# Team Formation

### Problem Statement :

```For an upcoming programming contest, Roy is forming some teams from the students of his university. A team can have any number of contestants.

Roy knows the skill level of each contestant. To make the teams work as a unit, he forms the teams based on some rules. Each of the team members must have a unique skill level for the team. If a member's skill level is  where , there exists another team member whose skill level is . Note that a contestant can write buggy code and thus can have a negative skill level.

The more contestants on the team, the more problems they can attempt at a time so Roy wants to form teams such that the smallest team is as large as possible.

Input Format

The first line contains an integer , the number of test cases.

Each of the next  lines contains a string of space-separated integers,  followed by  integers , a list of the contestants' skill levels.

Output Format

For each test case, print the size of largest possible smallest team on a separate line.```

### Solution :

```                            ```Solution in C :

In  C :

#include<stdio.h>
void merge(int a[],int low,int p,int high)
{
int n,m,i,j,k,c[100000];
n=p-low+1;
m=high-p;
if(n>0 || m>0)
{
i=low;
j=p+1;
k=low;
//printf("%d %d\n",n,m);
while(i<=p && j<=high)
{
while(a[i]<=a[j] && i<=p && j<=high)
{
c[k++]=a[i++];
}
while(a[i]>=a[j] && i<=p && j<=high)
{
c[k++]=a[j++];
}
}
if(i<=p)
{
while(i<=p)
{
c[k++]=a[i++];
}
}
if(j<=high)
{
while(j<=high)
{
c[k++]=a[j++];
}
}
for(i=low;i<=high;i++)
{
a[i]=c[i];
//printf("%d ",a[i]);
}
//printf("\n");
}
else
{
return;
}
}
void mergesort(int a[],int low,int high)
{
int p,i;
if(high>low)
{
p=(low+high)/2;
mergesort(a,low,p);
mergesort(a,p+1,high);
//printf("here is the %d %d %d\n",low,p,high);
merge(a,low,p,high);
}
else
{
return;
}
}
int main()
{
int a[100000],i,n,b[100010],precount,count,j,k,counter,t,t1=0,min;
scanf("%d",&t);
while(t1<t)
{
scanf("%d",&n);
for(i=0;i<n;i++)
{
scanf("%d",&a[i]);
}
mergesort(a,0,n-1);

precount=0;
count=0;
j=-1;
for(i=0;i<n+10;i++)
{
b[i]=0;
}
i=0;
while(i<n-1)
{
if(a[i]==a[i+1])
{
count++;
}
else
{
count++;
if(count<=precount)
{
k=j;
}
else // count>precount
{
j+=count-precount;
k=j;
}
counter=0;
while(counter<count)
{
b[k--]++;
counter++;
}
precount=count;
count=0;
if(a[i]!=(a[i+1]-1))
{
precount=0;
}
}
i++;
}

for(i=0;i<=j;i++)
{
//printf("%d %d\n",i,b[i]);
}
//printf("after\n");
if(n>1)
{
if(a[n-2]==a[n-1])
{
count++;
if(count<=precount)
{
k=j;
}
else // count>precount
{
j+=count-precount;
k=j;
}
counter=0;
while(counter<count)
{
b[k--]++;
counter++;
}
}
else if(a[n-2]==a[n-1]-1)
{
b[j]++;
}
else
{
b[++j]++;
}
}
min=1000000000;
for(i=0;i<=j;i++)
{
//printf("%d %d\n",i,b[i]);
if(min>b[i])
{
min=b[i];
}
}
if(n==0)
{
min=0;
}
if(n==1)
{
min=1;
}
printf("%d\n",min);
t1++;
}
return 0;
}```
```

```                        ```Solution in C++ :

In  C++  :

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

const int NMAX = 100010;

int T, N, V[NMAX], Ans;
multiset<pair<int,int> > S;

int main()
{
// freopen("c.in", "r", stdin);
//  freopen("c.out", "w", stdout);

scanf("%i", &T);
for(; T; T --)
{
scanf("%i", &N);
for(int i = 1; i <= N; ++ i)
scanf("%i", &V[i]);

sort(V + 1, V + N + 1);

S.clear();
S.insert(make_pair(V[1] - 1, 0));
Ans = 0x3f3f3f3f;

for(int i = 1; i <= N; ++ i)
{
while(!S.empty() && S.begin() -> first < V[i] - 1)
{
Ans = min(Ans, S.begin() -> second);
S.erase(S.begin());
}

if(S.empty())
S.insert(make_pair(V[i], 1));
else
{
if(S.begin() -> first == V[i])
S.insert(make_pair(V[i], 1));
else
{
int Nr = S.begin() -> second;
S.erase(S.begin());
S.insert(make_pair(V[i], Nr + 1));
}
}
}

while(!S.empty())
{
Ans = min(Ans, S.begin() -> second);
S.erase(S.begin());
}

printf("%i\n", Ans);
}
}```
```

```                        ```Solution in Java :

in   Java :

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;

public class Solution {
static InputStream is;
static PrintWriter out;
static String INPUT = "";

static void solve()
{
for(int T = ni();T >= 1;T--){
int n = ni();
int[] a = na(n);
if(n == 0){
out.println(0);
continue;
}
Arrays.sort(a);
Queue<Integer> q = new ArrayDeque<Integer>();
int f = 0;
int prev = -1999999999;
int min = 1999999999;
for(int i = 0;i < n;){
int j = i;
for(;j < n && a[i] == a[j];j++);
int cf = j-i;
if(prev+1 < a[i]){
for(int k = 0;k < f;k++){
min = Math.min(min, prev-q.poll()+1);
}
for(int k = 0;k < cf;k++){
}
}else{
if(cf > f){
for(int k = f;k < cf;k++){
}
}else{
for(int k = cf;k < f;k++){
min = Math.min(min, a[i]-q.poll());
}
}
}
prev = a[i];
f = cf;
i = j;
}
for(int k = 0;k < f;k++){
min = Math.min(min, prev-q.poll()+1);
}
out.println(min);
}
}

public static void main(String[] args) throws Exception
{
long S = System.currentTimeMillis();
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);

solve();
out.flush();
long G = System.currentTimeMillis();
tr(G-S+"ms");
}

private static boolean eof()
{
if(lenbuf == -1)return true;
int lptr = ptrbuf;
while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

try {
is.mark(1000);
while(true){
if(b == -1){
is.reset();
return true;
}else if(!isSpaceChar(b)){
is.reset();
return false;
}
}
} catch (IOException e) {
return true;
}
}

private static byte[] inbuf = new byte[1024];
static int lenbuf = 0, ptrbuf = 0;

{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}

private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

private static double nd() { return Double.parseDouble(ns()); }
private static char nc() { return (char)skip(); }

private static String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
}
return sb.toString();
}

private static char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
}
return n == p ? buf : Arrays.copyOf(buf, p);
}

private static char[][] nm(int n, int m)
{
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}

private static int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}

private static int ni()
{
int num = 0, b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
}

while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
}
}

private static long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
}

while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
}
}

private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}```
```

```                        ```Solution in Python :

In  Python3 :

import collections
import itertools

if not skills:
return 0

finished_team_lengths = []
current_team_starts = collections.deque()

def go(s, c):
while len(current_team_starts) < c:
current_team_starts.append(s)
while len(current_team_starts) > c:
finished_team_lengths.append(s - current_team_starts.popleft())

last_s = skills[0] - 1
for s, g in itertools.groupby(skills):
if s > last_s + 1:
go(last_s + 1, 0)
go(s, sum(1 for _ in g))
last_s = s
go(last_s + 1, 0)

return min(finished_team_lengths)

t = int(input())
for i in range(t):
```

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