Show problems as
Classic problem #223MediumMathGeometry

Rectangle Area

Real-world version: Total Rug Coverage
Tracked in this browser only
Read Rectangle Area on LeetCode(opens in a new tab)

The statement here is our own: the same inputs, outputs and technique.

Two rugs lie flat on a floor, each with its sides parallel to the floor's grid lines. A survey marker sits at the origin, so a coordinate may be negative.

The first rug spans from the corner (ax1, ay1) to the opposite corner (ax2, ay2), with ax1 the smaller horizontal coordinate and ay1 the smaller vertical one. The second rug spans from (bx1, by1) to (bx2, by2) under the same rule. A rug may be folded flat, in which case one of its sides has length zero and it covers nothing.

Return the area of floor that has at least one rug over it. Floor that both rugs cover counts once. Two rugs whose edges only meet along a line, or at a single point, do not share any area.

Examples

Example 1

Input
ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = 0, by1 = 0, bx2 = 4, by2 = 3
Output
24

The first rug covers 16 units of floor and the second covers 12. The floor they share runs horizontally from 0 to 2 and vertically from 0 to 2, so 4 units are under both and are counted once: 16 + 12 - 4 = 24.

Example 2

Input
ax1 = 0, ay1 = 0, ax2 = 2, ay2 = 2, bx1 = 2, by1 = 0, bx2 = 4, by2 = 2
Output
8

The rugs meet along the vertical line at 2 and share no area, so the total is 4 + 4 = 8.

Example 3

Input
ax1 = -5, ay1 = -5, ax2 = 5, ay2 = 5, bx1 = -1, by1 = -1, bx2 = 1, by2 = 1
Output
100

The smaller rug lies entirely on top of the larger one, so the covered floor is just the larger rug's 100 units.

Constraints

  • -10^4 <= ax1 <= ax2 <= 10^4
  • -10^4 <= ay1 <= ay2 <= 10^4
  • -10^4 <= bx1 <= bx2 <= 10^4
  • -10^4 <= by1 <= by2 <= 10^4

The signature

The editor starts with this. It matches the parent problem's shape, so a solution that works here works on a standard judge unchanged.

Python
def compute_area(ax1: int, ay1: int, ax2: int, ay2: int, bx1: int, by1: int, bx2: int, by2: int) -> int:
Java
public int computeArea(int ax1, int ay1, int ax2, int ay2, int bx1, int by1, int bx2, int by2)

More on the same topics