Minimum Time to Kill All Monsters — LeetCode 2403 Python Solution
HardLeetCode PremiumBit ManipulationArrayDynamic ProgrammingBitmask
- Problem
- #2403
- Pattern
- Bit Manipulation
- Reading time
- 3 min
- Source
- leetcode.com
The problem
You are given an integer array power where power[i] is the power of the ith monster. You start with 0 mana points, and each day you increase your mana points by gain where gain initially is equal to 1.
Example
- Input
- power = [3,1,4]
- Output
- 4
- Explanation
- The optimal way to beat all the monsters is to:
Python solution
Python
class Solution:
def minimumTime(self, power: List[int]) -> int:
@cache
def dfs(mask: int) -> int:
if mask == 0:
return 0
ans = inf
gain = 1 + (n - mask.bit_count())
for i, x in enumerate(power):
if mask >> i & 1:
ans = min(ans, dfs(mask ^ (1 << i)) + (x + gain - 1) // gain)
return ans
n = len(power)
return dfs((1 << n) - 1)Complexity
| Measure | Complexity |
|---|---|
| Time | O(2^n \times n) |
| Space | O(2^n) auxiliary |
Pattern: Bit Manipulation
Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 2403. Minimum Time to Kill All Monsters is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.
The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.
Related problems
Frequently asked questions
- How hard is LeetCode 2403. Minimum Time to Kill All Monsters?
- LeetCode 2403. Minimum Time to Kill All Monsters is rated Hard on LeetCode.
- What is the time complexity of LeetCode 2403. Minimum Time to Kill All Monsters?
- The Python solution on this page runs in O(2^n \times n).
- What is the space complexity of LeetCode 2403. Minimum Time to Kill All Monsters?
- The Python solution on this page uses O(2^n) auxiliary space.
- What topics does LeetCode 2403. Minimum Time to Kill All Monsters cover?
- LeetCode 2403. Minimum Time to Kill All Monsters is tagged Bit Manipulation, Array, Dynamic Programming and Bitmask on LeetCode.
- Is LeetCode 2403. Minimum Time to Kill All Monsters a premium problem?
- Yes. LeetCode 2403. Minimum Time to Kill All Monsters is a LeetCode Premium problem, so the full statement and test cases require a paid LeetCode subscription.