bx1) * (by2 - by1)
+
+    # 2. Calculate the area of the overlap (A intersect B)
+
+    # Determine the coordinates of the overlap rectangle: (ix1, iy1) to (ix2, iy2)
+
+    # The left edge of the overlap is the max of the two left edges
+    ix1 = max(ax1, bx1)
+    # The right edge of the overlap is the min of the two right edges
+    ix2 = min(ax2, bx2)
+
+    # The bottom edge of the overlap is the max of the two bottom edges
+    iy1 = max(ay1, by1)
+    # The top edge of the overlap is the min of the two top edges
+    iy2 = min(ay2, by2)
+
+    # Calculate the width and height of the overlap
+    overlap_width = max(0, ix2 - ix1)
+    overlap_height = max(0, iy2 - iy1)
+
+    # The max(0, ...) ensures that if the rectangles do not overlap
+    # (e.g., ix2 < ix1), the width/height is 0, and the overlap_area is 0.
+    overlap_area = overlap_width * overlap_height
+
+    # 3. Apply the Inclusion-Exclusion Principle
+    total_area = area_a + area_b - overlap_area
+
+    return total_area

pymath/rectangle_area/test_compute_area.py

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+import unittest
+from parameterized import parameterized
+from pymath.rectangle_area import compute_area
+
+
+class RectangleAreaTestCase(unittest.TestCase):
+    @parameterized.expand(
+        [
+            (0, 0, 1, 1, 2, 2, 3, 3, 2),
+            (0, 0, 2, 2, 1, 1, 3, 3, 7),
+            (-1, -1, 2, 2, 0, 0, 1, 1, 9),
+            (0, 0, 0, 0, 1, 1, 2, 2, 1),
+            (-8918, -419, -7715, 577, -8918, -419, -7715, 577, 1198188),
+        ]
+    )
+    def test_compute_area(
+        self,
+        ax1: int,
+        ay1: int,
+        ax2: int,
+        ay2: int,
+        bx1: int,
+        by1: int,
+        bx2: int,
+        by2: int,
+        expected,
+    ):
+        actual = compute_area(ax1, ay1, ax2, ay2, bx1, by1, bx2, by2)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()