POJ 1389 area of simple polygons (acreage merge, Segment tree + discretization)

Area of simple polygons

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 3257		Accepted: 1678

Description

There is n, 1 <= n <= rectangles in the 2-d xy-plane. The four sides of a rectangle is horizontal or vertical line segments. Rectangles is defined by their lower-left and Upper-right corner points. Each corner point was a pair of nonnegative integers in the range of 0 through 50,000 indicating its x and Y coordinate S.

Assume that the contour of their union was defi Ned by a set S of segments. We can use a subset of S to construct simple polygon (s). Please report the total area of the polygon (s) constructed by the subset of S. The area should is as large as possible. In a 2-d xy-plane, a polygon are defined by a finite set of segments such this every segment extreme (or endpoint) is share D by exactly edges and no subsets of edges have the same property. The segments is edges and their extremes are the vertices of the polygon. A polygon is simple if there are no pair of nonconsecutive edges sharing a point.

Example:consider the following three rectangles:

Rectangle 1: < (0, 0) (4, 4);

Rectangle 2: < (1, 1) (5, 2);

Rectangle 3: < (1, 1) (2, 5);.

The polygons constructed by these rectangles is 18.

Input

The input consists of multiple test cases. A line of 4-1 ' s separates each test case. An extra line of 4-1 ' s marks the end of the input. In each test case, the rectangles is given one by one in a line. In each line for a rectangle, 4 non-negative integers is given. The first is the x and Y coordinates of the lower-left corner. The next is the x and Y coordinates of the upper-right corner.

Output

For each test case, output the total area of all simple polygons in a line.

Sample Input

Sample Output

Source

Taiwan 2001 Test Instructions: There are many sets of test data, each group of test data has more than one row, each row has 4 integer x1,y1, x2,y2 represents a rectangle's leftmost bottom vertex and the top right vertex, with 4-1 end, asked to give the total area of the rectangle, the covered area is only added once. Problem solving: Each rectangle can be used to replace the rectangle by two segments (parallel to the upper and lower segments of the x-axis). Discretization of the x-coordinate point, and then using the line tree to maintain.

#include <stdio.h> #include <string.h> #include <algorithm>using namespace std; #define TYPEH INT// The height of type # define MID (L,r) ((L+R) >>1) const int MAXN = 50005; struct tree{int len,cover;//number of points >0 in each interval range, number of times each point is overwritten}root[maxn*4];struct rectedg{typeh H;//height per margin x axis in T l,r,cnt; The true left and right node of the line segment, Cnt=1 represents the bottom of the rectangle, cnt=0 is the top}edg[maxn*2];int w[maxn*2];    Discretization point set of the width point void builde (int l,int r,int k) {root[k].len=root[k].cover=0;    if (l==r-1) return;    int M=mid (L,R);    Builde (l,m,k<<1); Builde (m,r,k<<1|1);}    void Getlen (int l,int r,int k) {if (root[k].cover>0) Root[k].len = W[r]-w[l];    else if (l==r-1) root[k].len=0; else Root[k].len = Root[k<<1].len + Root[k<<1|1].len;}  void update (int l,int r,int k,int l,int r,int cnt) {if (l<=w[l]&&w[r]<=r) {root[k].cover + = cnt        ;        Getlen (L,R,K);    return;    } if (l==r-1) return;    int M=mid (L,R); if (L<=w[m]) update (L,M,K<<1, L, R, CNT);    if (w[m]<r) update (m,r,k<<1|1, L, R, CNT); Getlen (l,r,k);}    void Getunique (int& maxlen)//Segment tree width discretization, de-weight {int k=maxlen;    Maxlen=1;    Sort (w+1,w+1+k); for (int i=2; i<=k; i++) if (W[maxlen]!=w[i]) w[++maxlen]=w[i];} BOOL CMP (RECTEDG AA, RECTEDG BB)//Edge high Press from small to large to sort {return AA. H<bb. H;}   int Maxlen,tot; The length of the segment tree is the total number of sides void addrectedg (int h1,int h2,int l,int r) {edg[tot].l=l; edg[tot].r=r; Edg[tot]. H=H1; Edg[tot++].cnt=1; The bottom edg[tot].l=l of the rectangle; Edg[tot].r=r; Edg[tot]. H=H2; Edg[tot++].cnt=-1; The upper w[++maxlen]=l of the rectangle; W[++maxlen]=r;}    int main () {int x1,y1,x2,y2;        while (scanf ("%d%d%d%d", &x1,&y1,&x2,&y2) >0) {if (x1+y1+x2+y2==-4) break;        Maxlen=1;        tot=0;        if (x1<x2&&y1<y2) addrectedg (y1, y2, x1, x2);        if (X2>maxlen) maxlen=x2;       while (1) {scanf ("%d%d%d%d", &x1,&y1,&x2,&y2);     if (x1+y1+x2+y2==-4) break;            if (x1<x2&&y1<y2) addrectedg (y1, y2, x1, x2);        if (X2>maxlen) maxlen=x2;        } sort (edg,edg+tot,cmp);        Getunique (MaxLen);        Builde (1, MaxLen, 1);        Long Long area=0;            for (int i=0; i<tot-1; i++) {int l,r;            L=EDG[I].L;            R=EDG[I].R;            Update (1, MaxLen, 1, L, R, edg[i].cnt); Area + = (edg[i+1]. H-edg[i].           H) *root[1].len;         printf ("%d--%d len=%d, area =%d\n", W[l],w[r],root[1].len,area);    } printf ("%lld\n", area); }}

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POJ 1389 area of simple polygons (acreage merge, Segment tree + discretization)