Decode Ways问题及解法

问题描述：

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

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

Given an encoded message containing digits, determine the total number of ways to decode it.

示例：
Given encoded message "12", it could be decoded as "AB" (1 2) or "L" (12).

The number of ways decoding "12" is 2.

问题分析：

根据题意可知，这是一道动态规划题。dp是状态转移数组，对于s[i - 1] 和 s[i]的不同取值，dp的对应转换过程也不相同。

过程详见代码：

class Solution {
public:
    int numDecodings(string s) {
        int len = s.length();
        if (!len || s[0] == '0') return 0;
		vector dp(len + 1, 0);
		dp[1] = 1;
        dp[0] = 1;
		for (int i = 1; i < len; i++)
		{
            int t = (s[i - 1] - '0') * 10 + s[i] - '0';
            if(!t || t > 26 && t % 10 == 0) return 0;
            else if(t < 10 || t > 26) dp[i + 1] = dp[i];
            else if(t == 10 || t == 20) dp[i + 1] = dp[i - 1];
            else dp[i + 1] = dp[i] + dp[i - 1];
		}
		return dp[len];
    }
};