Python max Heap
Intuition\nTo maximize happiness, we want to prioritize placing the happiest people in the grid.\nA max-heap allows us to efficiently access the person with the
# Intuition\nTo maximize happiness, we want to prioritize placing the happiest people in the grid.\nA max-heap allows us to efficiently access the person with the highest happiness at any point.\n\n# Approach\nMax-Heap Construction: We convert the happiness list into a max-heap using heapq._heapify_max(we can insert negative numbers instead). This ensures the element with the highest happiness is at the root.\nGreedy Placement: We iterate through a loop (k times):\nWe pop the element with the highest happiness (tem) from the max-heap using heapq._heappop_max.\nWe check if placing this person would still allow for k neighbors (including themselves).\nIf tem - count >= 0 (enough neighbors available):\nAdd the happiness (tem) to the total (ans).\nIncrement the counter (count) for the placed person and their neighbors.\nIf not enough neighbors, we can\'t place this person effectively and move on.\nWe repeat until k people are placed.\n\n# Complexity\n- Time complexity:\nO(n log n) due to creating the max-heap (heapify) and repeated pops/maximum extractions (heappop_max).\n\n- Space complexity:\nO(1) as we use constant extra space for variables.\n\n# Code\n```\nimport heapq as hq \nclass Solution:\n    def maximumHappinessSum(self, happiness: List[int], k: int) -> int:\n        count=0\n        ans=0\n        hq._heapify_max(happiness)\n        while k:\n            tem=heapq._heappop_max(happiness)\n            if tem-count>=0:\n                ans+=tem-count\n            count+=1\n            k-=1\n        return ans\n        \n```
['Python3']