Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit 51a32cf

Browse files
feat: add solutions to lcp problem: No.25 (doocs#3649)
1 parent 85923b4 commit 51a32cf

File tree

6 files changed

+265
-0
lines changed

6 files changed

+265
-0
lines changed

‎lcp/LCP 25. 古董键盘/README.md‎

Lines changed: 155 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -42,4 +42,159 @@ edit_url: https://github.com/doocs/leetcode/edit/main/lcp/LCP%2025.%20%E5%8F%A4%
4242

4343
<!-- solution:start -->
4444

45+
### 方法一:动态规划
46+
47+
我们定义 $f[i][j]$ 表示按了 $i$ 次按键,且使用了前 $j$ 个字母的方案数。初始时 $f[0]$ 全部为 1ドル,ドル表示没有按键时只有一种方案,其余 $f[i][j] = 0$。
48+
49+
对于 $f[i][j],ドル我们考虑其转移方式。我们可以枚举第 $j$ 个字母一共使用了多少次,设为 $h,ドル其中 0ドル \leq h \leq \min(i, k),ドル那么我们可以从 $f[i - h][j - 1]$ 转移过来,且第 $j$ 个字母可以在 $i$ 次按键中使用 $h$ 次,方案数为 $\binom{i}{h}$。即:
50+
51+
$$
52+
f[i][j] = \sum_{h = 0}^{\min(i, k)} f[i - h][j - 1] \cdot \binom{i}{h}
53+
$$
54+
55+
最终答案即为 $f[n][26]$。
56+
57+
时间复杂度 $O(n \times k \times |\Sigma|),ドル空间复杂度 $O(n \times |\Sigma|)$。其中 $|\Sigma|$ 表示字母表大小。
58+
59+
<!-- tabs:start -->
60+
61+
#### Python3
62+
63+
```python
64+
class Solution:
65+
def keyboard(self, k: int, n: int) -> int:
66+
f = [[0] * 27 for _ in range(n + 1)]
67+
f[0] = [1] * 27
68+
mod = 10**9 + 7
69+
for i in range(1, n + 1):
70+
for j in range(1, 27):
71+
for h in range(min(k, i) + 1):
72+
f[i][j] += f[i - h][j - 1] * comb(i, h)
73+
f[i][j] %= mod
74+
return f[n][26]
75+
```
76+
77+
#### Java
78+
79+
```java
80+
class Solution {
81+
public int keyboard(int k, int n) {
82+
int[][] c = new int[n + 1][k + 1];
83+
for (int i = 0; i <= n; ++i) {
84+
c[i][0] = 1;
85+
}
86+
final int mod = (int) 1e9 + 7;
87+
for (int i = 1; i <= n; ++i) {
88+
for (int j = 1; j <= k; ++j) {
89+
c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
90+
}
91+
}
92+
int[][] f = new int[n + 1][27];
93+
Arrays.fill(f[0], 1);
94+
for (int i = 1; i <= n; ++i) {
95+
for (int j = 1; j < 27; ++j) {
96+
for (int h = 0; h <= Math.min(i, k); ++h) {
97+
f[i][j] = (f[i][j] + (int) ((long) f[i - h][j - 1] * c[i][h] % mod)) % mod;
98+
}
99+
}
100+
}
101+
return f[n][26];
102+
}
103+
}
104+
```
105+
106+
#### C++
107+
108+
```cpp
109+
class Solution {
110+
public:
111+
int keyboard(int k, int n) {
112+
int f[n + 1][27];
113+
memset(f, 0, sizeof(f));
114+
for (int j = 0; j < 27; ++j) {
115+
f[0][j] = 1;
116+
}
117+
int c[n + 1][k + 1];
118+
memset(c, 0, sizeof(c));
119+
c[0][0] = 1;
120+
const int mod = 1e9 + 7;
121+
for (int i = 1; i <= n; ++i) {
122+
c[i][0] = 1;
123+
for (int j = 1; j <= k; ++j) {
124+
c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
125+
}
126+
}
127+
for (int i = 1; i <= n; ++i) {
128+
for (int j = 1; j < 27; ++j) {
129+
for (int h = 0; h <= min(i, k); ++h) {
130+
f[i][j] = (f[i][j] + 1LL * f[i - h][j - 1] * c[i][h] % mod) % mod;
131+
}
132+
}
133+
}
134+
return f[n][26];
135+
}
136+
};
137+
```
138+
139+
#### Go
140+
141+
```go
142+
func keyboard(k int, n int) int {
143+
c := make([][]int, n+1)
144+
for i := range c {
145+
c[i] = make([]int, k+1)
146+
c[i][0] = 1
147+
}
148+
const mod int = 1e9 + 7
149+
for i := 1; i <= n; i++ {
150+
for j := 1; j <= k; j++ {
151+
c[i][j] = (c[i-1][j-1] + c[i-1][j]) % mod
152+
}
153+
}
154+
f := make([][27]int, n+1)
155+
for j := range f[0] {
156+
f[0][j] = 1
157+
}
158+
for i := 1; i <= n; i++ {
159+
for j := 1; j < 27; j++ {
160+
for h := 0; h <= min(i, k); h++ {
161+
f[i][j] = (f[i][j] + f[i-h][j-1]*c[i][h]%mod) % mod
162+
}
163+
}
164+
}
165+
return f[n][26]
166+
}
167+
```
168+
169+
#### TypeScript
170+
171+
```ts
172+
function keyboard(k: number, n: number): number {
173+
const c: number[][] = Array.from({ length: n + 1 }, () => Array(k + 1).fill(0));
174+
c[0][0] = 1;
175+
const mod = 10 ** 9 + 7;
176+
for (let i = 1; i <= n; ++i) {
177+
c[i][0] = 1;
178+
for (let j = 1; j <= k; ++j) {
179+
c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
180+
}
181+
}
182+
const f: number[][] = Array.from({ length: n + 1 }, () => Array(27).fill(0));
183+
f[0].fill(1);
184+
for (let i = 1; i <= n; ++i) {
185+
for (let j = 1; j < 27; ++j) {
186+
for (let h = 0; h <= Math.min(i, k); ++h) {
187+
const v = Number((BigInt(f[i - h][j - 1]) * BigInt(c[i][h])) % BigInt(mod));
188+
f[i][j] = (f[i][j] + v) % mod;
189+
}
190+
}
191+
}
192+
return f[n][26];
193+
}
194+
```
195+
196+
<!--- tabs:end -->
197+
198+
<!-- solution:end -->
199+
45200
<!-- problem:end -->
Lines changed: 28 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,28 @@
1+
class Solution {
2+
public:
3+
int keyboard(int k, int n) {
4+
int f[n + 1][27];
5+
memset(f, 0, sizeof(f));
6+
for (int j = 0; j < 27; ++j) {
7+
f[0][j] = 1;
8+
}
9+
int c[n + 1][k + 1];
10+
memset(c, 0, sizeof(c));
11+
c[0][0] = 1;
12+
const int mod = 1e9 + 7;
13+
for (int i = 1; i <= n; ++i) {
14+
c[i][0] = 1;
15+
for (int j = 1; j <= k; ++j) {
16+
c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
17+
}
18+
}
19+
for (int i = 1; i <= n; ++i) {
20+
for (int j = 1; j < 27; ++j) {
21+
for (int h = 0; h <= min(i, k); ++h) {
22+
f[i][j] = (f[i][j] + 1LL * f[i - h][j - 1] * c[i][h] % mod) % mod;
23+
}
24+
}
25+
}
26+
return f[n][26];
27+
}
28+
};

‎lcp/LCP 25. 古董键盘/Solution.go‎

Lines changed: 25 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,25 @@
1+
func keyboard(k int, n int) int {
2+
c := make([][]int, n+1)
3+
for i := range c {
4+
c[i] = make([]int, k+1)
5+
c[i][0] = 1
6+
}
7+
const mod int = 1e9 + 7
8+
for i := 1; i <= n; i++ {
9+
for j := 1; j <= k; j++ {
10+
c[i][j] = (c[i-1][j-1] + c[i-1][j]) % mod
11+
}
12+
}
13+
f := make([][27]int, n+1)
14+
for j := range f[0] {
15+
f[0][j] = 1
16+
}
17+
for i := 1; i <= n; i++ {
18+
for j := 1; j < 27; j++ {
19+
for h := 0; h <= min(i, k); h++ {
20+
f[i][j] = (f[i][j] + f[i-h][j-1]*c[i][h]%mod) % mod
21+
}
22+
}
23+
}
24+
return f[n][26]
25+
}
Lines changed: 24 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,24 @@
1+
class Solution {
2+
public int keyboard(int k, int n) {
3+
int[][] c = new int[n + 1][k + 1];
4+
for (int i = 0; i <= n; ++i) {
5+
c[i][0] = 1;
6+
}
7+
final int mod = (int) 1e9 + 7;
8+
for (int i = 1; i <= n; ++i) {
9+
for (int j = 1; j <= k; ++j) {
10+
c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
11+
}
12+
}
13+
int[][] f = new int[n + 1][27];
14+
Arrays.fill(f[0], 1);
15+
for (int i = 1; i <= n; ++i) {
16+
for (int j = 1; j < 27; ++j) {
17+
for (int h = 0; h <= Math.min(i, k); ++h) {
18+
f[i][j] = (f[i][j] + (int) ((long) f[i - h][j - 1] * c[i][h] % mod)) % mod;
19+
}
20+
}
21+
}
22+
return f[n][26];
23+
}
24+
}

‎lcp/LCP 25. 古董键盘/Solution.py‎

Lines changed: 11 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,11 @@
1+
class Solution:
2+
def keyboard(self, k: int, n: int) -> int:
3+
f = [[0] * 27 for _ in range(n + 1)]
4+
f[0] = [1] * 27
5+
mod = 10**9 + 7
6+
for i in range(1, n + 1):
7+
for j in range(1, 27):
8+
for h in range(min(k, i) + 1):
9+
f[i][j] += f[i - h][j - 1] * comb(i, h)
10+
f[i][j] %= mod
11+
return f[n][26]

‎lcp/LCP 25. 古董键盘/Solution.ts‎

Lines changed: 22 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,22 @@
1+
function keyboard(k: number, n: number): number {
2+
const c: number[][] = Array.from({ length: n + 1 }, () => Array(k + 1).fill(0));
3+
c[0][0] = 1;
4+
const mod = 10 ** 9 + 7;
5+
for (let i = 1; i <= n; ++i) {
6+
c[i][0] = 1;
7+
for (let j = 1; j <= k; ++j) {
8+
c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
9+
}
10+
}
11+
const f: number[][] = Array.from({ length: n + 1 }, () => Array(27).fill(0));
12+
f[0].fill(1);
13+
for (let i = 1; i <= n; ++i) {
14+
for (let j = 1; j < 27; ++j) {
15+
for (let h = 0; h <= Math.min(i, k); ++h) {
16+
const v = Number((BigInt(f[i - h][j - 1]) * BigInt(c[i][h])) % BigInt(mod));
17+
f[i][j] = (f[i][j] + v) % mod;
18+
}
19+
}
20+
}
21+
return f[n][26];
22+
}

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /