Formatted question description: https://leetcode.ca/all/1997.html

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

Level

Medium

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 the room 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 10^9 + 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 <= 10^5
  • 0 <= nextVisit[i] <= i

Solution

Use dynamic programming. Create an array dp of length n, where dp[i] is the first day to visit room i. Initially, dp[0] = 0. For 1 <= i < n, there is dp[i] = dp[i - 1] + (dp[i - 1] - dp[nextVisit[i]] + 1) + 1.

  • class Solution {
        public int firstDayBeenInAllRooms(int[] nextVisit) {
            final int MODULO = 1000000007;
            int length = nextVisit.length;
            int[] dp = new int[length];
            for (int i = 1; i < length; i++)
                dp[i] = ((dp[i - 1] * 2 - dp[nextVisit[i - 1]] + 2) % MODULO + MODULO) % MODULO;
            return dp[length - 1];
        }
    }
    
  • // OJ: https://leetcode.com/problems/first-day-where-you-have-been-in-all-the-rooms/
    // Time: O(N)
    // Space: O(N)
    class Solution {
    public:
        int firstDayBeenInAllRooms(vector<int>& A) {
            long mod = 1e9 + 7, N = A.size();
            vector<int> dp(N + 1);
            for (int i = 1; i < N; ++i) {
                dp[i] = ((long)2 + 2 * dp[i - 1] - dp[A[i - 1]] + mod) % mod;
            }
            return dp[N - 1];
        }
    };
    
  • # 1997. First Day Where You Have Been in All the Rooms
    # https://leetcode.com/problems/first-day-where-you-have-been-in-all-the-rooms
    
    class Solution:
        def firstDayBeenInAllRooms(self, nextVisit: List[int]) -> int:
            n = len(nextVisit)
            dp = [0] * n
            
            for i in range(1, n):
                dp[i] = (2 * dp[i - 1] - dp[nextVisit[i - 1]] + 2) % (10 ** 9 + 7)
            
            return dp[-1]
    
    

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