A message containing letters from A-Z is being encoded to numbers using the following mapping way:
‘A‘ -> 1 ‘B‘ -> 2 ... ‘Z‘ -> 26
Beyond that, now the encoded string can also contain the character ‘*‘, which can be treated as one of the numbers from 1 to 9.
Given the encoded message containing digits and the character ‘*‘, return the total number of ways to decode it.
Also, since the answer may be very large, you should return the output mod 109 + 7.
Example 1:
Input: "*" Output: 9 Explanation: The encoded message can be decoded to the string: "A", "B", "C", "D", "E", "F", "G", "H", "I".
Example 2:
Input: "1*" Output: 9 + 9 = 18
Note:
- The length of the input string will fit in range [1, 105].
- The input string will only contain the character ‘*‘ and digits ‘0‘ - ‘9‘.
一条包含字母
A-Z 的消息通过以下的方式进行了编码：
‘A‘ -> 1 ‘B‘ -> 2 ... ‘Z‘ -> 26
除了上述的条件以外，现在加密字符串可以包含字符 ‘*‘了，字符‘*‘可以被当做1到9当中的任意一个数字。
给定一条包含数字和字符‘*‘的加密信息，请确定解码方法的总数。
同时，由于结果值可能会相当的大，所以你应当对109 + 7取模。（翻译者标注：此处取模主要是为了防止溢出）
示例 1 :
输入: "*" 输出: 9 解释: 加密的信息可以被解密为: "A", "B", "C", "D", "E", "F", "G", "H", "I".
示例 2 :
输入: "1*" 输出: 9 + 9 = 18（翻译者标注：这里1*可以分解为1,* 或者当做1*来处理，所以结果是9+9=18）
说明 :
- 输入的字符串长度范围是 [1, 105]。
- 输入的字符串只会包含字符 ‘*‘ 和 数字‘0‘ - ‘9‘。
Runtime: 224 ms
Memory Usage: 19.9 MB
1 class Solution {
2 func numDecodings(_ s: String) -> Int {
3 var e0:Int64 = 1
4 var e1:Int64 = 0
5 var e2:Int64 = 0
6 var f0:Int64 = 0
7 var M:Int64 = Int64(1e9 + 7)
8 for c in s.characters
9 {
10 if c == "*"
11 {
12 f0 = 9 * e0 + 9 * e1 + 6 * e2
13 e1 = e0
14 e2 = e0
15 }
16 else
17 {
18 f0 = e1
19 if c > "0"
20 {
21 f0 += e0
22 }
23 if c <= "6"
24 {
25 f0 += e2
26 }
27 e1 = c == "1" ? e0 : 0
28 e2 = c == "2" ? e0 : 0
29 }
30 e0 = f0 % M
31 }
32 return Int(e0)
33 }
34 }
340ms
1 /* Solution Space */
2
3 class Solution
4 {
5 /* Algorithm */
6 func numDecodings( _ string1: String ) -> Int
7 {
8 let allChar: UInt8 = "*".utf8.first!
9 let zeroChar: UInt8 = "0".utf8.first!
10 let values: [ Int ] = string1.utf8.map(
11 {
12 if $0 == allChar
13 {
14 return -1
15 }
16 else
17 {
18 return Int( $0 - zeroChar )
19 }
20 }
21 )
22 let mod: Int = 1000000007
23
24 /* Dynamic Results */
25 var dynamicResults: [ Int ] = [ Int ].init( repeating: -1, count: ( values.count + 1 ) )
26 dynamicResults[ values.count ] = 1
27 if values[ values.count - 1 ] == 0
28 {
29 dynamicResults[ values.count - 1 ] = 0
30 }
31 else if values[ values.count - 1 ] == -1
32 {
33 dynamicResults[ values.count - 1 ] = 9
34 }
35 else
36 {
37 dynamicResults[ values.count - 1 ] = 1
38 }
39
40 /* Counting Function - Recursive */
41 func countDecodingsR( _ startIndex: Int ) -> Int
42 {
43 if dynamicResults[ startIndex ] != -1
44 {
45 return dynamicResults[ startIndex ]
46 }
47 if values[ startIndex ] == 0
48 {
49 dynamicResults[ startIndex ] = 0
50 return dynamicResults[ startIndex ]
51 }
52 dynamicResults[ startIndex ] = 0
53 if values[ startIndex ] == -1
54 {
55 dynamicResults[ startIndex ] =
56 (
57 dynamicResults[ startIndex ]
58 + ( 9 * countDecodingsR( startIndex + 1 ) ) % mod
59 ) % mod
60 if values[ startIndex + 1 ] == -1
61 {
62 dynamicResults[ startIndex ] =
63 (
64 dynamicResults[ startIndex ]
65 + ( 15 * countDecodingsR( startIndex + 2 ) ) % mod
66 ) % mod
67 }
68 else
69 {
70 if 10 + values[ startIndex + 1 ] <= 26
71 {
72 dynamicResults[ startIndex ] =
73 (
74 dynamicResults[ startIndex ]
75 + countDecodingsR( startIndex + 2 )
76 ) % mod
77 }
78 if 20 + values[ startIndex + 1 ] <= 26
79 {
80
81 dynamicResults[ startIndex ] =
82 (
83 dynamicResults[ startIndex ]
84 + countDecodingsR( startIndex + 2 )
85 ) % mod
86 }
87 }
88 }
89 else
90 {
91 dynamicResults[ startIndex ] =
92 (
93 dynamicResults[ startIndex ]
94 + countDecodingsR( startIndex + 1 )
95 ) % mod
96 if values[ startIndex + 1 ] == -1
97 {
98 var value: Int = values[ startIndex ] * 10
99 for digit in ( 1 ... 9 )
100 {
101 if value + digit <= 26
102 {
103 dynamicResults[ startIndex ] =
104 (
105 dynamicResults[ startIndex ]
106 + countDecodingsR( startIndex + 2 )
107 ) % mod
108 }
109 else
110 {
111 break
112 }
113 }
114 }
115 else
116 {
117 let value: Int = values[ startIndex ] * 10 + values[ startIndex + 1 ]
118 if value <= 26
119 {
120 dynamicResults[ startIndex ] =
121 (
122 dynamicResults[ startIndex ]
123 + countDecodingsR( startIndex + 2 )
124 ) % mod
125 }
126 }
127 }
128 return dynamicResults[ startIndex ]
129 }
130
131 /* Counting Function - Iterative */
132 func countDecodingsI()
133 {
134 var currentIndex: Int = ( values.count - 2 )
135 while currentIndex >= 0
136 {
137 if values[ currentIndex ] == 0
138 {
139 dynamicResults[ currentIndex ] = 0
140 currentIndex -= 1
141 continue
142 }
143 dynamicResults[ currentIndex ] = 0
144 if values[ currentIndex ] == -1
145 {
146 dynamicResults[ currentIndex ] =
147 (
148 dynamicResults[ currentIndex ]
149 + ( 9 * dynamicResults[ currentIndex + 1 ] ) % mod
150 ) % mod
151 if values[ currentIndex + 1 ] == -1
152 {
153 dynamicResults[ currentIndex ] =
154 (
155 dynamicResults[ currentIndex ]
156 + ( 15 * dynamicResults[ currentIndex + 2 ] ) % mod
157 ) % mod
158 }
159 else
160 {
161 if 10 + values[ currentIndex + 1 ] <= 26
162 {
163 dynamicResults[ currentIndex ] =
164 (
165 dynamicResults[ currentIndex ]
166 + dynamicResults[ currentIndex + 2 ]
167 ) % mod
168 }
169
170 if 20 + values[ currentIndex + 1 ] <= 26
171 {
172 dynamicResults[ currentIndex ] =
173 (
174 dynamicResults[ currentIndex ]
175 + dynamicResults[ currentIndex + 2 ]
176 ) % mod
177 }
178 }
179 }
180 else
181 {
182 dynamicResults[ currentIndex ] =
183 (
184 dynamicResults[ currentIndex ]
185 + dynamicResults[ currentIndex + 1 ]
186 ) % mod
187 if values[ currentIndex + 1 ] == -1
188 {
189 var value: Int = values[ currentIndex ] * 10
190 for digit in ( 1 ... 9 )
191 {
192 if value + digit <= 26
193 {
194 dynamicResults[ currentIndex ] =
195 (
196 dynamicResults[ currentIndex ]
197 + dynamicResults[ currentIndex + 2 ]
198 ) % mod
199 }
200 else
201 {
202 break
203 }
204 }
205 }
206 else
207 {
208 let value: Int = values[ currentIndex ] * 10 + values[ currentIndex + 1 ]
209 if value <= 26
210 {
211 dynamicResults[ currentIndex ] =
212 (
213 dynamicResults[ currentIndex ]
214 + dynamicResults[ currentIndex + 2 ]
215 ) % mod
216 }
217 }
218 }
219 currentIndex -= 1
220 }
221 }
222 countDecodingsI()
223 return dynamicResults[ 0 ]
224 }
225 }
780ms
1 class Solution {
2 func numDecodings(_ s: String) -> Int {
3 guard s.count > 0 else { return 0 }
4 let s = Array(s).map{ "\($0)" }
5 var dp = Array(repeating: 0, count: s.count)
6 dp[0] = s[0] == "*" ? 9 : s[0] == "0" ? 0 : 1
7 for i in 1..<s.count {
8 var r = (i > 1) ? dp[i-2] : 1
9 if s[i] == "*" {
10 dp[i] = dp[i] &+ dp[i-1] * 9
11 if s[i-1] == "1" { dp[i] = dp[i] &+ r * 9 }
12 if s[i-1] == "2" { dp[i] = dp[i] &+ r * 6 }
13 if s[i-1] == "*" { dp[i] = dp[i] &+ r * 15 }
14 } else if s[i] == "0" {
15 r = (i > 1) ? dp[i-2] : 1
16 if s[i-1] == "1" || s[i-1] == "2" { dp[i] += r * 1 }
17 if s[i-1] == "*" { dp[i] += r * 2 }
18 } else {
19 dp[i] = dp[i] &+ dp[i-1]
20 if s[i-1] == "1" || (s[i-1] == "2" && Int(s[i])! < 7) { dp[i] = dp[i] &+ ((i > 1) ? dp[i-2] : 1) }
21 if s[i-1] == "*" && Int(s[i])! < 7 { dp[i] = dp[i] &+ r * 2 }
22 if s[i-1] == "*" && Int(s[i])! >= 7 { dp[i] = dp[i] &+ r * 1 }
23 }
24 dp[i] %= 1000000007
25 }
26 return dp.last ?? 0
27 }
28 }
原文地址：https://www.cnblogs.com/strengthen/p/10479517.html
时间： 2024-11-02 19:26:12