# 1997. First Day Where You Have Been in All the Rooms

## Description

There are n rooms you need to visit, labeled from 0 to n - 1. Each day is labeled, starting from 0. You will go in and visit one room a day.

Initially on day 0, you visit room 0. The order you visit the rooms for the coming days is determined by the following rules and a given 0-indexed array nextVisit of length n:

• Assuming that on a day, you visit room i,
• if you have been in room i an odd number of times (including the current visit), on the next day you will visit a room with a lower or equal room number specified by nextVisit[i] where 0 <= nextVisit[i] <= i;
• if you have been in room i an even number of times (including the current visit), on the next day you will visit room (i + 1) mod n.

Return the label of the first day where you have been in all the rooms. It can be shown that such a day exists. Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nextVisit = [0,0]
Output: 2
Explanation:
- On day 0, you visit room 0. The total times you have been in room 0 is 1, which is odd.
On the next day you will visit room nextVisit[0] = 0
- On day 1, you visit room 0, The total times you have been in room 0 is 2, which is even.
On the next day you will visit room (0 + 1) mod 2 = 1
- On day 2, you visit room 1. This is the first day where you have been in all the rooms.


Example 2:

Input: nextVisit = [0,0,2]
Output: 6
Explanation:
Your room visiting order for each day is: [0,0,1,0,0,1,2,...].
Day 6 is the first day where you have been in all the rooms.


Example 3:

Input: nextVisit = [0,1,2,0]
Output: 6
Explanation:
Your room visiting order for each day is: [0,0,1,1,2,2,3,...].
Day 6 is the first day where you have been in all the rooms.


Constraints:

• n == nextVisit.length
• 2 <= n <= 105
• 0 <= nextVisit[i] <= i

## Solutions

• class Solution {
public int firstDayBeenInAllRooms(int[] nextVisit) {
int n = nextVisit.length;
long[] f = new long[n];
final int mod = (int) 1e9 + 7;
for (int i = 1; i < n; ++i) {
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1 + mod) % mod;
}
return (int) f[n - 1];
}
}

• class Solution {
public:
int firstDayBeenInAllRooms(vector<int>& nextVisit) {
int n = nextVisit.size();
vector<long long> f(n);
const int mod = 1e9 + 7;
for (int i = 1; i < n; ++i) {
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1 + mod) % mod;
}
return f[n - 1];
}
};

• class Solution:
def firstDayBeenInAllRooms(self, nextVisit: List[int]) -> int:
n = len(nextVisit)
f = [0] * n
mod = 10**9 + 7
for i in range(1, n):
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1) % mod
return f[-1]


• func firstDayBeenInAllRooms(nextVisit []int) int {
n := len(nextVisit)
f := make([]int, n)
const mod = 1e9 + 7
for i := 1; i < n; i++ {
f[i] = (f[i-1] + 1 + f[i-1] - f[nextVisit[i-1]] + 1 + mod) % mod
}
return f[n-1]
}

• function firstDayBeenInAllRooms(nextVisit: number[]): number {
const n = nextVisit.length;
const mod = 1e9 + 7;
const f: number[] = new Array<number>(n).fill(0);
for (let i = 1; i < n; ++i) {
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1 + mod) % mod;
}
return f[n - 1];
}


• public class Solution {
public int FirstDayBeenInAllRooms(int[] nextVisit) {
int n = nextVisit.Length;
long[] f = new long[n];
int mod = (int)1e9 + 7;
for (int i = 1; i < n; ++i) {
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1 + mod) % mod;
}
return (int)f[n - 1];
}
}