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Destroy Sequential Targets

Number: 2548

Difficulty: Medium

Paid? No

Companies: Intuit

Problem Description

Given an array of positive integers "nums" representing target positions on a number line and an integer "space", you have a machine that, when seeded with a number nums[i], can destroy all targets that can be represented as nums[i] + c * space (for any non-negative integer c). The goal is to destroy the maximum number of targets and to return the smallest possible value from "nums" that, when used to seed the machine, achieves that maximum destruction.

Key Insights

  • The machine destroys targets in an arithmetic progression based on the seed.
  • Targets that share the same remainder when divided by "space" will all be destroyed if one of them is chosen as the seed.
  • Counting the frequency of each remainder (mod "space") in "nums" gives the number of targets that can be destroyed.
  • It is important to track the minimum value of "nums" belonging to each remainder group because if multiple groups yield the same maximum count, you must choose the smallest seed.

Space and Time Complexity

Time Complexity: O(n), where n is the number of targets in "nums". Space Complexity: O(n) in the worst-case scenario, where all targets have distinct remainders (or equivalently O(min(n, space))).

Solution

To solve the problem, iterate over the "nums" array and for each value compute its remainder modulo "space". Use a hash table (or dictionary) to map each remainder to a pair consisting of the count of values with that remainder and the minimum value encountered with that remainder.

  1. Initialize an empty hash map.
  2. For each target value in the array:
    • Calculate remainder = value % space.
    • If this remainder is already in the map, increment its count and update the minimum value if the current value is smaller.
    • Otherwise, create an entry with count set to 1 and the current value as the minimum.
  3. After processing the entire array, iterate over the hash map to determine which remainder has the maximum count.
  4. If multiple remainders have the same maximum frequency, choose the one with the smallest minimum value.
  5. Return that minimum value as the final answer.

This solution effectively leverages the property that targets falling in the same modulo "space" group can all be destroyed by seeding any one of them.

Code Solutions

# Python Solution
class Solution:
    def destroyTargets(self, nums, space):
        # Dictionary to map remainder to (count, min_value)
        remainder_map = {}
        # Loop through each target value in nums
        for num in nums:
            remainder = num % space
            # Update the count and the minimum value for this remainder
            if remainder in remainder_map:
                count, min_value = remainder_map[remainder]
                remainder_map[remainder] = (count + 1, min(min_value, num))
            else:
                remainder_map[remainder] = (1, num)
        
        # Initialize variables for tracking the maximum targets destroyed and the result seed
        max_count = 0
        result_seed = float('inf')
        # Iterate over each remainder group to find the optimal seed
        for count, min_value in remainder_map.values():
            if count > max_count or (count == max_count and min_value < result_seed):
                max_count = count
                result_seed = min_value
        return result_seed

# Example usage:
# sol = Solution()
# print(sol.destroyTargets([3,7,8,1,1,5], 2)) # Output: 1
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