# Light OJ: 1267 – Points in Rectangle (II)

Solution Idea:

This problem is similar to Codeforces gym 101484: B. Nicoleta’s Cleaning. We need a line sweep technique and some data structure to solve this problem. We need to convert each rectangle to opening and closing with respect to its x coordinates. Then we need to sort all points and open and close together. then for each opening element we need to count how many points are before opening point let is is X and for each closing, we need to count how many points are before and on the closing point in the range, lower y coordinate to upper y coordinate let it is Y. Then the number of points inside the rectangle is Y-X. For each given point we need to update it when we find it through scan line in x coordinate of it.

```#include <bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cerr<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;

//using namespace __gnu_pbds;
//typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

struct data
{
int type,x,st,ed,id;
};

vector<int>x,y;
vector<data>v;

bool cmp(data a, data b)
{
if(a.x<b.x) return true;
if(a.x==b.x)
return a.type<b.type;
return false;
}

#define mx 300005

int tree[mx];

void update(int idx, int val)
{
for(; idx<mx && idx; idx+=(idx&-idx))
tree[idx]+=val;
}

int query(int idx)
{
int ret=0;
for(; idx; idx-=(idx&-idx))
ret+=tree[idx];
return ret;
}

int ans[mx];

int main()
{
//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);
int t;
sf(t);
TEST_CASE(t)
{
int n,m;
sff(n,m);
for(int i=0; i<n; i++)
{
int a,b;
sff(a,b);
data temp;
temp.type=2;
temp.x=a;
temp.ed=temp.st=b;
v.pb(temp);
x.pb(a);
y.pb(b);
}

for(int i=0; i<m; i++)
{
int a,b,c,d;
sff(a,b);
sff(c,d);
x.pb(a);
x.pb(c);
y.pb(b);
y.pb(d);
data temp;
temp.type=3;
temp.x=c;
temp.st=b;
temp.ed=d;
temp.id=i;
v.pb(temp);
data temp1;
temp1.type=1;
temp1.x=a;
temp1.st=b;
temp1.ed=d;
temp1.id=i;
v.pb(temp1);
}

//    sort(all(x));
sort(all(y));
sort(all(v),cmp);

for(int i=0; i<SZ(v); i++)
{
data temp=v[i];
if(temp.type==1)
{
int a=lower_bound(all(y),temp.st)-y.begin()+1;
int b=lower_bound(all(y),temp.ed)-y.begin()+1;
int xx=query(b);
int yy=query(a-1);
ans[temp.id]=xx-yy;
}
else if(temp.type==3)
{
int a=lower_bound(all(y),temp.st)-y.begin()+1;
int b=lower_bound(all(y),temp.ed)-y.begin()+1;
int xx=query(b);
int yy=query(a-1);
ans[temp.id]=(xx-yy)-ans[temp.id];
}
else
{
int a=lower_bound(all(y),temp.st)-y.begin()+1;
update(a,1);
//            int yy=query(a-1); // Never do this while range update on BIT -_-
//            ans[temp.id]=xx;
}
}

LINE_PRINT_CASE;
for(int i=0; i<m; i++)
printf("%d\n",ans[i]);
ms(tree,0);
x.clear();
y.clear();
v.clear();
}
return 0;
}```