[LintCode] Decode Ways 解码方法

A message containing letters from A-Z is being encoded to numbers using the following mapping:

'A' -> 1
'B' -> 2
...
'Z' -> 26
Given an encoded message containing digits, determine the total number of ways to decode it.

Example
Given encoded message 12, it could be decoded as AB (1 2) or L (12).
The number of ways decoding 12 is 2.

LeetCode上的原题，请参见我之前的博客Decode Ways。

解法一：

class Solution {
public:
    /**
     * @param s a string,  encoded message
     * @return an integer, the number of ways decoding
     */
    int numDecodings(string& s) {
        if (s.empty()) return ;
        int n = s.size();
        vector<int> dp(n + , );
        for (int i = ; i < n + ; ++i) {
            if (s[i - ] == '') dp[i] = ;
            else dp[i] = dp[i - ];
            if (i >=  && (s[i - ] == '' || (s[i - ] == '' && s[i - ] <= ''))) {
                dp[i] += dp[i -];
            }
        }
        return dp.back();
    }
};

解法二：

class Solution {
public:
    /**
     * @param s a string,  encoded message
     * @return an integer, the number of ways decoding
     */
    int numDecodings(string& s) {
        if (s.empty()) return ;
        vector<int> dp(s.size() + , );
        dp[] = ;
        for (int i = ; i < dp.size(); ++i) {
            if (s[i - ] >= '' && s[i - ] <= '') dp[i] += dp[i - ];
            if (i >=  && s.substr(i - , ) <= "" && s.substr(i - , ) >= "") {
                dp[i] += dp[i - ];
            }
        }
        return dp.back();
    }
};

解法三：

class Solution {
public:
    /**
     * @param s a string,  encoded message
     * @return an integer, the number of ways decoding
     */
    int numDecodings(string& s) {
        if (s.empty() || s.front() == '') return ;
        int c1 = , c2 = ;
        for (int i = ; i < s.size(); ++i) {
            if (s[i] == '') c1 = ;
            if (s[i - ] == '' || (s[i - ] == '' && s[i] <= '')) {
                c1 = c1 + c2;
                c2 = c1 - c2;
            } else {
                c2 = c1;
            }
        }
        return c1;
    }
};