leetcode-218-天际线问题

题目描述：

 

 

 

 方法一：分治 O(nlogn)

class Solution:
    def getSkyline(self, buildings: List[List[int]]) -> List[List[int]]:
        if not buildings:return []
        if len(buildings)==1:
            return [[buildings[0][0], buildings[0][2]], [buildings[0][1], 0]]
        mid = len(buildings)//2
        left = self.getSkyline(buildings[:mid])
        right = self.getSkyline(buildings[mid:])
        return self.merge(left,right)
    
    def merge(self,left,right):
        l,r = 0,0
        lh,rh = 0,0
        res = []
        while l<len(left) and r<len(right):
            if left[l][0]<right[r][0]:
                cp = [left[l][0], max(left[l][1], rh)]
                lh = left[l][1]
                l += 1
            elif left[l][0] > right[r][0]:
                cp = [right[r][0], max(right[r][1], lh)]
                rh = right[r][1]
                r += 1
            # 相等情况
            else:
                cp = [left[l][0], max(left[l][1], right[r][1])]
                lh = left[l][1]
                rh = right[r][1]
                l += 1
                r += 1
            if len(res)==0 or res[-1][1]!=cp[1]:
                res.append(cp)
        res.extend(left[l:] or right[r:])
        return res

方法二：

class Solution:
    def getSkyline(self, buildings: List[List[int]]) -> List[List[int]]:
        import bisect
        res = [[0, 0]]
        # 记录 [left, height], [right, height]
        loc = []
        for l, r, h in buildings:
            # 为了排序让 left那边靠前, 所以让高度取负
            loc.append([l, -h])
            loc.append([r, h])
        loc.sort()
        heap = [0]

        for x, h in loc:
            if h < 0:
                bisect.insort(heap, h)
            else:
                heap.remove(-h)
            cur = -heap[0]
            if res[-1][1] != cur:
                res.append([x, cur])

        return res[1:]

方法三：堆*

class Solution:
    def getSkyline(self, buildings):
        import heapq
        events = sorted([(L, -H, R) for L, R, H in buildings] + list({(R, 0, 0) for _, R, _ in buildings } ))
        res = [[0, 0]]
        heap = [[0, float("inf")]]
        for x, H, R in events:
            while x >= heap[0][1]:
                heapq.heappop(heap)
            if H:
                heapq.heappush(heap, [H, R])
            if res[-1][1] != -heap[0][0]:
                res.append([x, -heap[0][0]])
        return res[1:]