# Decode Ways II(dp)

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:**

1. The length of the input string will fit in range \[1, 10

   5

   ].
2. The input string will only contain the character '\*' and digits '0' - '9'.

分析

dp，前面一步（一个字母）来或者前面2步（2个字母合并）来。

数字判断\*和digit判断

```
class Solution:
    def decodeWay(self, s1, s2):
        ret = 0
        if s1 == '-':
            if s2.isdigit() and 1 <=int(s2) <=9:
                ret = 1
            elif s2 == '*':
                ret = 9
        elif s1.isdigit() and 0 < int(s1) <= 2:
            if s2.isdigit() and int(s1+s2) <= 26:
                ret = 1
            elif s2 == '*':
                ret = 9 if int(s1) == 1 else 6
        elif s1 == '*':
            if s2.isdigit():
               ret = 2 if  0<= int(s2) <=6 else 1
            elif s2 == '*':
                ret = 15
        return ret

    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        if not s or len(s) == 0:
            return 0
        dp1 = dp2 = 1
        MOD = 10 ** 9 + 7
        lc = '-'
        ret = 0

        for i,c in enumerate(s):
            if i == 0:
                ret = self.decodeWay('-', c)
            else:
                ret = (self.decodeWay('-', c)*dp1 + dp2*self.decodeWay(lc,c))% MOD
            lc = c
            dp1, dp2 = ret,dp1
        return ret
```

dp

```
class Solution:
    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        if not s or s[0] == '0':
            return 0
        n = len(s)

        p = 9 if s[0] == '*' else 1#0 if s[0]=='0' else 1

        pp = 1
        cur = 0
        M = 10**9 + 7

        for i in range(1,n):
            if s[i] == '*':
                cur = p*9# 因为不用数组用cur，所以每次赋新值，不是cur+=
                if s[i-1] == '*':
                    cur = (cur+pp*15)%M
                else:
                    num = int(s[i-1])
                    if num <=2 and num >0:
                       cur =(cur+pp * 9)%M if num == 1 else (cur+pp * 6)%M
            else:
                num1 = int(s[i])
                cur = p if num1 > 0 else 0#每次cur一定要先赋值

                if s[i-1] == '*':
                    cur= (cur+pp*2)%M if num1 <=6 else (cur+pp)%M
                else:
                    num2 = int(s[i-1:i+1])
                    if num2 < 27 and num2 >9:
                       cur = (cur+pp)%M
            p,pp = cur,p


        return p#p=cur，用cur n=1不行
```


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