908. Smallest Range I
Description
You are given an integer array nums
and an integer k
.
In one operation, you can choose any index i
where 0 <= i < nums.length
and change nums[i]
to nums[i] + x
where x
is an integer from the range [-k, k]
. You can apply this operation at most once for each index i
.
The score of nums
is the difference between the maximum and minimum elements in nums
.
Return the minimum score of nums
after applying the mentioned operation at most once for each index in it.
Example 1:
Input: nums = [1], k = 0 Output: 0 Explanation: The score is max(nums) - min(nums) = 1 - 1 = 0.
Example 2:
Input: nums = [0,10], k = 2 Output: 6 Explanation: Change nums to be [2, 8]. The score is max(nums) - min(nums) = 8 - 2 = 6.
Example 3:
Input: nums = [1,3,6], k = 3 Output: 0 Explanation: Change nums to be [4, 4, 4]. The score is max(nums) - min(nums) = 4 - 4 = 0.
Constraints:
1 <= nums.length <= 104
0 <= nums[i] <= 104
0 <= k <= 104
Solutions
Solution 1: Mathematics
According to the problem description, we can subtract $k$ from the maximum value in the array and add $k$ to the minimum value in the array, which can reduce the difference between the maximum and minimum values in the array.
Therefore, the final answer is the larger value between $\max(\textit{nums}) - \min(\textit{nums}) - 2 \times k$ and $0$.
The time complexity is $O(n)$, where $n$ is the length of the array $\textit{nums}$. The space complexity is $O(1)$.
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