add 218

218._The _Skyline_Problem .md

+### 218. The Skyline Problem
+
+题目:
+<https://leetcode.com/problems/The-Skyline-Problem/>
+
+
+难度:
+
+Hard
+
+思路
+
+观察发现，skyline的points的横坐标一定是某个building的左边界或者右边界。
+
+开始，假设只有2个建筑物，拿出第一个buiding B1，我们先把它的左上顶点加进我们的output结果skyline中，然后继续拿下一个building B2，我们现在需要将B2的左上顶点对应的x coordinate与B1的右上顶点所对应的x coordinate做比较：
+
+- 如果前者小且B2的高度大于B1的高度，则我们将B2的左上顶点也加入skyline中去。
+- 如果前者小且B2的高度小于于B1的高度，则忽略B2的左上顶点
+
+接下来考虑更多建筑物的情况，从左到右扫描，当我们遇到一个楼的左边界时，把它push到一个heap中。如果后面扫描的楼的高度比heap中最高的楼还高，那么它的左上顶点一定会被加入到skyline中。当我们遇到一个building的右边界时,我们需要将其从heap中pop掉，如果heap中max height有变化，则push到结果中。
+
+
+
+#### 程序代码解释
+
+- liveBuildings代表（左上顶点已经被加入output中但右上顶点还没有做判断的building）的右上顶点的集合，形式为[(height, x-coordinate)…..]
+- skyline是output
+- 程序里面的这句代码```while idx < n and buildings[idx][0] == start:```是为了防止有左右坐标完全相同但是height不同的building的存在，it's not useless!!!
+- python里面的heapq模块如果有不懂的同学可以看看这个文章：[heapq](http://blog.csdn.net/calling_wisdom/article/details/41676133)
+
+
+```python
+class Solution(object):
+    def getSkyline(self, buildings):
+        """
+        :type buildings: List[List[int]]
+        :rtype: List[List[int]]
+        """
+        idx, n = 0, len(buildings)
+        liveBuildings, skyline = [], []
+        while idx < n or len(liveBuildings) > 0:
+            if len(liveBuildings) == 0 or (idx < n and buildings[idx][0] <= -liveBuildings[0][1]):
+                start = buildings[idx][0]
+                while idx < n and buildings[idx][0] == start:
+                    heapq.heappush(liveBuildings, [-buildings[idx][2], -buildings[idx][1]])
+                    idx += 1
+            else:
+                start = -liveBuildings[0][1]
+                while len(liveBuildings) > 0 and -liveBuildings[0][1] <= start:
+                    heapq.heappop(liveBuildings)
+            height = len(liveBuildings) and -liveBuildings[0][0]
+            if len(skyline) == 0 or skyline[-1][1] != height:
+                skyline.append([start, height])
+        return skyline
+```
+#####另外还有一个超级6的大神的代码，但是今天我要赶报告，就只先贴代码了
+
+```python
+class Solution(object):
+    def getSkyline(self, buildings):
+        """
+        :type buildings: List[List[int]]
+        :rtype: List[List[int]]
+        """
+        events = sorted([(L, -H, R) for L, R, H in buildings] + list(set((R, 0, None) for L, R, H in buildings)))
+        #events = sorted(event for L, R, H in buildings for event in ((L, -H, R), (R, 0, None)))
+        res, hp = [[0, 0]], [(0, float("inf"))]
+        for x, negH, R in events:
+            while x >= hp[0][1]: 
+                heapq.heappop(hp)
+            if negH: heapq.heappush(hp, (negH, R))
+            if res[-1][1] + hp[0][0]: 
+                res += [x, -hp[0][0]],
+        return res[1:]
+```
+
+```Java
+public class Solution {
+    public List<int[]> getSkyline(int[][] buildings) {
+        List<int[]> result = new ArrayList<int[]>();
+        if (buildings == null || buildings.length == 0 || buildings[0].length == 0) {
+            return result;
+        }
+        
+        List<Height> heights = new ArrayList<Height>();
+        for (int[] building : buildings) {
+            heights.add(new Height(building[0], -building[2]));
+            heights.add(new Height(building[1], building[2]));
+        }
+        Collections.sort(heights, new Comparator<Height>() {
+            @Override
+            public int compare(Height h1, Height h2) {
+                return h1.index != h2.index ? h1.index - h2.index : h1.height - h2.height;
+            }
+        });
+        
+        PriorityQueue<Integer> pq = new PriorityQueue<Integer>(1000, Collections.reverseOrder());
+        pq.offer(0);
+        int prev = 0;
+        for (Height h : heights) {
+            if (h.height < 0) {
+                pq.offer(-h.height);
+            } else {
+                pq.remove(h.height);
+            }
+            int cur = pq.peek();
+            if (cur != prev) {
+                result.add(new int[]{h.index, cur});
+                prev = cur;
+            }
+        }
+        
+        return result;
+    }
+    
+    class Height {
+        int index;
+        int height;
+        Height(int index, int height) {
+            this.index = index;
+            this.height = height;
+        }
+    }
+}
+```
+
+
+
+Author: Keqi Huang
+
+If you like it, please spread your support
+
+![Support](https://github.com/Lisanaaa/myTODOs/blob/master/WechatIMG17.jpeg)