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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 }