#include <iostream>
/*
Axis‑aligned rectangles are simply rectangles whose edges are parallel to the
coordinate axes — meaning their sides are horizontal and vertical.
That single assumption makes the overlap test dramatically simpler and faster.
*/
/*
Rectangle overlap detection (axis-aligned)
Each rectangle is defined by:
- x, y : coordinates of its top-left corner
- w, h : width and height
Two rectangles DO NOT overlap if any separating condition is true:
- One is completely to the left of the other
- One is completely to the right of the other
- One is completely above the other
- One is completely below the other
Otherwise, they overlap.
This is the standard O(1) test for axis-aligned rectangles.
*/
struct Rect {
double x; // top-left X
double y; // top-left Y
double w; // width
double h; // height
};
/*
Returns true if rectangles A and B overlap.
*/
bool rectanglesOverlap(const Rect& A, const Rect& B) {
// Compute edges of A
double A_left = A.x;
double A_right = A.x + A.w;
double A_top = A.y;
double A_bottom = A.y + A.h;
// Compute edges of B
double B_left = B.x;
double B_right = B.x + B.w;
double B_top = B.y;
double B_bottom = B.y + B.h;
// Separating conditions:
if (A_right <= B_left) return false; // A is left of B
if (B_right <= A_left) return false; // B is left of A
if (A_bottom <= B_top) return false; // A is above B
if (B_bottom <= A_top) return false; // B is above A
return true; // Otherwise, they overlap
}
int main() {
Rect A{10, 10, 30, 20}; // Example rectangle A
Rect B{25, 15, 40, 25}; // Overlaps A
Rect C{100, 100, 10, 10}; // Does not overlap A
std::cout << "A vs B overlap? " << (rectanglesOverlap(A, B) ? "YES" : "NO") << "\n";
std::cout << "A vs C overlap? " << (rectanglesOverlap(A, C) ? "YES" : "NO") << "\n";
}
/*
run:
A vs B overlap? YES
A vs C overlap? NO
*/
