@@ -94,11 +94,15 @@ tags:
9494
9595<!-- solution:start -->
9696
97- ### 方法一:差分有序哈希表
97+ ### 方法一:差分思想 + 哈希表
9898
99- 我们利用差分思想,使用有序哈希表 ` height ` 记录每个位置的高度变化, ` cnt ` 记录建筑物的数量变化。对有序哈希表求前缀和,即可得到每个位置的高度和建筑物数量 。
99+ 我们可以利用差分思想,用一个哈希表 $\textit{ cnt}$ 记录每个位置的建筑物数量变化,用另一个哈希表 $\textit{d}$ 记录每个位置的高度变化 。
100100
101- 最后遍历有序哈希表,对于每个位置,如果高度和建筑物数量都不为 0,则说明该位置有建筑物,判断此时的建筑物是否与上个建筑物的平均高度相同,如果相同,则合并,否则加入结果集。
101+ 接下来,我们对哈希表 $\textit{d}$ 按照键值进行排序,用一个变量 $\textit{s}$ 记录当前位置的高度和,用一个变量 $\textit{m}$ 记录当前位置的建筑物数量。
102+ 103+ 然后遍历哈希表 $\textit{d},ドル对于每个位置,如果 $\textit{m}$ 不为 0,说明此前有建筑物,我们计算出平均高度,如果当前位置的建筑物与上个建筑物的平均高度相同,则合并,否则加入结果集。
104+ 105+ 最后返回结果集即可。
102106
103107时间复杂度 $O(n \times \log n),ドル空间复杂度 $O(n)$。其中 $n$ 为建筑物数量。
104108
@@ -109,25 +113,26 @@ tags:
109113``` python
110114class Solution :
111115 def averageHeightOfBuildings (self buildings : List[List[int ]]) -> List[List[int ]]:
112- height = defaultdict(int )
113116 cnt = defaultdict(int )
114- for s, e, h in buildings:
115- cnt[s] += 1
116- cnt[e] -= 1
117- height[s] += h
118- height[e] -= h
117+ d = defaultdict(int )
118+ for start, end, height in buildings:
119+ cnt[start] += 1
120+ cnt[end] -= 1
121+ d[start] += height
122+ d[end] -= height
123+ s = m = 0
124+ last = - 1
119125 ans = []
120- i = h = n = 0
121- for j in sorted (cnt.keys()):
122- if n:
123- t = [i, j, h // n]
124- if ans and ans[- 1 ][1 ] == i and ans[- 1 ][2 ] == t[- 1 ]:
125- ans[- 1 ][1 ] = j
126+ for k, v in sorted (d.items()):
127+ if m:
128+ avg = s // m
129+ if ans and ans[- 1 ][2 ] == avg and ans[- 1 ][1 ] == last:
130+ ans[- 1 ][1 ] = k
126131 else :
127- ans.append(t )
128- i = j
129- h += height[j ]
130- n += cnt[j]
132+ ans.append([last, k, avg] )
133+ s += v
134+ m += cnt[k ]
135+ last = k
131136 return ans
132137```
133138
@@ -136,36 +141,34 @@ class Solution:
136141``` java
137142class Solution {
138143 public int [][] averageHeightOfBuildings (int [][] buildings ) {
139- TreeMap <Integer , Integer >height = new TreeMap <>
140- TreeMap<Integer , Integer > cnt = new TreeMap<> ();
141- for (var v : buildings) {
142- int s = v [0 ], e = v [1 ], h = v [2 ];
143- cnt. put(s, cnt . getOrDefault(s, 0 ) + 1 );
144- cnt. put(e, cnt . getOrDefault(e, 0 ) - 1 );
145- height . put(s , height. getOrDefault(s, 0 ) + h );
146- height . put(e, height. getOrDefault(e, 0 ) - h );
144+ Map <Integer , Integer >cnt = new HashMap <>
145+ TreeMap<Integer , Integer > d = new TreeMap<> ();
146+ for (var e : buildings) {
147+ int start = e [0 ], end = e [1 ], height = e [2 ];
148+ cnt. merge(start, 1 , Integer :: sum );
149+ cnt. merge(end, - 1 , Integer :: sum );
150+ d . merge(start , height, Integer :: sum );
151+ d . merge(end, - height, Integer :: sum );
147152 }
148- int i = 0 , h = 0 , n = 0 ;
149- List<int[]> res = new ArrayList<> ();
150- for (int j : cnt. keySet()) {
151- if (n > 0 ) {
152- int [] t = new int [] {i, j, h / n};
153- int k = res. size() - 1 ;
154- if (k >= 0 && res. get(k)[1 ] == i && res. get(k)[2 ] == t[2 ]) {
155- res. get(k)[1 ] = j;
153+ int s = 0 , m = 0 ;
154+ int last = - 1 ;
155+ List<int[]> ans = new ArrayList<> ();
156+ for (var e : d. entrySet()) {
157+ int k = e. getKey(), v = e. getValue();
158+ if (m > 0 ) {
159+ int avg = s / m;
160+ if (! ans. isEmpty() && ans. get(ans. size() - 1 )[2 ] == avg
161+ && ans. get(ans. size() - 1 )[1 ] == last) {
162+ ans. get(ans. size() - 1 )[1 ] = k;
156163 } else {
157- res . add(t );
164+ ans . add(new int [] {last, k, avg} );
158165 }
159166 }
160- h += height. get(j);
161- n += cnt. get(j);
162- i = j;
163- }
164- int [][] ans = new int [res. size()][3 ];
165- for (i = 0 ; i < ans. length; ++ i) {
166- ans[i] = res. get(i);
167+ s += v;
168+ m += cnt. get(k);
169+ last = k;
167170 }
168- return ans;
171+ return ans. toArray( new int [ 0 ][]) ;
169172 }
170173}
171174```
@@ -176,27 +179,35 @@ class Solution {
176179class Solution {
177180public:
178181 vector<vector<int >> averageHeightOfBuildings(vector<vector<int >>& buildings) {
179- map<int, int> height, cnt;
180- for (auto& v : buildings) {
181- int s = v[ 0] , e = v[ 1] , h = v[ 2] ;
182- cnt[ s] ++, cnt[ e] --;
183- height[ s] += h, height[ e] -= h;
182+ unordered_map<int, int> cnt;
183+ map<int, int> d;
184+ 185+ for (const auto& e : buildings) {
186+ int start = e[0], end = e[1], height = e[2];
187+ cnt[start]++;
188+ cnt[end]--;
189+ d[start] += height;
190+ d[end] -= height;
184191 }
192+ 193+ int s = 0 , m = 0 ;
194+ int last = -1 ;
185195 vector<vector<int >> ans;
186- int i = 0, h = 0, n = 0;
187- for (auto& [ j, _ ] : cnt ) {
188- if (n ) {
189- vector< int > t = {i, j, h / n} ;
190- if (ans.size () && ans.back()[ 1 ] == i && ans.back()[ 2 ] == t [ 2 ] ) {
191- ans.back()[ 1] = j ;
196+ 197+ for (const auto & [k, v ] : d ) {
198+ if (m > 0 ) {
199+ int avg = s / m ;
200+ if (! ans.empty () && ans.back()[2 ] == avg && ans.back()[1 ] == last ) {
201+ ans.back()[1] = k ;
192202 } else {
193- ans.push_back(t );
203+ ans.push_back({last, k, avg} );
194204 }
195205 }
196- i = j ;
197- h += height [ j ] ;
198- n += cnt [ j ] ;
206+ s += v ;
207+ m += cnt[k ];
208+ last = k ;
199209 }
210+ 200211 return ans;
201212 }
202213};
@@ -206,39 +217,80 @@ public:
206217
207218``` go
208219func averageHeightOfBuildings (buildings [][]int ) [][]int {
209- height := make(map[int]int)
210220 cnt := make (map [int ]int )
211- for _, v := range buildings {
212- s, e, h := v[0], v[1], v[2]
213- cnt[s]++
214- cnt[e]--
215- height[s] += h
216- height[e] -= h
221+ d := make (map [int ]int )
222+ 223+ for _ , e := range buildings {
224+ start , end , height := e[0 ], e[1 ], e[2 ]
225+ cnt[start]++
226+ cnt[end]--
227+ d[start] += height
228+ d[end] -= height
217229 }
218- keys := make([]int, len(cnt))
219- for k := range cnt {
230+ 231+ s , m := 0 , 0
232+ last := -1
233+ var ans [][]int
234+ 235+ keys := make ([]int , 0 , len (d))
236+ for k := range d {
220237 keys = append (keys, k)
221238 }
222239 sort.Ints (keys)
223- i, h, n := 0, 0, 0
224- ans := [][]int{}
225- for _, j := range keys {
226- if n > 0 {
227- t := []int{i, j, h / n}
228- if len(ans) > 0 && ans[len(ans)-1][1 ] == i && ans[len(ans)-1][2 ] == t[2] {
229- ans[len(ans)-1][1] = j
240+ 241+ for _ , k := range keys {
242+ v := d[k]
243+ if m > 0 {
244+ avg := s / m
245+ if len (ans) > 0 && ans[len (ans)-1 ][2 ] == avg && ans[len (ans)-1 ][1 ] == last {
246+ ans[len (ans)-1 ][1 ] = k
230247 } else {
231- ans = append(ans, t )
248+ ans = append (ans, [] int {last, k, avg} )
232249 }
233250 }
234- i = j
235- h += height[j ]
236- n += cnt[j]
251+ s += v
252+ m += cnt[k ]
253+ last = k
237254 }
255+ 238256 return ans
239257}
240258```
241259
260+ #### TypeScript
261+ 262+ ``` ts
263+ function averageHeightOfBuildings(buildings : number [][]): number [][] {
264+ const = new Map <number , number >();
265+ const = new Map <number , number >();
266+ for (const of buildings ) {
267+ cnt .set (start , (cnt .get (start ) || 0 ) + 1 );
268+ cnt .set (end , (cnt .get (end ) || 0 ) - 1 );
269+ d .set (start , (d .get (start ) || 0 ) + height );
270+ d .set (end , (d .get (end ) || 0 ) - height );
271+ }
272+ let [s, m] = [0 , 0 ];
273+ let last = - 1 ;
274+ const : number [][] = [];
275+ const = Array .from (d .keys ()).sort ((a , b ) => a - b );
276+ for (const of sortedKeys ) {
277+ const = d .get (k )! ;
278+ if (m > 0 ) {
279+ const = Math .floor (s / m );
280+ if (ans .length > 0 && ans .at (- 1 )! [2 ] === avg && ans .at (- 1 )! [1 ] === last ) {
281+ ans [ans .length - 1 ][1 ] = k ;
282+ } else {
283+ ans .push ([last , k , avg ]);
284+ }
285+ }
286+ s += v ;
287+ m += cnt .get (k )! ;
288+ last = k ;
289+ }
290+ return ans ;
291+ }
292+ ```
293+ 242294<!-- tabs:end -->
243295
244296<!-- solution:end -->
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