Light OJ: 1267 – Points in Rectangle (II)

0

Problem Link: http://www.lightoj.com/volume_showproblem.php?problem=1267

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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//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;
}

Codeforces gym 101484: B. Nicoleta’s Cleaning

1

Problem Link : http://codeforces.com/gym/101484/problem/B

Solution Idea:

    To solve this problem we need line sweep technique and some data structure. At first convert each rectangle in two element with respect to it x coordinate which both x coordinate have same y coordinates. Now call first x point opening and 2nd x point closing of a rectangle. Now take a array of custom data type. and store every opening and closing of rectangles and the query points and sort the the array in the basis of x coordinate of each element and in case of a tie take closing element first then query point and then opening point.

    Now run a loop on the x axis and update every range by 1 if we find a opening and by -1 if we find a closing and if we find a query point just query the value of that point.

    Handle the boundary condition carefully.



#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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//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 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;
        temp.id=i;
        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=1;
        temp.x=c;
        temp.st=b;
        temp.ed=d;
        v.pb(temp);
        data temp1;
        temp1.type=3;
        temp1.x=a;
        temp1.st=b;
        temp1.ed=d;
        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;
            update(a+1,-1);
            update(b,+1);
        }
        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;
            update(a+1,+1);
            update(b,-1);
        }
        else
        {
            int a=lower_bound(all(y),temp.st)-y.begin()+1;
            int xx=query(a);
//            int yy=query(a-1); // Never do this while range update on BIT -_-
            ans[temp.id]=xx;
        }
    }


    for(int i=0; i<n; i++)
        printf("%d\n",ans[i]);

    return 0;
}