# Interval Selection

### Problem Statement :

```Given a set of n intervals, find the size of its largest possible subset of intervals such that no three intervals in the subset share a common point.

Input Format

The first line contains an integer, s, denoting the number of interval sets you must find answers for. The s.(n+1) subsequent lines describe each of the s interval sets as follows:

1.The first line contains an integer, n, denoting the number of intervals in the list.
Each line i of the n subsequent lines contains two space-separated integers describing the respective starting (ai) and ending (bi) boundaries of an interval.
Constraints
1 <= s <= 100
2 <= n <= 1000
1 <=  ai <= bi <= 10^9
Output Format

For each of the s interval sets, print an integer denoting the size of the largest possible subset of intervals in the given set such that no three points in the subset overlap.```

### Solution :

```                            ```Solution in C :

In C++ :

#include <algorithm>
#include <cstdio>
using namespace std;

pair<int,int> a[1002];

int main() {
int i,m,n,x,y,z,may;

for (scanf("%d",&z);z;--z) {
scanf("%d",&n);
for (i=1;i<=n;++i) {
scanf("%d%d",&a[i].second,&a[i].first);
}
sort(a+1,a+n+1);
a[x=y=m=0]=make_pair(-1,-1);
for (i=1;i<=n;++i) {
may=-1;
if (a[x].first<a[i].second) {
may=x;
}
if ((y>may) && (a[y].first<a[i].second)) {
may=y;
}
if (may==x) {
x=i;
++m;
}
else if (may==y) {
y=i;
++m;
}
}
printf("%d\n",m);
}
return 0;
}

In Java :

import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Solution {
static class Foo53 {
void main() {
try {
for (int i = 0; i < T; i++) {
int[][] arr = new int[N][2];
for (int j = 0; j < N; j++) {
arr[j][0] = Integer.parseInt(s[0].trim());
arr[j][1] = Integer.parseInt(s[1].trim());
}
int res = foo(arr);
System.out.println(res);
}
} catch (Exception e) {
e.printStackTrace();
} finally {
if (br != null) {
try { br.close(); } catch (Exception e) { e.printStackTrace(); }
}
}
}

Deque<Integer> deque;
int foo(int[][] arr) {
int res = 0;
int n = arr.length;
Arrays.sort(arr, new Comparator<int[]>() {
public int compare(int[] a, int[] b) {
return a[0] - b[0];
}
});
for (int[] a : arr) {
int left = a[0], right = a[1];
while (!deque.isEmpty() && deque.getFirst() < left)
deque.removeFirst();
if (deque.size() < 2) {
res++;
} else {
if (deque.getLast() > right) {
deque.removeLast();
}
}
}
return res;
}
if (!deque.isEmpty() && deque.getLast() > val) {
} else {
}
}
}

public static void main(String[] args) {
Foo53 foo = new Foo53();
foo.main();
}
}

In C :

#include <stdio.h>
#include <stdlib.h>

long long v,zas[1100],d[3000][3],ii,jj,kk,s[10000][2];
long long aa[1100],a[1100][1100],i,j,k,l,m,n,t,tt;

int com(const void*x, const void *y)
{
long long *xx,*yy;

xx = (long long *)x;
yy = (long long *)y;

if(xx[0]>yy[0]) return 1;
if(xx[0]==yy[0] && xx[2]==1) return 1;

return -1;
}

int main()
{

scanf("%lld",&t);
for(tt=0;tt<t;tt++)
{
scanf("%lld",&n);
for(i=0;i<n;i++) scanf("%lld %lld", &s[i][0], &s[i][1]);

// s[0][0] = -5;
// s[0][1] = -1;

// for(i=0;i<n;i++)
//  for(j=0;j<n;j++) a[i][j] =0;

for(i=0;i<n;i++)
{
d[2*i][0]=s[i][0];
d[2*i][1]=i;
d[2*i][2]=0;

d[2*i+1][0]=s[i][1];
d[2*i+1][1]=i;
d[2*i+1][2]=1;
}

qsort(d,n*2,sizeof(d[0]),com);

l=0;
m=0;
v=0;

for(i=0;i<2*n;i++)
{
ii = d[i][1];

if(d[i][2]==0)
{
for(j=0;j<l;j++)
{
a[ii][zas[j]] = a[zas[j]][ii] = aa[zas[j]]+1;
if(a[ii][zas[j]]>v) v = a[ii][zas[j]];
}

zas[l] = ii;
l++;
aa[ii] = m+1;
if(aa[ii]>v) v = aa[ii];
}
else
{
if(aa[ii]>m) m=aa[ii];

j=0;
while(zas[j]!=ii) j++;
l--;
zas[j] = zas[l];

for(j=0;j<l;j++)
if(a[ii][zas[j]] > aa[zas[j]])
aa[zas[j]] = a[ii][zas[j]];
}
}

printf("%lld\n",v);

//for(i=0;i<2*n;i++) printf("%lld %lld %lld\n",d[i][0],d[i][1],d[i][2]);

}

return 0;
}

In Python3 :

t = int(input())
for _ in range(t):
n = int(input())
I = []
for _ in range(n):
a, b = list(map(int, input().split()))
I.append((a, b))
I.sort(key = lambda x: (x[1], x[0]))
temp = -1
lasta = 0
lastb = 0
res = 0
for a, b in I:
if a>lastb:
res+=1
lasta = a
lastb = b
elif a>temp:
res+=1
temp = lastb
lasta = a
lastb = b
print(res)```
```

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