2548 Destroy Sequential Targets

Destroy Sequential Targets

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

class Solution:
    def destroyTargets(self, nums: List[int], space: int) -> int:
        remainder_count = {}
        # Dictionary to store minimum number for each remainder
        min_number = {}
        
        # Group numbers by remainder and track minimum in each group
        for num in nums:
            r = num % space
            remainder_count[r] = remainder_count.get(r, 0) + 1
            min_number[r] = min(min_number.get(r, float('inf')), num)
        
        max_targets = max(remainder_count.values())
        min_seed = float('inf')
        
        # Find minimum seed that can destroy maximum targets
        for r in remainder_count:
            if remainder_count[r] == max_targets:
                min_seed = min(min_seed, min_number[r])
        
        return min_seed