水平面上有 N 座大楼，每座大楼都是矩阵的形状，可以用一个三元组表示 (start, end, height)，分别代表其在x轴上的起点，终点和高度。大楼之间从远处看可能会重叠，求出 N 座大楼的外轮廓线。

外轮廓线的表示方法为若干三元组，每个三元组包含三个数字 (start, end, height)，代表这段轮廓的起始位置，终止位置和高度。

点击进入在线评测

样例1

输入:
[
[1, 3, 3],
[2, 4, 4],
[5, 6, 1]
]
输出:
[
[1, 2, 3],
[2, 4, 4],
[5, 6, 1]
]
说明:
建筑物如下图所示，黄色部分表示建筑物

样例2

输入:
[
[1, 4, 3],
[6, 9, 5]
]
输出:
[
[1, 4, 3],
[6, 9, 5]
]
说明:
建筑物如下图所示，黄色部分表示建筑物

【题解】

使用[九章算法强化班]中讲过的 HashHeap 和扫描线算法。 Java 可以用 TreeSet / TreeMap， C++ 可以用 Map.

import java.util.*;

public class Solution {

class HashHeap {
ArrayList<Integer> heap;
String mode;
int size_t;
HashMap<Integer, Node> hash;

class Node {
public Integer id;
public Integer num;

Node(Node now) {
id = now.id;
num = now.num;
}

Node(Integer first, Integer second) {

this.id = first;
this.num = second;
}
}

public HashHeap(String mod) {
// TODO Auto-generated constructor stub
heap = new ArrayList<Integer>();
mode = mod;
hash = new HashMap<Integer, Node>();
size_t = 0;
}

public int peek() {
return heap.get(0);
}

public int size() {
return size_t;
}

public Boolean isEmpty() {
return (heap.size() == 0);
}

int parent(int id) {
if (id == 0) {
return -1;
}
return (id - 1) / 2;
}

int lson(int id) {
return id * 2 + 1;
}

int rson(int id) {
return id * 2 + 2;
}

boolean comparesmall(int a, int b) {
if (a <= b) {
if (mode == "min")
return true;
else
return false;
} else {
if (mode == "min")
return false;
else
return true;
}

}

void swap(int idA, int idB) {
int valA = heap.get(idA);
int valB = heap.get(idB);

int numA = hash.get(valA).num;
int numB = hash.get(valB).num;
hash.put(valB, new Node(idA, numB));
hash.put(valA, new Node(idB, numA));
heap.set(idA, valB);
heap.set(idB, valA);
}

public Integer poll() {
size_t--;
Integer now = heap.get(0);
Node hashnow = hash.get(now);
if (hashnow.num == 1) {
swap(0, heap.size() - 1);
hash.remove(now);
heap.remove(heap.size() - 1);
if (heap.size() > 0) {
siftdown(0);
}
} else {
hash.put(now, new Node(0, hashnow.num - 1));
}
return now;
}

public void add(int now) {
size_t++;
if (hash.containsKey(now)) {
Node hashnow = hash.get(now);
hash.put(now, new Node(hashnow.id, hashnow.num + 1));

} else {
heap.add(now);
hash.put(now, new Node(heap.size() - 1, 1));
}

siftup(heap.size() - 1);
}

public void delete(int now) {
size_t--;
Node hashnow = hash.get(now);
int id = hashnow.id;
int num = hashnow.num;
if (hashnow.num == 1) {

swap(id, heap.size() - 1);
hash.remove(now);
heap.remove(heap.size() - 1);
if (heap.size() > id) {
siftup(id);
siftdown(id);
}
} else {
hash.put(now, new Node(id, num - 1));
}
}

void siftup(int id) {
while (parent(id) > -1) {
int parentId = parent(id);
if (comparesmall(heap.get(parentId), heap.get(id)) == true) {
break;
} else {
swap(id, parentId);
}
id = parentId;
}
}

void siftdown(int id) {
while (lson(id) < heap.size()) {
int leftId = lson(id);
int rightId = rson(id);
int son;
if (rightId >= heap.size()
|| (comparesmall(heap.get(leftId), heap.get(rightId)) == true)) {
son = leftId;
} else {
son = rightId;
}
if (comparesmall(heap.get(id), heap.get(son)) == true) {
break;
} else {
swap(id, son);
}
id = son;
}
}
}

class Edge {
int pos;
int height;
boolean isStart;

public Edge(int pos, int height, boolean isStart) {
this.pos = pos;
this.height = height;
this.isStart = isStart;
}

}

class EdgeComparator implements Comparator<Edge> {
@Override
public int compare(Edge arg1, Edge arg2) {
Edge l1 = (Edge) arg1;
Edge l2 = (Edge) arg2;
if (l1.pos != l2.pos)
return compareInteger(l1.pos, l2.pos);
if (l1.isStart && l2.isStart) {
return compareInteger(l2.height, l1.height);
}
if (!l1.isStart && !l2.isStart) {
return compareInteger(l1.height, l2.height);
}
return l1.isStart ? -1 : 1;
}

int compareInteger(int a, int b) {
return a <= b ? -1 : 1;
}
}

List<List<Integer>> output(List<List<Integer>> res) {
List<List<Integer>> ans = new ArrayList<List<Integer>>();
if (res.size() > 0) {
int pre = res.get(0).get(0);
int height = res.get(0).get(1);
for (int i = 1; i < res.size(); i++) {
List<Integer> now = new ArrayList<Integer>();
int id = res.get(i).get(0);
if (height > 0) {
now.add(pre);
now.add(id);
now.add(height);
ans.add(now);
}
pre = id;
height = res.get(i).get(1);
}
}
return ans;
}

public List<List<Integer>> buildingOutline(int[][] buildings) {
// write your code here
List<List<Integer>> res = new ArrayList<List<Integer>>();

if (buildings == null || buildings.length == 0
|| buildings[0].length == 0) {
return res;
}
ArrayList<Edge> edges = new ArrayList<Edge>();
for (int[] building : buildings) {
Edge startEdge = new Edge(building[0], building[2], true);
edges.add(startEdge);
Edge endEdge = new Edge(building[1], building[2], false);
edges.add(endEdge);
}
Collections.sort(edges, new EdgeComparator());

HashHeap heap = new HashHeap("max");

List<Integer> now = null;
for (Edge edge : edges) {
if (edge.isStart) {
if (heap.isEmpty() || edge.height > heap.peek()) {
now = new ArrayList<Integer>(Arrays.asList(edge.pos,
edge.height));
res.add(now);
}
heap.add(edge.height);
} else {
heap.delete(edge.height);
if (heap.isEmpty() || edge.height > heap.peek()) {
if (heap.isEmpty()) {
now = new ArrayList<Integer>(Arrays.asList(edge.pos, 0));
} else {
now = new ArrayList<Integer>(Arrays.asList(edge.pos,
heap.peek()));
}
res.add(now);
}
}
}
return output(res);
}

}
更多题解参见：九章官网