2453. Destroy Sequential Targets
Description
You are given a 0-indexed array nums
consisting of positive integers, representing targets on a number line. You are also given an integer space
.
You have a machine which can destroy targets. Seeding the machine with some nums[i]
allows it to destroy all targets with values that can be represented as nums[i] + c * space
, where c
is any non-negative integer. You want to destroy the maximum number of targets in nums
.
Return the minimum value of nums[i]
you can seed the machine with to destroy the maximum number of targets.
Example 1:
Input: nums = [3,7,8,1,1,5], space = 2 Output: 1 Explanation: If we seed the machine with nums[3], then we destroy all targets equal to 1,3,5,7,9,... In this case, we would destroy 5 total targets (all except for nums[2]). It is impossible to destroy more than 5 targets, so we return nums[3].
Example 2:
Input: nums = [1,3,5,2,4,6], space = 2 Output: 1 Explanation: Seeding the machine with nums[0], or nums[3] destroys 3 targets. It is not possible to destroy more than 3 targets. Since nums[0] is the minimal integer that can destroy 3 targets, we return 1.
Example 3:
Input: nums = [6,2,5], space = 100 Output: 2 Explanation: Whatever initial seed we select, we can only destroy 1 target. The minimal seed is nums[1].
Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 109
1 <= space <= 109
Solutions
Solution 1: Modulo + Enumeration
We traverse the array $nums$ and use a hash table $cnt$ to count the frequency of each number modulo $space$. The higher the frequency, the more targets can be destroyed. We find the group with the highest frequency and take the minimum value in the group.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $nums$.
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