Destroy Sequential Targets

• Initialize maxDestroyed = 0 and bestSeed = infinity.
• Iterate through each number seedNum in the nums array, treating it as a potential seed.
• For each seedNum, initialize a counter currentDestroyed = 0.
• Calculate the remainder r = seedNum % space.
• Start a nested loop, iterating through every targetNum in the nums array.
• Inside the nested loop, check if targetNum % space == r. If it is, increment currentDestroyed.
• After the inner loop finishes, compare currentDestroyed with maxDestroyed.
• If currentDestroyed > maxDestroyed, update maxDestroyed = currentDestroyed and bestSeed = seedNum.
• If currentDestroyed == maxDestroyed, update bestSeed = Math.min(bestSeed, seedNum) to handle the tie-breaking rule.
• After iterating through all possible seeds, return bestSeed.

The core idea is to test every possible seed. Since any nums[i] can be a seed, we can loop through all of them. For a chosen seed, say seed_val, all targets t that satisfy t % space == seed_val % space will be destroyed. We can implement this with a nested loop structure. The outer loop selects a seed_val from nums. The inner loop iterates through all target_val in nums and counts how many have the same remainder modulo space as the seed_val. We maintain two variables: maxDestroyed to store the maximum count found so far, and bestSeed to store the corresponding seed. If a new seed results in a count greater than maxDestroyed, we update both maxDestroyed and bestSeed. If a new seed results in a count equal to maxDestroyed, we update bestSeed only if the new seed is smaller than the current bestSeed.

1class Solution {2    public int destroyTargets(int[] nums, int space) {3        int maxDestroyed = 0;4        int bestSeed = Integer.MAX_VALUE;5 6        for (int seedNum : nums) {7            int currentDestroyed = 0;8            int remainder = seedNum % space;9 10            for (int targetNum : nums) {11                if (targetNum % space == remainder) {12                    currentDestroyed++;13                }14            }15 16            if (currentDestroyed > maxDestroyed) {17                maxDestroyed = currentDestroyed;18                bestSeed = seedNum;19            } else if (currentDestroyed == maxDestroyed) {20                bestSeed = Math.min(bestSeed, seedNum);21            }22        }23        return bestSeed;24    }25}

• Create a HashMap<Integer, Integer> called counts to store the frequency of each remainder.
• Initialize maxCount = 0.
• First Pass: Iterate through each num in nums:
  • Calculate remainder = num % space.
  • Increment the count for this remainder in the counts map.
  • Update maxCount = Math.max(maxCount, counts.get(remainder)).
• Initialize resultSeed = Integer.MAX_VALUE.
• Second Pass: Iterate through each num in nums:
  • Calculate remainder = num % space.
  • If the count for this remainder in the counts map is equal to maxCount:
    • This num is part of a group with the maximum possible size.
    • Update resultSeed = Math.min(resultSeed, num).
• Return resultSeed.

The key insight is that the condition nums[i] + c * space is equivalent to num % space == nums[i] % space. This partitions the nums array into equivalence classes based on their remainders modulo space. We can solve this problem efficiently in two passes using a hash map.

First Pass: We iterate through the nums array to build a frequency map. The map will store each remainder (num % space) as a key and the count of numbers with that remainder as the value. While doing this, we can also keep track of the maximum frequency found.

Second Pass: After determining the maximum frequency, we iterate through the nums array again. For each number, we check if its remainder group has a frequency equal to the maximum frequency. If it does, this number is a potential seed for a maximally-sized group. We keep track of the minimum such number encountered.

This two-pass method correctly identifies the maximum number of targets we can destroy and then finds the minimum seed required to achieve that.

1import java.util.HashMap;2import java.util.Map;3 4class Solution {5    public int destroyTargets(int[] nums, int space) {6        Map<Integer, Integer> counts = new HashMap<>();7        int maxCount = 0;8 9        // First pass: count frequencies of remainders and find the max frequency10        for (int num : nums) {11            int remainder = num % space;12            int newCount = counts.getOrDefault(remainder, 0) + 1;13            counts.put(remainder, newCount);14            if (newCount > maxCount) {15                maxCount = newCount;16            }17        }18 19        int resultSeed = Integer.MAX_VALUE;20 21        // Second pass: find the minimum seed that achieves the max frequency22        for (int num : nums) {23            int remainder = num % space;24            if (counts.get(remainder) == maxCount) {25                resultSeed = Math.min(resultSeed, num);26            }27        }28 29        return resultSeed;30    }31}