#2453

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Destroy Sequential Targets

Find the minimum seed value to destroy the most targets on a number line, using array scanning and hash lookup.

Problem Statement

You are given an array nums, where each element represents a target on a number line. Along with this array, you're provided an integer space. A machine can be seeded with an element nums[i], and it will destroy all targets with values in the form nums[i] + c * space, where c is a non-negative integer. The goal is to find the minimum value from nums[i] that can destroy the maximum number of targets.

Your task is to return the smallest number from nums that can be seeded to destroy the maximum number of targets. If multiple numbers can destroy the same maximum number of targets, return the smallest one.

Examples

Example 1

Input: nums = [3,7,8,1,1,5], space = 2

Output: 1

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

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

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

Solution Approach

Hashmap-based counting

We can iterate over the array and use a hashmap to count how many targets can be destroyed for each possible seed. For each nums[i], the machine can destroy all targets equal to nums[i] + c * space. By maintaining a count of destroyed targets for each seed, we can efficiently find the one that destroys the most targets.

Modulo tracking

Another effective approach is to track the remainder when each number in nums is divided by space. This allows us to group the numbers by their potential destruction sequence. By storing the count of targets destroyed by each modulo group, we can quickly identify the seed that destroys the most targets.

Efficient array traversal

By combining array scanning with the above hashmap or modulo tracking method, we can traverse the array and perform efficient lookups to keep track of the destruction count. This avoids unnecessary comparisons and minimizes the time complexity.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on the approach, but using a hashmap or modulo tracking reduces the need for brute-force comparisons, making it much more efficient than checking all possible pairs. Space complexity is also impacted by the need to store counts for each number and its modulo class, which may require O(n) space in the worst case.

What Interviewers Usually Probe

Looks for knowledge of hashmaps and modulo operations.
Tests the ability to implement efficient algorithms without brute force.
Assesses problem-solving skills in optimizing performance with large input sizes.

Common Pitfalls or Variants

Common pitfalls

Confusing the seed with the number of destroyed targets, leading to incorrect output.
Failing to track numbers modulo space, resulting in inefficient solutions.
Not handling large input sizes efficiently, causing timeouts.

Follow-up variants

What if targets are ordered? Does it change the approach?
What happens if all numbers are the same?
Can you optimize further by using binary search on sorted nums?

FAQ

What pattern should I focus on for Destroy Sequential Targets?

The core pattern is array scanning combined with hash lookup or modulo operations to track which seed destroys the most targets.

How do I handle large arrays in this problem?

Using a hashmap or modulo approach ensures you don't need to compare every element to every other element, making the solution more scalable.

Why is modulo important in this problem?

Modulo helps group numbers that can be destroyed by the same seed, allowing you to track destruction sequences more efficiently.

What is the expected time complexity of this problem?

The time complexity depends on the approach you use, but it can be reduced to O(n) using a hashmap or modulo tracking.

What should I do if multiple numbers destroy the same number of targets?

Return the smallest number among them, as specified in the problem statement.

terminal

Solution

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.

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class Solution:
    def destroyTargets(self, nums: List[int], space: int) -> int:
        cnt = Counter(v % space for v in nums)
        ans = mx = 0
        for v in nums:
            t = cnt[v % space]
            if t > mx or (t == mx and v < ans):
                ans = v
                mx = t
        return ans

Continue Practicing

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