# 836.Rectangle Overlap

836.Rectangle Overlap

A rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) are the coordinates of its bottom-left corner, and (x2, y2) are the coordinates of its top-right corner.
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, return whether they overlap.
Example 1:
Input: rec1 = [0,0,2,2], rec2 = [1,1,3,3]
Output: true
Example 2:
Input: rec1 = [0,0,1,1], rec2 = [1,0,2,1]
Output: false
Notes:
Both rectangles rec1 and rec2 are lists of 4 integers.
All coordinates in rectangles will be between -10^9 and 10^9.

class Solution {
//To Left Test; line: px, py, qx,qy;point: sx,sy;
//p.x * q.y - p.y* q.x + q.x * s.y - q.y * s.x + s.x * p.y - s.y * p.x;
bool toLeft(vector<int>rec1,int px, int py,int qx, int qy)
{
vector<long int> tmp(4,0);
int start=0;
for(int i=0;i<3;i+=2)
for(int j=1;j<4;j+=2)
{
int sx=rec1[i];
int sy=rec1[j];
tmp[start++] = (long)px*qy-(long)py*qx +(long)qx*sy -(long)qy*sx + (long)sx*py -(long)sy *px ;
}
// cout<< px <<" "<<py<<" "<<qx<<" "<<qy<<endl;
// cout<<tmp[0] <<" "<< tmp[1] <<" "<<tmp[2] <<" "<< tmp[3]<<endl;
if( tmp[0]<=0 && tmp[1]<=0 && tmp[2]<=0 && tmp[3]<=0) return true;
return false;
}
public:
bool isRectangleOverlap(vector<int>& rec1, vector<int>& rec2) {
return !(toLeft(rec1,rec2[0],rec2[1],rec2[2],rec2[1]) || toLeft(rec1,rec2[2],rec2[1],rec2[2],rec2[3]) || toLeft(rec1,rec2[2],rec2[3],rec2[0],rec2[3] ) || toLeft(rec1,rec2[0],rec2[3],rec2[0],rec2[1]));
}
};

class Solution {
public:
bool isRectangleOverlap(vector<int>& rec1, vector<int>& rec2) {
return (long)max(rec2[2],rec1[2])-min(rec2[0],rec1[0]) < (long)rec2[2]-rec2[0]+ rec1[2]-rec1[0] && (long)max(rec2[3],rec1[3])-min(rec2[1],rec1[1]) < (long)rec2[3]-rec2[1]+rec1[3]-rec1[1] ;
}
};