Algorithm 找到重叠矩形区域的有效算法是什么 我的处境 输入：一组矩形 每个矩形由如下4个双精度组成：（x0，y0，x1，y1） 它们不会以任何角度“旋转”，它们都是相对于屏幕“上/下”和“左/右”的“正常”矩形 它们是随机放置的-它们可能在边缘接触、重叠或没有任何接触 我将有几百个矩形 这是用C语言实现的# 我需要找到 由其重叠形成的区域-画布中多个矩形“覆盖”的所有区域（例如，两个矩形的交点） 我不需要重叠的几何图形，只需要面积（例如：4平方英寸） 重叠不应该被计数多次-例如，想象3个具有相同大小和位置的矩形-它们正好位于彼此的顶部-该区域应该被计数一次（而不是三次） 例子 下图包含三个矩形：A、B、C A和B重叠（如虚线所示） B和C重叠（如虚线所示） 我要找的是显示破折号的区域

-

---

您可以找到x轴和y轴上的重叠，并将它们相乘

int LineOverlap(int line1a, line1b, line2a, line2b) 
{
  // assume line1a <= line1b and line2a <= line2b
  if (line1a < line2a) 
  {
    if (line1b > line2b)
      return line2b-line2a;
    else if (line1b > line2a)
      return line1b-line2a;
    else 
      return 0;
  }
  else if (line2a < line1b)
    return line2b-line1a;
  else 
    return 0;
}


int RectangleOverlap(Rect rectA, rectB) 
{
  return LineOverlap(rectA.x1, rectA.x2, rectB.x1, rectB.x2) *
    LineOverlap(rectA.y1, rectA.y2, rectB.y1, rectB.y2);
}

int-LineOverlap（int-line1a、line1b、line2a、line2b）
{
//假设第1a行（第2a行）
回流管1B-2A；
其他的
返回0；
}
否则如果（第2a行<第1b行）
回流管2B-1A；
其他的
返回0；
}
int矩形重叠（Rect rectA，rectB）
{
返回线重叠（rectA.x1、rectA.x2、rectB.x1、rectB.x2）*
线重叠（rectA.y1、rectA.y2、rectB.y1、rectB.y2）；
}

一种解决方法是将其绘制到画布上！使用半透明颜色绘制每个矩形。NET运行时将使用优化的本机代码进行绘图，甚至使用硬件加速器

然后，你必须读回像素。每个像素是背景色、矩形色还是其他颜色？如果两个或多个矩形重叠，它就可以成为另一种颜色

---

如果这是一个太多的欺骗，我会推荐四叉树作为另一个回答，或。

这是一些快速和肮脏的代码，我在TopCoder SRM 160 Div 2中使用

t=顶部
b=博特托姆
l=左
r=右

public class Rect
{
    public int t, b, l, r;

    public Rect(int _l, int _b, int _r, int _t)
    {
        t = _t;
        b = _b;
        l = _l;
        r = _r;
    }   

    public bool Intersects(Rect R)
    {
        return !(l > R.r || R.l > r || R.b > t || b > R.t);
    }

    public Rect Intersection(Rect R)
    {
        if(!this.Intersects(R))
            return new Rect(0,0,0,0);
        int [] horiz = {l, r, R.l, R.r};
        Array.Sort(horiz);
        int [] vert = {b, t, R.b, R.t};
        Array.Sort(vert);

        return new Rect(horiz[1], vert[1], horiz[2], vert[2]);
    } 

    public int Area()
    {
        return (t - b)*(r-l);
    }

    public override string ToString()
    {
        return l + " " + b + " " + r + " " + t;
    }
}

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如果您的矩形是稀疏的（大部分不是相交的），那么值得一看递归维度集群。否则，四叉树似乎是最好的选择（正如其他海报所提到的那样）

这是电脑游戏中碰撞检测中的常见问题，因此不缺乏解决方法的资源

这是一篇很好的总结RCD的博客文章

---

这是一篇Dobbs博士的文章，总结了各种适合的碰撞检测算法。

这种类型的碰撞检测通常被称为AABB（轴对齐边界框），这是一个很好的起点。

下面是一些我脑海中听上去可能有用的东西：

创建一个具有双键和矩形+布尔值列表的字典，如下所示：

0. empty set, zero sum
1. enter a, add a to set (1 rectangle in set)
2. enter d, add d to set (>1 rectangles in set = overlap, store this y-coordinate)
3. leave a, remove a from set (now back from >1 rectangles in set, add to sum: y - stored_y
4. enter c, add c to set (>1 rectangles in set = overlap, store this y-coordinate)
5. leave d, remove d from set (now back from >1 rectangles in set, add to sum: y - stored_y)
6. multiply sum with width of strip to get overlapping areas

字典>>矩形

对于集合中的每个矩形，找到x0和x1值的对应列表，并将该矩形添加到该列表中，其中x0的布尔值为true，x1的布尔值为false。这样，您现在就拥有了每个矩形输入（true）或离开（false）x方向的所有x坐标的完整列表

从该字典中获取所有键（所有不同的x坐标），对它们进行排序，并按顺序循环，确保可以同时获得当前x值和下一个x值（两者都需要）。这将为您提供单独的矩形条

维护一组当前正在查看的矩形，这些矩形一开始为空。对于在第3点中迭代的每个x值，如果矩形注册为真值，则将其添加到该矩形集中，否则将其删除

对于条形图，按矩形的y坐标对其进行排序

在条带中的矩形中循环，计算重叠距离（我还不清楚如何有效地进行此操作）

计算条带宽度乘以重叠距离的高度以获得面积

例如，5个矩形，从a到e相互重叠绘制：

aaaaaaaaaaaaaaaa          bbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaa          bbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaa          bbbbbbbbbbbbbbbbb
aaaaaaaaaaaaaaaa          bbbbbbbbbbbbbbbbb
aaaaaaaadddddddddddddddddddddddddddddbbbbbb
aaaaaaaadddddddddddddddddddddddddddddbbbbbb
        ddddddddddddddddddddddddddddd
        ddddddddddddddddddddddddddddd
        ddddddddddddddeeeeeeeeeeeeeeeeee
        ddddddddddddddeeeeeeeeeeeeeeeeee
        ddddddddddddddeeeeeeeeeeeeeeeeee
ccccccccddddddddddddddeeeeeeeeeeeeeeeeee
ccccccccddddddddddddddeeeeeeeeeeeeeeeeee
cccccccccccc          eeeeeeeeeeeeeeeeee
cccccccccccc          eeeeeeeeeeeeeeeeee
cccccccccccc
cccccccccccc

以下是x坐标列表：

v       v  v   v      v   v         v  v  v   
|aaaaaaa|aa|aaaa      |   bbbbbbbbbb|bb|bbb
|aaaaaaa|aa|aaaa      |   bbbbbbbbbb|bb|bbb
|aaaaaaa|aa|aaaa      |   bbbbbbbbbb|bb|bbb
|aaaaaaa|aa|aaaa      |   bbbbbbbbbb|bb|bbb
|aaaaaaaddd|dddddddddd|ddddddddddddddbb|bbb
|aaaaaaaddd|dddddddddd|ddddddddddddddbb|bbb
|       ddd|dddddddddd|dddddddddddddd  |
|       ddd|dddddddddd|dddddddddddddd  |
|       ddd|ddddddddddeeeeeeeeeeeeeeeeee
|       ddd|ddddddddddeeeeeeeeeeeeeeeeee
|       ddd|ddddddddddeeeeeeeeeeeeeeeeee
ccccccccddd|ddddddddddeeeeeeeeeeeeeeeeee
ccccccccddd|ddddddddddeeeeeeeeeeeeeeeeee
cccccccccccc          eeeeeeeeeeeeeeeeee
cccccccccccc          eeeeeeeeeeeeeeeeee
cccccccccccc
cccccccccccc

该列表将是（其中每个v仅给出一个从0开始向上的坐标）：

因此，每个条带将是（从上到下排序的矩形）：

对于每条带，重叠部分应为：

0-1: none
1-2: a/d, d/c
2-3: a/d
3-4: none
4-5: d/e
5-6: b/d, d/e
6-7: none
7-8: none

我可以想象，用于上下检查的sort+enter/leave算法的变体也是可行的：

对我们当前在条带中分析的矩形进行排序，从上到下，对于具有相同顶部坐标的矩形，也按底部坐标进行排序

迭代y坐标，当您输入矩形时，将其添加到集合中；当您离开矩形时，将其从集合中移除

每当集合中有多个矩形时，就有重叠（如果确保添加/删除所有具有当前查看的相同上/下坐标的矩形，则多个重叠矩形不会有问题）

对于上面的1-2条，您可以这样迭代：

0. empty set, zero sum
1. enter a, add a to set (1 rectangle in set)
2. enter d, add d to set (>1 rectangles in set = overlap, store this y-coordinate)
3. leave a, remove a from set (now back from >1 rectangles in set, add to sum: y - stored_y
4. enter c, add c to set (>1 rectangles in set = overlap, store this y-coordinate)
5. leave d, remove d from set (now back from >1 rectangles in set, add to sum: y - stored_y)
6. multiply sum with width of strip to get overlapping areas

实际上，你也不需要在这里维护一个实际的集合，只要你在里面的矩形的计数，每当它从1变为2，存储y，每当它从2变为1，计算当前y存储的y，并求和这个差值

---

希望这是可以理解的，正如我所说的，这是我脑子里想不出来的，没有经过任何测试。

如果你拆分每个矩形，你可以简化这个问题

0-1: none
1-2: a/d, d/c
2-3: a/d
3-4: none
4-5: d/e
5-6: b/d, d/e
6-7: none
7-8: none

0. empty set, zero sum
1. enter a, add a to set (1 rectangle in set)
2. enter d, add d to set (>1 rectangles in set = overlap, store this y-coordinate)
3. leave a, remove a from set (now back from >1 rectangles in set, add to sum: y - stored_y
4. enter c, add c to set (>1 rectangles in set = overlap, store this y-coordinate)
5. leave d, remove d from set (now back from >1 rectangles in set, add to sum: y - stored_y)
6. multiply sum with width of strip to get overlapping areas

1 2 3 4 5 6 1 +---+---+ | | 2 + A +---+---+ | | B | 3 + + +---+---+ | | | | | 4 +---+---+---+---+ + | | 5 + C + | | 6 +---+---+ 1 3 4 5 6 1 2 3 4 6 4 * 4 1 3 4 5 6 1 +---+ | 1 | 0 0 0 2 +---+---+---+ | 1 | 1 | 1 | 0 3 +---+---+---+---+ | 1 | 1 | 2 | 1 | 4 +---+---+---+---+ 0 0 | 1 | 1 | 6 +---+---+

#include <iostream>
#include <vector>

using namespace std;


class Rectangle {
public:
    int x[2], y[2];

    Rectangle(int x1, int y1, int x2, int y2) {
        x[0] = x1;
        y[0] = y1;
        x[1] = x2;
        y[1] = y2; 
    };
    void print(void) {
        cout << "Rect: " << x[0] << " " << y[0] << " " << x[1] << " " << y[1] << " " <<endl;
    };
};

// return the iterator of rec in list
vector<Rectangle *>::iterator bin_search(vector<Rectangle *> &list, int begin, int end, Rectangle *rec) {
    cout << begin << " " <<end <<endl;
    int mid = (begin+end)/2;
    if (list[mid]->y[0] == rec->y[0]) {
        if (list[mid]->y[1] == rec->y[1])
            return list.begin() + mid;
        else if (list[mid]->y[1] < rec->y[1]) {
            if (mid == end)
                return list.begin() + mid+1;
            return bin_search(list,mid+1,mid,rec);
        }
        else {
            if (mid == begin)
                return list.begin()+mid;
            return bin_search(list,begin,mid-1,rec);
        }
    }
    else if (list[mid]->y[0] < rec->y[0]) {
        if (mid == end) {
            return list.begin() + mid+1;
        }
        return bin_search(list, mid+1, end, rec);
    }
    else {
        if (mid == begin) {
            return list.begin() + mid;
        }
        return bin_search(list, begin, mid-1, rec);
    }
}

// add rect to rects
void add_rec(Rectangle *rect, vector<Rectangle *> &rects) {
    if (rects.size() == 0) {
        rects.push_back(rect);
    }
    else {
        vector<Rectangle *>::iterator it = bin_search(rects, 0, rects.size()-1, rect);
        rects.insert(it, rect);
    }
}

// remove rec from rets
void remove_rec(Rectangle *rect, vector<Rectangle *> &rects) {
    vector<Rectangle *>::iterator it = bin_search(rects, 0, rects.size()-1, rect);
    rects.erase(it);
}

// calculate the total vertical length covered by rectangles in the active set
int vert_dist(vector<Rectangle *> as) {
    int n = as.size();

    int totallength = 0;
    int start, end;

    int i = 0;
    while (i < n) {
        start = as[i]->y[0];
        end = as[i]->y[1];
        while (i < n && as[i]->y[0] <= end) {
            if (as[i]->y[1] > end) {
                end = as[i]->y[1];
            }
            i++;
        }
        totallength += end-start;
    }
    return totallength;
}

bool mycomp1(Rectangle* a, Rectangle* b) {
    return (a->x[0] < b->x[0]);
}

bool mycomp2(Rectangle* a, Rectangle* b) {
    return (a->x[1] < b->x[1]);
}

int findarea(vector<Rectangle *> rects) {
    vector<Rectangle *> start = rects;
    vector<Rectangle *> end = rects;
    sort(start.begin(), start.end(), mycomp1);
    sort(end.begin(), end.end(), mycomp2);

    // active set
    vector<Rectangle *> as;

    int n = rects.size();

    int totalarea = 0;
    int current = start[0]->x[0];
    int next;
    int i = 0, j = 0;
    // big loop
    while (j < n) {
        cout << "loop---------------"<<endl;
        // add all recs that start at current
        while (i < n && start[i]->x[0] == current) {
            cout << "add" <<endl;
            // add start[i] to AS
            add_rec(start[i], as);
            cout << "after" <<endl;
            i++;
        }
        // remove all recs that end at current
        while (j < n && end[j]->x[1] == current) {
            cout << "remove" <<endl;
            // remove end[j] from AS
            remove_rec(end[j], as);
            cout << "after" <<endl;
            j++;
        }

        // find next event x
        if (i < n && j < n) {
            if (start[i]->x[0] <= end[j]->x[1]) {
                next = start[i]->x[0];
            }
            else {
                next = end[j]->x[1];
            }
        }
        else if (j < n) {
            next = end[j]->x[1];
        }

        // distance to next event
        int horiz = next - current;
        cout << "horiz: " << horiz <<endl;

        // figure out vertical dist
        int vert = vert_dist(as);
        cout << "vert: " << vert <<endl;

        totalarea += vert * horiz;

        current = next;
    }
    return totalarea;
}

int main() {
    vector<Rectangle *> rects;
    rects.push_back(new Rectangle(0,0,1,1));

    rects.push_back(new Rectangle(1,0,2,3));

    rects.push_back(new Rectangle(0,0,3,3));

    rects.push_back(new Rectangle(1,0,5,1));

    cout << findarea(rects) <<endl;
}

GridLocation gl = new GridLocation(curX, curY);
if(usedLocations.contains(gl) && usedLocations2.add(gl)) {
  ret += width*height;
} else {
  usedLocations.add(gl);
}

import numpy as np

A = np.zeros((100, 100))
B = np.zeros((100, 100))

A[rect1.top : rect1.bottom,  rect1.left : rect1.right] = 1
B[rect2.top : rect2.bottom,  rect2.left : rect2.right] = 1

area_of_union     = np.sum((A + B) > 0)
area_of_intersect = np.sum((A + B) > 1)

import java.io.*;
import java.util.*;

class Solution {

static class Rectangle{
         int x;
         int y;
         int dx;
         int dy;

         Rectangle(int x, int y, int dx, int dy){
           this.x = x;
           this.y = y;
           this.dx = dx;
           this.dy = dy;
         }

         Range getBottomLeft(){
            return new Range(x, y);
         }

         Range getTopRight(){
            return new Range(x + dx, y + dy);
         }

         @Override
         public int hashCode(){
            return (x+y+dx+dy)/4;
         }

         @Override
         public boolean equals(Object other){
            Rectangle o = (Rectangle) other;
            return o.x == this.x && o.y == this.y && o.dx == this.dx && o.dy == this.dy;
         }

        @Override
        public String toString(){
            return String.format("X = %d, Y = %d, dx : %d, dy : %d", x, y, dx, dy);
        }
     }     

     static class RW{
         Rectangle r;
         boolean start;

         RW (Rectangle r, boolean start){
           this.r = r;
           this.start = start;
         }

         @Override
         public int hashCode(){
             return r.hashCode() + (start ? 1 : 0);
         }

         @Override
         public boolean equals(Object other){
              RW o = (RW)other;
             return o.start == this.start && o.r.equals(this.r);
         }

        @Override
        public String toString(){
            return "Rectangle : " + r.toString() + ", start = " + this.start;
        }
     }

     static class Range{
         int l;
         int u;   

       public Range(int l, int u){
         this.l = l;
         this.u = u;
       }

         @Override
         public int hashCode(){
            return (l+u)/2;
         }

         @Override
         public boolean equals(Object other){
            Range o = (Range) other;
            return o.l == this.l && o.u == this.u;
         }

        @Override
        public String toString(){
            return String.format("L = %d, U = %d", l, u);
        }
     }

     static class XComp implements Comparator<RW>{
             @Override
             public int compare(RW rw1, RW rw2){
                 //TODO : revisit these values.
                 Integer x1 = -1;
                 Integer x2 = -1;

                 if(rw1.start){
                     x1 = rw1.r.x;
                 }else{
                     x1 = rw1.r.x + rw1.r.dx;
                 }   

                 if(rw2.start){
                     x2 = rw2.r.x;
                 }else{
                     x2 = rw2.r.x + rw2.r.dx;
                 }

                 return x1.compareTo(x2);
             }
     }

     static class YComp implements Comparator<RW>{
             @Override
             public int compare(RW rw1, RW rw2){
                 //TODO : revisit these values.
                 Integer y1 = -1;
                 Integer y2 = -1;

                 if(rw1.start){
                     y1 = rw1.r.y;
                 }else{
                     y1 = rw1.r.y + rw1.r.dy;
                 }   

                 if(rw2.start){
                     y2 = rw2.r.y;
                 }else{
                     y2 = rw2.r.y + rw2.r.dy;
                 }

                 return y1.compareTo(y2);
             }
     }

     public static void main(String []args){
         Rectangle [] rects = new Rectangle[4];

         rects[0] = new Rectangle(10, 10, 10, 10);
         rects[1] = new Rectangle(15, 10, 10, 10);
         rects[2] = new Rectangle(20, 10, 10, 10);
         rects[3] = new Rectangle(25, 10, 10, 10);

         int totalArea = getArea(rects, false);
         System.out.println("Total Area : " + totalArea);

         int overlapArea = getArea(rects, true);              
         System.out.println("Overlap Area : " + overlapArea);
     }


     static int getArea(Rectangle []rects, boolean overlapOrTotal){
         printArr(rects);

         // step 1: create two wrappers for every rectangle
         RW []rws = getWrappers(rects);       

         printArr(rws);        

         // steps 2 : sort rectangles by their x-coordinates
         Arrays.sort(rws, new XComp());   

         printArr(rws);        

         // step 3 : group the rectangles in every range.
         Map<Range, List<Rectangle>> rangeGroups = groupRects(rws, true);

         for(Range xrange : rangeGroups.keySet()){
             List<Rectangle> xRangeRects = rangeGroups.get(xrange);
             System.out.println("Range : " + xrange);
             System.out.println("Rectangles : ");
             for(Rectangle rectx : xRangeRects){
                System.out.println("\t" + rectx);               
             }
         }   

         // step 4 : iterate through each of the pairs and their rectangles

         int sum = 0;
         for(Range range : rangeGroups.keySet()){
             List<Rectangle> rangeRects = rangeGroups.get(range);
             sum += getOverlapOrTotalArea(rangeRects, range, overlapOrTotal);
         }
         return sum;         
     }    

     static Map<Range, List<Rectangle>> groupRects(RW []rws, boolean isX){
         //group the rws with either x or y coordinates.

         Map<Range, List<Rectangle>> rangeGroups = new HashMap<Range, List<Rectangle>>();

         List<Rectangle> rangeRects = new ArrayList<Rectangle>();            

         int i=0;
         int prev = Integer.MAX_VALUE;

         while(i < rws.length){
             int curr = isX ? (rws[i].start ? rws[i].r.x : rws[i].r.x + rws[i].r.dx): (rws[i].start ? rws[i].r.y : rws[i].r.y + rws[i].r.dy);

             if(prev < curr){
                Range nRange = new Range(prev, curr);
                rangeGroups.put(nRange, rangeRects);
                rangeRects = new ArrayList<Rectangle>(rangeRects);
             }
             prev = curr;

             if(rws[i].start){
               rangeRects.add(rws[i].r);
             }else{
               rangeRects.remove(rws[i].r);
             }

           i++;
         }
       return rangeGroups;
     }

     static int getOverlapOrTotalArea(List<Rectangle> rangeRects, Range range, boolean isOverlap){
         //create horizontal sweep lines similar to vertical ones created above

         // Step 1 : create wrappers again
         RW []rws = getWrappers(rangeRects);

         // steps 2 : sort rectangles by their y-coordinates
         Arrays.sort(rws, new YComp());

         // step 3 : group the rectangles in every range.
         Map<Range, List<Rectangle>> yRangeGroups = groupRects(rws, false);

         //step 4 : for every range if there are more than one rectangles then computer their area only once.

         int sum = 0;
         for(Range yRange : yRangeGroups.keySet()){
             List<Rectangle> yRangeRects = yRangeGroups.get(yRange);

             if(isOverlap){
                 if(yRangeRects.size() > 1){
                     sum += getArea(range, yRange);
                 }
             }else{
                 if(yRangeRects.size() > 0){
                     sum += getArea(range, yRange);
                 }
             }
         }         
         return sum;
     } 

    static int getArea(Range r1, Range r2){
      return (r2.u-r2.l)*(r1.u-r1.l);      
    }

    static RW[] getWrappers(Rectangle []rects){
         RW[] wrappers = new RW[rects.length * 2];

         for(int i=0,j=0;i<rects.length;i++, j+=2){
             wrappers[j] = new RW(rects[i], true); 
             wrappers[j+1] = new RW(rects[i], false); 
         }
         return wrappers;
     }

    static RW[] getWrappers(List<Rectangle> rects){
         RW[] wrappers = new RW[rects.size() * 2];

         for(int i=0,j=0;i<rects.size();i++, j+=2){
             wrappers[j] = new RW(rects.get(i), true); 
             wrappers[j+1] = new RW(rects.get(i), false); 
         }
         return wrappers;
     }

  static void printArr(Object []a){
    for(int i=0; i < a.length;i++){
      System.out.println(a[i]);
    }
    System.out.println();
  }     

    #include <iostream>
using namespace std;

int rectoverlap (int ax1, int ay1, int ax2, int ay2, int bx1, int by1, int bx2, int by2)
{
    int width, heigh, area;

    if (ax2<bx1 || ay2<by1 || ax1>bx2 || ay1>by2) {
        cout << "Rectangles are not overlapped" << endl;
        return 0;
    }
    if (ax2>=bx2 && bx1>=ax1){
        width=bx2-bx1;
        heigh=by2-by1;
    } else if (bx2>=ax2 && ax1>=bx1) {
        width=ax2-ax1;
        heigh=ay2-ay1;
    } else {
        if (ax2>bx2){
            width=bx2-ax1;
        } else {
            width=ax2-bx1;
        }
        if (ay2>by2){
            heigh=by2-ay1;
        } else {
            heigh=ay2-by1;
        }
    }
    area= heigh*width;
    return (area);
}

int main()
{
    int ax1,ay1,ax2,ay2,bx1,by1,bx2,by2;
    cout << "Inter the x value for bottom left for rectangle A" << endl;
    cin >> ax1;
    cout << "Inter the y value for bottom left for rectangle A" << endl;
    cin >> ay1;
    cout << "Inter the x value for top right for rectangle A" << endl;
    cin >> ax2;
    cout << "Inter the y value for top right for rectangle A" << endl;
    cin >> ay2;
    cout << "Inter the x value for bottom left for rectangle B" << endl;
    cin >> bx1;
    cout << "Inter the y value for bottom left for rectangle B" << endl;
    cin >> by1;
    cout << "Inter the x value for top right for rectangle B" << endl;
    cin >> bx2;
    cout << "Inter the y value for top right for rectangle B" << endl;
    cin >> by2;
    cout << "The overlapped area is " <<  rectoverlap (ax1, ay1, ax2, ay2, bx1, by1, bx2, by2) << endl;
}

var totArea = rects.Sum(x => x.Width * x.Height);

var overlappingArea =totArea-GetArea(rects)

   #region rectangle overlapping
        /// <summary>
        /// see algorithm for detecting overlapping areas here: https://stackoverflow.com/a/245245/3225391
        /// or easier here:
        /// http://codercareer.blogspot.co.il/2011/12/no-27-area-of-rectangles.html
        /// </summary>
        /// <param name="dim"></param>
        /// <returns></returns>
        public static float GetArea(RectangleF[] rects)
        {
            List<float> xs = new List<float>();
            foreach (var item in rects)
            {
                xs.Add(item.X);
                xs.Add(item.Right);
            }
            xs = xs.OrderBy(x => x).Cast<float>().ToList();
            rects = rects.OrderBy(rec => rec.X).Cast<RectangleF>().ToArray();
            float area = 0f;
            for (int i = 0; i < xs.Count - 1; i++)
            {
                if (xs[i] == xs[i + 1])//not duplicate
                    continue;
                int j = 0;
                while (rects[j].Right < xs[i])
                    j++;
                List<Range> rangesOfY = new List<Range>();
                var rangeX = new Range(xs[i], xs[i + 1]);
                GetRangesOfY(rects, j, rangeX, out rangesOfY);
                area += GetRectArea(rangeX, rangesOfY);
            }
            return area;
        }

        private static void GetRangesOfY(RectangleF[] rects, int rectIdx, Range rangeX, out List<Range> rangesOfY)
        {
            rangesOfY = new List<Range>();
            for (int j = rectIdx; j < rects.Length; j++)
            {
                if (rangeX.less < rects[j].Right && rangeX.greater > rects[j].Left)
                {
                    rangesOfY = Range.AddRange(rangesOfY, new Range(rects[j].Top, rects[j].Bottom));
#if DEBUG
                    Range rectXRange = new Range(rects[j].Left, rects[j].Right);
#endif
                }
            }
        }

        static float GetRectArea(Range rangeX, List<Range> rangesOfY)
        {
            float width = rangeX.greater - rangeX.less,
                area = 0;

            foreach (var item in rangesOfY)
            {
                float height = item.greater - item.less;
                area += width * height;
            }
            return area;
        }

        internal class Range
        {
            internal static List<Range> AddRange(List<Range> lst, Range rng2add)
            {
                if (lst.isNullOrEmpty())
                {
                    return new List<Range>() { rng2add };
                }

                for (int i = lst.Count - 1; i >= 0; i--)
                {
                    var item = lst[i];
                    if (item.IsOverlapping(rng2add))
                    {
                        rng2add.Merge(item);
                        lst.Remove(item);
                    }
                }
                lst.Add(rng2add);
                return lst;
            }
            internal float greater, less;
            public override string ToString()
            {
                return $"ln{less} gtn{greater}";
            }

            internal Range(float less, float greater)
            {
                this.less = less;
                this.greater = greater;
            }

            private void Merge(Range rng2add)
            {
                this.less = Math.Min(rng2add.less, this.less);
                this.greater = Math.Max(rng2add.greater, this.greater);
            }
            private bool IsOverlapping(Range rng2add)
            {
                return !(less > rng2add.greater || rng2add.less > greater);
                //return
                //    this.greater < rng2add.greater && this.greater > rng2add.less
                //    || this.less > rng2add.less && this.less < rng2add.greater

                //    || rng2add.greater < this.greater && rng2add.greater > this.less
                //    || rng2add.less > this.less && rng2add.less < this.greater;
            }
        }
        #endregion rectangle overlapping

int rectoverlap (int ax1, int ay1, int ax2, int ay2, int bx1, int by1, int bx2, int by2)
{
    int width, height, area;

    if (ax2<bx1 || ay2<by1 || ax1>bx2 || ay1>by2) {
        cout << "Rectangles are not overlapped" << endl;
        return 0;
    }

    if (ax2>=bx2 && bx1>=ax1){
        width=bx2-bx1;
    } else if (bx2>=ax2 && ax1>=bx1) {
        width=ax2-ax1;
    } else if (ax2>bx2) {
        width=bx2-ax1;
    } else {
        width=ax2-bx1;
    }

    if (ay2>=by2 && by1>=ay1){
        height=by2-by1;
    } else if (by2>=ay2 && ay1>=by1) {
        height=ay2-ay1;
    } else if (ay2>by2) {
        height=by2-ay1;
    } else {
        height=ay2-by1;
    }

    area = heigh*width;
    return (area);
}