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3385. Minimum Time to Break Locks II πŸ”’

Description

Bob is stuck in a dungeon and must break n locks, each requiring some amount of energy to break. The required energy for each lock is stored in an array called strength where strength[i] indicates the energy needed to break the ith lock.

To break a lock, Bob uses a sword with the following characteristics:

  • The initial energy of the sword is 0.
  • The initial factor X by which the energy of the sword increases is 1.
  • Every minute, the energy of the sword increases by the current factor X.
  • To break the ith lock, the energy of the sword must reach at least strength[i].
  • After breaking a lock, the energy of the sword resets to 0, and the factor X increases by 1.

Your task is to determine the minimum time in minutes required for Bob to break all n locks and escape the dungeon.

Return the minimum time required for Bob to break all n locks.

 

Example 1:

Input: strength = [3,4,1]

Output: 4

Explanation:

Time Energy X Action Updated X
0 0 1 Nothing 1
1 1 1 Break 3rd Lock 2
2 2 2 Nothing 2
3 4 2 Break 2nd Lock 3
4 3 3 Break 1st Lock 3

The locks cannot be broken in less than 4 minutes; thus, the answer is 4.

Example 2:

Input: strength = [2,5,4]

Output: 6

Explanation:

Time Energy X Action Updated X
0 0 1 Nothing 1
1 1 1 Nothing 1
2 2 1 Break 1st Lock 2
3 2 2 Nothing 2
4 4 2 Break 3rd Lock 3
5 3 3 Nothing 3
6 6 3 Break 2nd Lock 4

The locks cannot be broken in less than 6 minutes; thus, the answer is 6.

 

Constraints:

  • n == strength.length
  • 1 <= n <= 80
  • 1 <= strength[i] <= 106
  • n == strength.length

Solutions

Solution 1

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