Rectangle Overlap Problem & Solution

An axis-aligned rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) is the coordinate of its bottom-left corner, and (x2, y2) is the coordinate of its top-right corner. Its top and bottom edges are parallel to the X-axis, and its left and right edges are parallel to the Y-axis.

Two rectangles overlap if the area of their intersection is positive. To be clear, two rectangles that only touch at the corner or edges do not overlap.

Given two axis-aligned rectangles rec1 and rec2, return true if they overlap, otherwise return false.

See the rectangle overlap problem on LeetCode.

C++ Solution

#pragma GCC optimize("Ofast")
#pragma GCC optimization("unroll-loops")
#pragma GCC target("avx,avx2,fma")

static const int _=[](){std::ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);return 0;}();

class Solution {
  bool isRectangleOverlap(vector<int>& rec1, vector<int>& rec2) {
    int x1 = rec1[0];
    int y1 = rec1[1];
    int x2 = rec1[2];
    int y2 = rec1[3];

    int x3 = rec2[0];
    int y3 = rec2[1];
    int x4 = rec2[2];
    int y4 = rec2[3];

    // Tests if the second rectangle is to the left, right, top, or bottom of the first.
    return !(y4 <= y1 || y2 <= y3 || x2 <= x3 || x4 <= x1);

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