91. Decode Ways

91. Decode Ways

1. 题目

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).

2. 思路

本题求解的是在给定的条件下(既前文中A->1，B->2)给到一个数字，比如226 有多少种解释方法。这题可以使用动态规划的方法来求解。假设dp[i]为以i为结尾的字符串解码方式数量的总和。那么dp[i]的递推规则是：

1. 如果s[i-1] != "0",则dp[i] += dp[ i - 1 ] ，代表了一次解一位，则剩下n-1个字符需要解
2. 如果一次解2位，则要求是s[i-2:i] <"27" and s[i-2:i] >'09'，dp[i] += dp[i-2]

3.实现

class Solution(object):
    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        if s == '':
            return 0
        dp = [0 for x in range(len(s)+1)]
        dp[0] = 1
        for i in range(1, len(s)+1):
            if s[i-1] != "0":
                dp[i] += dp[i-1]
            if i != 1 and s[i-2:i] < "27" and s[i-2:i] > "09":
                dp[i] += dp[i-2]
        return dp[-1]