0091. Decode Ways

# 91. Decode Ways#

## 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).
``````

## 题目大意 #

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

## 解题思路 #

• 给出一个数字字符串，题目要求把数字映射成 26 个字母，映射以后问有多少种可能的翻译方法。
• 这题思路也是 DP。`dp[n]` 代表翻译长度为 n 个字符的字符串的方法总数。由于题目中的数字可能出现 0，0 不能翻译成任何字母，所以出现 0 要跳过。dp[0] 代表空字符串，只有一种翻译方法，`dp[0] = 1`。dp[1] 需要考虑原字符串是否是 0 开头的，如果是 0 开头的，`dp[1] = 0`，如果不是 0 开头的，`dp[1] = 1`。状态转移方程是 `dp[i] += dp[i-1] (当 1 ≤ s[i-1 : i] ≤ 9)；dp[i] += dp[i-2] (当 10 ≤ s[i-2 : i] ≤ 26)`。最终结果是 `dp[n]`

## 代码 #

``````
package leetcode

func numDecodings(s string) int {
n := len(s)
dp := make([]int, n+1)
dp[0] = 1
for i := 1; i <= n; i++ {
if s[i-1] != '0' {
dp[i] += dp[i-1]
}
if i > 1 && s[i-2] != '0' && (s[i-2]-'0')*10+(s[i-1]-'0') <= 26 {
dp[i] += dp[i-2]
}
}
return dp[n]
}

``````

Nov 25, 2022