6868
6969<!-- solution:start -->
7070
71- ### 方法一
71+ ### 方法一:DFS
72+ 73+ 我们可以枚举所有长度为 $n$ 的数字的第一个数字,然后使用深度优先搜索的方法,递归地构造所有符合条件的数字。
74+ 75+ 具体地,我们首先定义一个边界值 $\textit{boundary} = 10^{n-1},ドル表示我们需要构造的数字的最小值。然后,我们从 1ドル$ 到 9ドル$ 枚举第一个数字,对于每一个数字 $i,ドル我们递归地构造以 $i$ 为第一个数字的长度为 $n$ 的数字。
76+ 77+ 时间复杂度 $(n \times 2^n \times |\Sigma|),ドル其中 $|\Sigma|$ 表示数字集合,本题中 $|\Sigma| = 9$。空间复杂度 $O(2^n)$。
7278
7379<!-- tabs:start -->
7480
@@ -77,50 +83,51 @@ tags:
7783``` python
7884class Solution :
7985 def numsSameConsecDiff (self n : int , k : int ) -> List[int ]:
80- ans = []
81- 82- def dfs (n , k , t ):
83- if n == 0 :
84- ans.append(t)
86+ def dfs (x : int ):
87+ if x >= boundary:
88+ ans.append(x)
8589 return
86- last = t % 10
90+ last = x % 10
8791 if last + k <= 9 :
88- dfs(n - 1 , k, t * 10 + last + k)
92+ dfs(x * 10 + last + k)
8993 if last - k >= 0 and k != 0 :
90- dfs(n - 1 , k, t * 10 + last - k)
94+ dfs(x * 10 + last - k)
9195
96+ ans = []
97+ boundary = 10 ** (n - 1 )
9298 for i in range (1 , 10 ):
93- dfs(n - 1 , k, i)
99+ dfs(i)
94100 return ans
95101```
96102
97103#### Java
98104
99105``` java
100106class Solution {
107+ private List<Integer > ans = new ArrayList<> ();
108+ private int boundary;
109+ private int k;
110+ 101111 public int [] numsSameConsecDiff (int n , int k ) {
102- List<Integer > res = new ArrayList<> ();
112+ this . k = k;
113+ boundary = (int ) Math . pow(10 , n - 1 );
103114 for (int i = 1 ; i < 10 ; ++ i) {
104- dfs(n - 1 , k, i, res );
115+ dfs(i );
105116 }
106- int [] ans = new int [res. size()];
107- for (int i = 0 ; i < res. size(); ++ i) {
108- ans[i] = res. get(i);
109- }
110- return ans;
117+ return ans. stream(). mapToInt(i - > i). toArray();
111118 }
112119
113- private void dfs (int n , int k , int t , List< Integer > res ) {
114- if (n == 0 ) {
115- res . add(t );
120+ private void dfs (int x ) {
121+ if (x >= boundary ) {
122+ ans . add(x );
116123 return ;
117124 }
118- int last = t % 10 ;
119- if (last + k <= 9 ) {
120- dfs(n - 1 , k, t * 10 + last + k, res );
125+ int last = x % 10 ;
126+ if (last + k < 10 ) {
127+ dfs(x * 10 + last + k);
121128 }
122- if (last - k > =0 && k ! =0 ) {
123- dfs(n - 1 , k, t * 10 + last - k, res );
129+ if (k ! =0 && last - k > =0 ) {
130+ dfs(x * 10 + last - k);
124131 }
125132 }
126133}
@@ -131,109 +138,111 @@ class Solution {
131138``` cpp
132139class Solution {
133140public:
134- vector<int > ans;
135- 136141 vector<int > numsSameConsecDiff(int n, int k) {
137- for (int i = 1; i < 10; ++i)
138- dfs(n - 1, k, i);
139- return ans;
140- }
141- 142- void dfs (int n, int k, int t) {
143- if (n == 0) {
144- ans.push_back(t);
145- return;
142+ vector<int > ans;
143+ int boundary = pow(10, n - 1);
144+ auto dfs = [ &] (auto&& dfs, int x) {
145+ if (x >= boundary) {
146+ ans.push_back(x);
147+ return;
148+ }
149+ int last = x % 10;
150+ if (last + k < 10) {
151+ dfs(dfs, x * 10 + last + k);
152+ }
153+ if (k != 0 && last - k >= 0) {
154+ dfs(dfs, x * 10 + last - k);
155+ }
156+ };
157+ for (int i = 1; i < 10; ++i) {
158+ dfs(dfs, i);
146159 }
147- int last = t % 10;
148- if (last + k <= 9) dfs(n - 1, k, t * 10 + last + k);
149- if (last - k >= 0 && k != 0) dfs(n - 1, k, t * 10 + last - k);
160+ return ans;
150161 }
151162};
152163```
153164
154165#### Go
155166
156167```go
157- func numsSameConsecDiff(n int, k int) []int {
158- var ans [] int
159- var dfs func(n, k, t int)
160- dfs = func(n, k, t int) {
161- if n == 0 {
162- ans = append(ans, t )
168+ func numsSameConsecDiff(n int, k int) (ans []int) {
169+ bounary := int(math.Pow10(n - 1))
170+ var dfs func(int)
171+ dfs = func(x int) {
172+ if x >= bounary {
173+ ans = append(ans, x )
163174 return
164175 }
165- last := t % 10
166- if last+k <= 9 {
167- dfs(n-1, k, t *10+ last+ k)
176+ last := x % 10
177+ if last+k < 10 {
178+ dfs(x *10 + last + k)
168179 }
169- if last- k >= 0 && k ! = 0 {
170- dfs(n-1, k, t *10+ last- k)
180+ if k > 0 && last-k > = 0 {
181+ dfs(x *10 + last - k)
171182 }
172183 }
173-
174184 for i := 1; i < 10; i++ {
175- dfs(n-1, k, i)
185+ dfs(i)
176186 }
177- return ans
187+ return
178188}
179189```
180190
181191#### TypeScript
182192
183193``` ts
184194function numsSameConsecDiff(n : number , k : number ): number [] {
185- const = new Set < number >() ;
195+ const : number [] = [] ;
186196 const = 10 ** (n - 1 );
187- 188- const = (nums : number ) => {
189- if (nums >= boundary ) {
190- ans .add (nums );
197+ const = (x : number ) => {
198+ if (x >= boundary ) {
199+ ans .push (x );
191200 return ;
192201 }
193- 194- const num = nums % 10 ;
195- for ( const x of [ num + k , num - k ]) {
196- if ( 0 <= x && x < 10 ) {
197- dfs ( nums * 10 + x );
198- }
202+ const last = x % 10 ;
203+ if ( last + k < 10 ) {
204+ dfs ( x * 10 + last + k );
205+ }
206+ if ( k > 0 && last - k >= 0 ) {
207+ dfs ( x * 10 + last - k );
199208 }
200209 };
201- 202210 for (let i = 1 ; i < 10 ; i ++ ) {
203211 dfs (i );
204212 }
205- 206- return [... ans ];
213+ return ans ;
207214}
208215```
209216
210217#### JavaScript
211218
212219``` js
213- function numsSameConsecDiff (n , k ) {
214- const ans = new Set ();
220+ /**
221+ * @param {number} n
222+ * @param {number} k
223+ * @return {number[]}
224+ */
225+ var numsSameConsecDiff = function (n , k ) {
226+ const ans = [];
215227 const boundary = 10 ** (n - 1 );
216- 217- const dfs = nums => {
218- if (nums >= boundary) {
219- ans .add (nums);
228+ const dfs = x => {
229+ if (x >= boundary) {
230+ ans .push (x);
220231 return ;
221232 }
222- 223- const num = nums % 10 ;
224- for ( const x of [num + k, num - k]) {
225- if ( 0 <= x && x < 10 ) {
226- dfs (nums * 10 + x);
227- }
233+ const last = x % 10 ;
234+ if (last + k < 10 ) {
235+ dfs (x * 10 + last + k);
236+ }
237+ if (k > 0 && last - k >= 0 ) {
238+ dfs (x * 10 + last - k);
228239 }
229240 };
230- 231241 for (let i = 1 ; i < 10 ; i++ ) {
232242 dfs (i);
233243 }
234- 235- return [... ans];
236- }
244+ return ans;
245+ };
237246```
238247
239248<!-- tabs: end -->
0 commit comments