LeetCode 850. Rectangle Area II

Posted 2022-05-18 hankunyan

经典line sweep问题，和 perfect rectangle 很类似，但是要考虑多个矩形左边界一样的情况，加个id来区分。

和另一道类似的题 the skyline problem 不同的是，没有很多 corner cases，对 x 排序非常简单。 

难点是在 active set 里，和 merge intervals 那题一样，计算 total_y，乘以两个相邻 event 的 delta_x。

class Solution 
public:
    struct interval 
        int start, end;
        bool operator<(const interval &i) const 
            if (start == i.start)
                return end < i.end;
            return start < i.start;
        
    ;
    
    struct edge 
        int x;
        interval i;
        int type; // left <- 1, right <- -1
        int id;
    ;
    
    int rectangleArea(vector<vector<int>>& rectangles) 
        vector<edge> vec;
        for (int i=0;i<rectangles.size();++i)
            auto rect=rectangles[i];
            vec.push_back(rect[0],rect[1],rect[3],1,i);
            vec.push_back(rect[2],rect[1],rect[3],-1,i);
        
        sort(vec.begin(),vec.end(),[](edge e1, edge e2)
            return e1.x < e2.x;
        );
        
        set<pair<interval,int>> active_set; // <interval,id>
        active_set.insert(vec[0].i,vec[0].id);
        int prev_x=vec[0].x;
        
        int res=0;
        for (int i=1;i<vec.size();++i)
            int delta_x=vec[i].x-prev_x;
            
            // merge interval
            int s=-1,e=-1;
            int total_y=0;
            for (auto m:active_set)
                interval i=m.first;
                int id=m.second;
                if (s==-1 || i.start>e)
                    total_y += e-s;
                    s = i.start; e = i.end;
                else
                    e = max(e,i.end);
                
            
            total_y += e-s;
            
            res = (res + long(delta_x)*total_y) % 1000000007;
            
            if (vec[i].type==1) active_set.insert(vec[i].i,vec[i].id);
            else active_set.erase(vec[i].i,vec[i].id);
            
            prev_x = vec[i].x;
        
        return res;
    
;

时间复杂度 O(nlogn)

 

Reference

https://leetcode.com/problems/rectangle-area-ii/solution/

Computational Geometry - Line Sweep - 3 - Rectangles Union (Arabic)