LeetCode-91-Decode Ways

算法描述：

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

'A' -> 1
'B' -> 2
...
'Z' -> 26

Given a non-empty string containing only digits, determine the total number of ways to decode it.

Example 1:

Input: "12"
Output: 2
Explanation: It could be decoded as "AB" (1 2) or "L" (12).

Example 2:

Input: "226"
Output: 3
Explanation: It could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).

解题思路：动态规划，一个字符的情况下，只有一种解码方式。两个字符情况下，如果小于等于26，则有另外一种解码方式。递推公式很重要。

        vector<int> dp(s.size()+1,0);
        dp[0] =1;
        dp[1] = s[0]=='0'? 0: 1;
        for(int i=2; i <= s.size(); i++){
            int first = stoi(s.substr(i-1,1));
            int second = stoi(s.substr(i-2,2));
            if(first >= 1 && first <= 9){
                dp[i] += dp[i-1];
            }
            if(second >= 10 && second <= 26){
                dp[i] += dp[i-2];
            }
        }
        return dp[s.size()];
    }