# Kindergarten Adventures

### Problem Statement :

```Meera teaches a class of n students, and every day in her classroom is an adventure. Today is drawing day!

The students are sitting around a round table, and they are numbered from 1 to n in the clockwise direction. This means that the students are numbered 1, 2, 3, . . . , n-1, n, and students 1 and n are sitting next to each other.

After letting the students draw for a certain period of time, Meera starts collecting their work to ensure she has time to review all the drawings before the end of the day. However, some of her students aren't finished drawing! Each student i needs ti extra minutes to complete their drawing.

Meera collects the drawings sequentially in the clockwise direction, starting with student ID x, and it takes her exactly 1 minute to review each drawing. This means that student x gets 0 extra minutes to complete their drawing, student x+1 gets 1 extra minute, student x+2 gets 2 extra minutes, and so on. Note that Meera will still spend 1 minute for each student even if the drawing isn't ready.

Given the values of t1, t2,  . . .,  tn , help Meera choose the best possible x to start collecting drawings from, such that the number of students able to complete their drawings is maximal. Then print x on a new line. If there are multiple such IDs, select the smallest one.

Input Format

The first line contains a single positive integer, n , denoting the number of students in the class.
The second line contains n space-separated integers describing the respective amounts of time that each student needs to finish their drawings (i.e .t1,  t2,  . . .,  tn ).

Constraints

1  <=  n   <= 10^5
1  <=  ti  <= n

Output Format

Print an integer denoting the ID number, , where Meera should start collecting the drawings such that a maximal number of students can complete their drawings. If there are multiple such IDs, select the smallest one.```

### Solution :

```                            ```Solution in C :

In  C++ :

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef int _loop_int;
#define REP(i,n) for(_loop_int i=0;i<(_loop_int)(n);++i)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a);i<(_loop_int)(b);++i)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1;i>=(_loop_int)(a);--i)

#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define DEBUG_VEC(v) cout<<#v<<":";REP(i,v.size())cout<<" "<<v[i];cout<<endl
#define ALL(a) (a).begin(),(a).end()

#define CHMIN(a,b) a=min((a),(b))
#define CHMAX(a,b) a=max((a),(b))

// mod
const ll MOD = 1000000007ll;
#define FIX(a) ((a)%MOD+MOD)%MOD

// floating
typedef double Real;
const Real EPS = 1e-11;
#define EQ0(x) (abs(x)<EPS)
#define EQ(a,b) (abs(a-b)<EPS)
typedef complex<Real> P;

int n;
int t[125252];
int imos[125252];

int main(){
scanf("%d",&n);
REP(i,n)scanf("%d",t+i);
REP(i,n){
int tt = t[i];
int from = i+1;
int to = (i-tt+n)%n;
if(from<=to){
imos[from]++;
imos[to+1]--;
}else{
imos[0]++;
imos[to+1]--;
imos[from]++;
imos[n]--;
}
}
REP(i,n+1)imos[i+1]+=imos[i];
int ans = -1;
int val = -1;
REP(i,n){
if(imos[i]>val){
ans = i;
val = imos[i];
}
}
printf("%d\n",ans+1);
return 0;
}

In  Java :

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int [] tab = new int[n];

for(int i = 0; i < n; i++) {
int k = sc.nextInt();

if(k == 0) {
continue;
}

tab[(i + 1) % n]++;
int p = i - k + 1;
if(p < 0) {
p += n;
}

tab[p]--;
}

int max = -100000;
int res = 0;
int sum = 0;

for(int i = 0; i < n; i++) {
sum += tab[i];

if(sum > max) {
max = sum;
res = i;
}
}

System.out.println(res + 1);
}
}

In C :

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

int main() {
int n;
scanf("%d", &n);
int *dc = calloc(n, sizeof(int));
int count = 0;
for (int i = 0; i < n; i++) {
int x;
scanf("%d", &x);
if (x < n) {
int start = (i+1)%n;
int end = (start-x+n)%n;
dc[start]++;
dc[end]--;
if (end <= start) count++;
}
}
int id = 0;
int val = 0;
for (int i = 0; i < n; i++) {
count += dc[i];
if (count > val) {
val = count;
id = i;
}
}
printf("%d", id+1);
free(dc);
return 0;
}

In Python3 :

import sys
n = int(sys.stdin.readline())
t = [int(x) for x in sys.stdin.readline().split()]

current_available = 0
become_unavailable = [0] * (3 * n)
best_index = 1
best_result = 0
for i in range(2*n):
el = t[i % n]
become_unavailable[i + (n - el)] += 1
if current_available > best_result:
best_result = current_available
best_index = i % n + 1
if current_available == best_result:
best_index = min(i % n + 1, best_index)
current_available += 1
current_available -= become_unavailable[i]

print(best_index)```
```

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