048.扫描线 + 线段树
矩形面积并
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=3e5+5;
struct rectangle{
int x1,y1,x2,y2;
}rec[N/2];
struct lines{
int x,y1,y2,k;
}L[N];
int Ysort[N];
int total[N<<2];
int cover[N<<2];
int cnt[N<<2];
void up(int x){
if(cnt[x]>0)cover[x]=total[x];
else cover[x]=cover[x<<1]+cover[x<<1|1];
}
void built(int x,int l,int r){
if(l<r){
int mid=(l+r)>>1;
built(x<<1,l,mid);
built(x<<1|1,mid+1,r);
}
total[x]=Ysort[r+1]-Ysort[l];
cover[x]=0;
cnt[x]=0;
}
void change(int x,int l,int r,int ql,int qr,int k){
if(ql<=l&&r<=qr){
cnt[x]+=k;
}else{
int mid=(l+r)>>1;
if(ql<=mid)change(x<<1,l,mid,ql,qr,k);
if(qr>mid)change(x<<1|1,mid+1,r,ql,qr,k);
}
up(x);
}
int init(int n){
for(int i=1,j=i+n;i<=n;++i,++j){
L[i]={rec[i].x1,rec[i].y1,rec[i].y2,1};
L[j]={rec[i].x2,rec[i].y1,rec[i].y2,-1};
Ysort[i]=rec[i].y1;
Ysort[j]=rec[i].y2;
}
int siz=n<<1;
sort(L+1,L+siz+1,[&](auto a,auto b){return a.x<b.x;});
sort(Ysort+1,Ysort+siz+1);
int m=unique(Ysort+1,Ysort+siz+1)-(Ysort+1);
Ysort[m+1]=Ysort[m];
return m;
}
ll merge_S(int n){
int m=init(n);
built(1,1,m);
ll ans=0;
int pre=0;
int siz=n<<1;
for(int i=1;i<=siz;i++){
ans+=1LL*cover[1]*(L[i].x-pre);
pre=L[i].x;
int l=lower_bound(Ysort+1,Ysort+m+1,L[i].y1)-Ysort;
int r=lower_bound(Ysort+1,Ysort+m+1,L[i].y2)-Ysort-1;
change(1,1,m,l,r,L[i].k);
}
return ans;
}
void solve(){
int n;
cin>>n;
for(int i=1;i<=n;++i){
cin>>rec[i].x1>>rec[i].y1>>rec[i].x2>>rec[i].y2;
}
cout<<merge_S(n);
}
int main(void){
cin.tie(0)->sync_with_stdio(0);
int T=1;
//cin>>T;
while(T--)solve();
}
矩形周长并
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e5+5;
struct rectangle{
int x1,y1,x2,y2;
}rec[N/2];
struct lines_y{
int x,y1,y2,k;
}Ly[N];
struct lines_x{
int y,x1,x2,k;
}Lx[N];
int Ysort[N],Xsort[N];
int total[N<<2];
int cover[N<<2];
int cnt[N<<2];
void up(int x){
if(cnt[x]>0)cover[x]=total[x];
else cover[x]=cover[x<<1]+cover[x<<1|1];
}
void change(int x,int l,int r,int ql,int qr,int k){
if(ql<=l&&r<=qr){
cnt[x]+=k;
}else{
int mid=(l+r)>>1;
if(ql<=mid)change(x<<1,l,mid,ql,qr,k);
if(qr>mid)change(x<<1|1,mid+1,r,ql,qr,k);
}
up(x);
}
void built_y(int x,int l,int r){
if(l<r){
int mid=(l+r)>>1;
built_y(x<<1,l,mid);
built_y(x<<1|1,mid+1,r);
}
total[x]=Ysort[r+1]-Ysort[l];
cover[x]=0;
cnt[x]=0;
}
int init_y(int n){
for(int i=1,j=i+n;i<=n;++i,++j){
Ly[i]={rec[i].x1,rec[i].y1,rec[i].y2,1};
Ly[j]={rec[i].x2,rec[i].y1,rec[i].y2,-1};
Ysort[i]=rec[i].y1;
Ysort[j]=rec[i].y2;
}
int siz=n<<1;
sort(Ly+1,Ly+siz+1,[&](auto a,auto b){return a.x<b.x;});
sort(Ysort+1,Ysort+siz+1);
int m=unique(Ysort+1,Ysort+siz+1)-(Ysort+1);
Ysort[m+1]=Ysort[m];
return m;
}
ll scan_y(int n){
int m=init_y(n);
built_y(1,1,m);
ll ans=0;
int pre;
int siz=n<<1;
for(int i=1;i<=siz;i++){
pre=cover[1];
int l=lower_bound(Ysort+1,Ysort+m+1,Ly[i].y1)-Ysort;
int r=lower_bound(Ysort+1,Ysort+m+1,Ly[i].y2)-Ysort-1;
change(1,1,m,l,r,Ly[i].k);
ans+=abs(pre-cover[1]);
}
return ans;
}
void built_x(int x,int l,int r){
if(l<r){
int mid=(l+r)>>1;
built_x(x<<1,l,mid);
built_x(x<<1|1,mid+1,r);
}
total[x]=Xsort[r+1]-Xsort[l];
cover[x]=0;
cnt[x]=0;
}
int init_x(int n){
for(int i=1,j=i+n;i<=n;++i,++j){
Lx[i]={rec[i].y1,rec[i].x1,rec[i].x2,1};
Lx[j]={rec[i].y2,rec[i].x1,rec[i].x2,-1};
Xsort[i]=rec[i].x1;
Xsort[j]=rec[i].x2;
}
int siz=n<<1;
sort(Lx+1,Lx+siz+1,[&](auto a,auto b){return a.y<b.y;});
sort(Xsort+1,Xsort+siz+1);
int m=unique(Xsort+1,Xsort+siz+1)-(Xsort+1);
Xsort[m+1]=Xsort[m];
return m;
}
ll scan_x(int n){
int m=init_x(n);
built_x(1,1,m);
ll ans=0;
int pre;
int siz=n<<1;
for(int i=1;i<=siz;i++){
pre=cover[1];
int l=lower_bound(Xsort+1,Xsort+m+1,Lx[i].x1)-Xsort;
int r=lower_bound(Xsort+1,Xsort+m+1,Lx[i].x2)-Xsort-1;
change(1,1,m,l,r,Lx[i].k);
ans+=abs(pre-cover[1]);
}
return ans;
}
ll merge_C(int n){
return scan_x(n)+scan_y(n);
}
void solve(){
int n;
cin>>n;
for(int i=1;i<=n;++i){
cin>>rec[i].x1>>rec[i].y1>>rec[i].x2>>rec[i].y2;
}
cout<<merge_C(n);
}
int main(void){
cin.tie(0)->sync_with_stdio(0);
int T=1;
//cin>>T;
while(T--)solve();
}
矩形面积并
const int N=1000;
const int P=1000000007;
struct lines{int x,y1,y2,k;}L[N];
int Y[N];
int total[N<<2];
int cover[N<<2];
int cnt[N<<2];
class Solution {
void up(int x){
if(cnt[x])cover[x]=total[x];
else cover[x]=cover[x<<1]+cover[x<<1|1];
}
void change(int x,int l,int r,int ql,int qr,int k){
if(ql<=l&&r<=qr){
cnt[x]+=k;
}
else{
int mid=(l+r)>>1;
if(ql<=mid)change(x<<1,l,mid,ql,qr,k);
if(qr>mid)change(x<<1|1,mid+1,r,ql,qr,k);
}
up(x);
}
void built(int x,int l,int r){
if(l<r){
int mid=(l+r)>>1;
built(x<<1,l,mid);
built(x<<1|1,mid+1,r);
}
total[x]=Y[r+1]-Y[l];
cover[x]=0;
cnt[x]=0;
}
public:
int rectangleArea(vector<vector<int>>& rectangles) {
int n=rectangles.size();
if(n==1){
int x1=rectangles[0][0];
int y1=rectangles[0][1];
int x2=rectangles[0][2];
int y2=rectangles[0][3];
return 1LL*(x2-x1)*(y2-y1)%P;
}
for(int i=1,j=i+n;i<=n;++i,++j){
int x1=rectangles[i-1][0];
int y1=rectangles[i-1][1];
int x2=rectangles[i-1][2];
int y2=rectangles[i-1][3];
L[i]={x1,y1,y2,1};
L[j]={x2,y1,y2,-1};
Y[i]=y1;
Y[j]=y2;
}
int siz=n<<1;
sort(Y+1,Y+siz+1);
sort(L+1,L+siz+1,[&](auto a,auto b){return a.x<b.x;});
int m=unique(Y+1,Y+siz+1)-(Y+1);
Y[m+1]=Y[m];
built(1,1,m);
long long ans=0;
int pre=0;
for(int i=1;i<=siz;++i){
ans=(ans+1LL*cover[1]*(L[i].x-pre)%P)%P;
pre=L[i].x;
int l=lower_bound(Y+1,Y+m+1,L[i].y1)-Y;
int r=lower_bound(Y+1,Y+m+1,L[i].y2)-Y-1;
change(1,1,m,l,r,L[i].k);
}
return ans;
}
};
分割面积
const int N=200000;
class Solution {
struct lines{int y,x1,x2,k;}L[N];
int X[N];
int total[N<<2];
int cnt[N<<2];
int cover[N<<2];
void up(int x){
cover[x]=cnt[x]==0?cover[x<<1]+cover[x<<1|1]:total[x];
}
void built(int x,int l,int r){
if(l<r){
int mid=(l+r)>>1;
built(x<<1,l,mid);
built(x<<1|1,mid+1,r);
}
total[x]=X[r+1]-X[l];
cover[x]=cnt[x]=0;
}
void change(int x,int l,int r,int ql,int qr,int k){
if(ql<=l&&r<=qr){
cnt[x]+=k;
}
else{
int mid=(l+r)>>1;
if(ql<=mid)change(x<<1,l,mid,ql,qr,k);
if(qr>mid)change(x<<1|1,mid+1,r,ql,qr,k);
}
up(x);
}
public:
double separateSquares(vector<vector<int>>& squares) {
int n=squares.size();
for(int i=1,j=i+n;i<=n;++i,++j){
int x1=squares[i-1][0];
int y1=squares[i-1][1];
int a=squares[i-1][2];
int x2=x1+a;
int y2=y1+a;
X[i]=x1;
X[j]=x2;
L[i]={y1,x1,x2,1};
L[j]={y2,x1,x2,-1};
}
int siz=n<<1;
sort(X+1,X+siz+1);
sort(L+1,L+siz+1,[&](auto a,auto b){return a.y<b.y;});
int m=unique(X+1,X+siz+1)-(X+1);
X[m+1]=X[m];
built(1,1,m);
long long sum=0;
int pre=0;
for(int i=1;i<=siz;++i){
long long len=L[i].y-pre;
sum+=cover[1]*len;
pre=L[i].y;
int l=lower_bound(X+1,X+m+1,L[i].x1)-X;
int r=lower_bound(X+1,X+m+1,L[i].x2)-X-1;
change(1,1,m,l,r,L[i].k);
}
built(1,1,m);
long long cur=0;
pre=0;
for(int i=1;i<=siz;++i){
long long len=L[i].y-pre;
cur+=cover[1]*len;
long long need=cur-(sum-cur);
if(need>=0&&cover[1]>0){
return L[i].y - 0.5*need/cover[1];
}
pre=L[i].y;
int l=lower_bound(X+1,X+m+1,L[i].x1)-X;
int r=lower_bound(X+1,X+m+1,L[i].x2)-X-1;
change(1,1,m,l,r,L[i].k);
}
return -1;
}
};
I am the bone of my sword
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