Destroy Sequential Targets

Problem 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.

Key Insights

• The machine can destroy targets that are spaced apart by a fixed integer value (space).
• Different seeds will destroy different sets of targets based on their values and the space.
• To maximize the number of destroyed targets, we need to evaluate how many targets can be destroyed with each possible seed.
• The optimal seed is the one that allows for the destruction of the maximum number of targets while being the smallest possible value.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem, we can use a hash table (or dictionary) to count how many targets can be destroyed for each possible seed value. The key steps in the algorithm are as follows:

1. Create a dictionary to store the count of destroyable targets for each starting seed value.
2. Iterate through each target in the input array nums.
3. For each target, calculate its seed value (the target modulo space).
4. Increment the count of targets that can be destroyed for that seed value.
5. Track the maximum count of destroyed targets and the corresponding minimum seed value.
6. Return the minimum seed value that yields the maximum count of destroyed targets.

Code Solutions