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This approach uses a max-heap (priority queue) to efficiently track and retrieve the two heaviest stones. By inserting stones with negative values, we use a min-heap implementation in certain languages to simulate max-heap behavior.
Time Complexity: O(n log n), where n is the number of stones. This accounts for the heap operations.
Space Complexity: O(n), to maintain the heap of stones.
1import java.util.PriorityQueue;
2
3public class Solution {
4 public int lastStoneWeight(int[] stones) {
5 PriorityQueue<Integer> maxHeap = new PriorityQueue<>((a, b) -> b - a);
6 for (int stone : stones) {
7 maxHeap.add(stone);
8 }
9 while (maxHeap.size() > 1) {
10 int first = maxHeap.poll();
11 int second = maxHeap.poll();
12 if (first != second) {
13 maxHeap.add(first - second);
14 }
15 }
16 return maxHeap.isEmpty() ? 0 : maxHeap.poll();
17 }
18}In this Java solution, we use PriorityQueue with a custom comparator to maintain a max-heap. We poll the two largest stones, and their difference is added back if non-zero. The final stone weight is returned, or zero if none remain.
This approach uses a multiset or bag (analogous to balanced trees or sorted lists in some languages) to manage dynamically sorted stone weights. This allows for direct access to largest elements and supports efficient inserts/removals without full re-sorting.
Time Complexity: O(n^2), due to insert and remove operations in SortedList being O(log n).
Space Complexity: O(n), for storage within the SortedList.
1#include <vector>
class Solution {
public:
int lastStoneWeight(std::vector<int>& stones) {
std::multiset<int> sortedStones(stones.begin(), stones.end());
while (sortedStones.size() > 1) {
auto it1 = std::prev(sortedStones.end());
int first = *it1; sortedStones.erase(it1);
auto it2 = std::prev(sortedStones.end());
int second = *it2; sortedStones.erase(it2);
if (first != second) {
sortedStones.insert(first - second);
}
}
return sortedStones.empty() ? 0 : *sortedStones.begin();
}
};Using std::multiset in C++, sorted access is granted with prev functions utilized for efficient retrieval and organization addressing of the stones as differences arise.