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

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Array Dynamic Programming

Problem 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.

Solution

/**
 * @param {number[]} nextVisit
 * @return {number}
 */
var firstDayBeenInAllRooms = function(nextVisit) {
  const MOD = 1e9 + 7;
  const n = nextVisit.length;
  const dp = new Array(n).fill(0);

  for (let i = 1; i < n; i++) {
    dp[i] = (2 * dp[i - 1] + 2 - dp[nextVisit[i - 1]] + MOD) % MOD;
  }

  return dp[n - 1];
};
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