[LeetCode] 639. Decode Ways II 解码方法 II

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, 105].
2. The input string will only contain the character '*' and digits '0' - '9'.

91. Decode Ways  的拓展，这次字符串里面可能含有'*'， 它可以1~9中的任何一个，求总的解码方法数。

解法：还是DP，主要是如何处理'*'。

Java:

    public int numDecodings(String s) {
        /* initial conditions */
        long[] dp = new long[s.length()+1];
        dp[0] = 1;
        if(s.charAt(0) == '0'){
            return 0;
        }
        dp[1] = (s.charAt(0) == '*') ? 9 : 1;

        /* bottom up method */
        for(int i = 2; i <= s.length(); i++){
            char first = s.charAt(i-2);
            char second = s.charAt(i-1);

            // For dp[i-1]
            if(second == '*'){
                dp[i] += 9*dp[i-1];
            }else if(second > '0'){
                dp[i] += dp[i-1];
            }

            // For dp[i-2]
            if(first == '*'){
                if(second == '*'){
                    dp[i] += 15*dp[i-2];
                }else if(second <= '6'){
                    dp[i] += 2*dp[i-2];
                }else{
                    dp[i] += dp[i-2];
                }
            }else if(first == '1' || first == '2'){
                if(second == '*'){
                    if(first == '1'){
                       dp[i] += 9*dp[i-2];
                    }else{ // first == '2'
                       dp[i] += 6*dp[i-2];
                    }
                }else if( ((first-'0')*10 + (second-'0')) <= 26 ){
                    dp[i] += dp[i-2];
                }
            }

            dp[i] %= 1000000007;
        }
        /* Return */
        return (int)dp[s.length()];
    }　

Python:

class Solution(object):
    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        if len(s) == 0 or s[0] == '0':
            return 0

        dp = [0] * (len(s) + 1)
        dp[0] = 1
        dp[1] = 9 if s[0] == '*' else 1

        for i in xrange(2, len(dp)):
            first = s[i-2]
            second = s[i-1]
            # for dp[i-1]
            if second == '*':
                dp[i] = dp[i-1] * 9
            elif second != '0':
                dp[i] = dp[i-1]

            # for dp[i-2]
            if first == '*':
                if second == '*':
                    dp[i] += 15 * dp[i-2]
                elif second <= '6':
                    dp[i] += 2 * dp[i-2]
                else:
                    dp[i] += dp[i-2]
            elif first == '1' or first == '2':
                if second == '*':
                    if first == '1':
                        dp[i] += 9 * dp[i-2]
                    else:
                        dp[i] += 6 * dp[i-2]
                elif first == '1' or (first == '2' and second <= '6'):
                    dp[i] += dp[i-2]   

            dp[i] %= 1000000007         

        return dp[-1]   　　

Python:

class Solution(object):
    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        M, W = 1000000007, 3
        dp = [0] * W
        dp[0] = 1
        dp[1] = 9 if s[0] == '*' else dp[0] if s[0] != '0' else 0
        for i in xrange(1, len(s)):
            if s[i] == '*':
                dp[(i + 1) % W] = 9 * dp[i % W]
                if s[i - 1] == '1':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + 9 * dp[(i - 1) % W]) % M
                elif s[i - 1] == '2':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + 6 * dp[(i - 1) % W]) % M
                elif s[i - 1] == '*':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + 15 * dp[(i - 1) % W]) % M
            else:
                dp[(i + 1) % W] = dp[i % W] if s[i] != '0' else 0
                if s[i - 1] == '1':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + dp[(i - 1) % W]) % M
                elif s[i - 1] == '2' and s[i] <= '6':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + dp[(i - 1) % W]) % M
                elif s[i - 1] == '*':
                    dp[(i + 1) % W] = (dp[(i + 1) % W] + (2 if s[i] <= '6' else 1) * dp[(i - 1) % W]) % M
        return dp[len(s) % W]　

C++：

class Solution {
public:
    int numDecodings(string s) {
        int n = s.size(), M = 1e9 + 7;
        vector<long> dp(n + 1, 0);
        dp[0] = 1;
        if (s[0] == '0') return 0;
        dp[1] = (s[0] == '*') ? 9 : 1;
        for (int i = 2; i <= n; ++i) {
            if (s[i - 1] == '0') {
                if (s[i - 2] == '1' || s[i - 2] == '2') {
                    dp[i] += dp[i - 2];
                } else if (s[i - 2] == '*') {
                    dp[i] += 2 * dp[i - 2];
                } else {
                    return 0;
                }
            } else if (s[i - 1] >= '1' && s[i - 1] <= '9') {
                dp[i] += dp[i - 1];
                if (s[i - 2] == '1' || (s[i - 2] == '2' && s[i - 1] <= '6')) {
                    dp[i] += dp[i - 2];
                } else if (s[i - 2] == '*') {
                    dp[i] += (s[i - 1] <= '6') ? (2 * dp[i - 2]) : dp[i - 2];
                }
            } else { // s[i - 1] == '*'
                dp[i] += 9 * dp[i - 1];
                if (s[i - 2] == '1') dp[i] += 9 * dp[i - 2];
                else if (s[i - 2] == '2') dp[i] += 6 * dp[i - 2];
                else if (s[i - 2] == '*') dp[i] += 15 * dp[i - 2];
            }
            dp[i] %= M;
        }
        return dp[n];
    }
};　　

C++:

class Solution {
public:
    int numDecodings(string s) {
        long e0 = 1, e1 = 0, e2 = 0, f0, f1, f2, M = 1e9 + 7;
        for (char c : s) {
            if (c == '*') {
                f0 = 9 * e0 + 9 * e1 + 6 * e2;
                f1 = e0;
                f2 = e0;
            } else {
                f0 = (c > '0') * e0 + e1 + (c <= '6') * e2;
                f1 = (c == '1') * e0;
                f2 = (c == '2') * e0;
            }
            e0 = f0 % M;
            e1 = f1;
            e2 = f2;
        }
        return e0;
    }
};

　　

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