You are given an array nums
of n
positive integers.
You can perform two types of operations on any element of the array any number of times:
- If the element is even, divide it by
2
.- For example, if the array is
[1,2,3,4]
, then you can do this operation on the last element, and the array will be[1,2,3,2].
- For example, if the array is
- If the element is odd, multiply it by
2
.- For example, if the array is
[1,2,3,4]
, then you can do this operation on the first element, and the array will be[2,2,3,4].
- For example, if the array is
The deviation of the array is the maximum difference between any two elements in the array.
Return the minimum deviation the array can have after performing some number of operations.
Example 1:
Input: nums = [1,2,3,4]
Output: 1
Explanation: You can transform the array to [1,2,3,2], then to [2,2,3,2], then the deviation will be 3 - 2 = 1.
Example 2:
Input: nums = [4,1,5,20,3]
Output: 3
Explanation: You can transform the array after two operations to [4,2,5,5,3], then the deviation will be 5 - 2 = 3.
Example 3:
Input: nums = [2,10,8]
Output: 3
Constraints:
-
n == nums.length
-
2 <= n <= 5 * 104
-
1 <= nums[i] <= 109
SOLUTION:
import heapq
class Solution:
def minimumDeviation(self, nums: List[int]) -> int:
pq = []
for a in nums:
heapq.heappush(pq, [a // (a & -a), a])
res = float('inf')
ma = max(a for a, a0 in pq)
while len(pq) == len(nums):
a, a0 = heapq.heappop(pq)
res = min(res, ma - a)
if a % 2 == 1 or a < a0:
ma = max(ma, a * 2)
heapq.heappush(pq, [a * 2, a0])
return res
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