3376. Minimum Time to Break Locks I LeetCode Solution

In this guide, you will get 3376. Minimum Time to Break Locks I LeetCode Solution with the best time and space complexity. The solution to Minimum Time to Break Locks I problem is provided in various programming languages like C++, Java, and Python. This will be helpful for you if you are preparing for placements, hackathons, interviews, or practice purposes. The solutions provided here are very easy to follow and include detailed explanations.

Table of Contents

1. Problem Statement
2. Complexity Analysis
3. Minimum Time to Break Locks I solution in C++
4. Minimum Time to Break Locks I solution in Java
5. Minimum Time to Break Locks I solution in Python
6. Additional Resources

Problem Statement of Minimum Time to Break Locks I

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 a given value k.

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], k = 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], k = 2
Output: 5
Explanation:

Time
Energy
x
Action
Updated x

0
0
1
Nothing
1

1
1
1
Nothing
1

2
2
1
Break 1st Lock
3

3
3
3
Nothing
3

4
6
3
Break 2nd Lock
5

5
5
5
Break 3rd Lock
7

The locks cannot be broken in less than 5 minutes; thus, the answer is 5.

Constraints:

n == strength.length
1 <= n <= 8
1 <= K <= 10
1 <= strength[i] <= 106

Complexity Analysis

• Time Complexity: O(n \cdot 2^n)
• Space Complexity: O(2^n)

3376. Minimum Time to Break Locks I LeetCode Solution in C++

class Solution {
 public:
  int findMinimumTime(vector<int>& strength, int K) {
    return find(strength, /*x=*/1, 0, K);
  }

 private:
  int find(const vector<int>& strength, int x, int mask, int k) {
    if (mask == (1 << strength.size()) - 1)
      return 0;
    int res = INT_MAX;
    for (int i = 0; i < strength.size(); ++i)
      if ((mask >> i & 1) == 0) {
        const int time = (strength[i] - 1) / x + 1;  // ceil(strength[i] / x)
        res = min(res, time + find(strength, x + k, mask | 1 << i, k));
      }
    return res;
  }
};
/* code provided by PROGIEZ */

3376. Minimum Time to Break Locks I LeetCode Solution in Java

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// code provided by PROGIEZ

3376. Minimum Time to Break Locks I LeetCode Solution in Python

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 # code by PROGIEZ

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