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# 91     Decode Ways

## 91. [Decode Ways](https://leetcode.com/problems/decode-ways/description/)

## 1. Question

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. Implementation

**(1) DP**

```java
class Solution {
    public int numDecodings(String s) {
        if (s == null || s.length() == 0 || s.charAt(0) == '0') {
            return 0;
        }

        int[] dp = new int[s.length() + 1];
        dp[0] = 1;
        dp[1] = 1;

        for (int i = 2; i <= s.length(); i++) {
            int oneDigit = s.charAt(i - 1) - '0';
            int twoDigits = (s.charAt(i - 2) - '0') * 10 + oneDigit;

            if (oneDigit >= 1 && oneDigit <= 9) {
                dp[i] += dp[i - 1];
            }

            if (twoDigits >= 10 && twoDigits <= 26) {
                dp[i] += dp[i - 2];
            }
        }
        return dp[s.length()];
    }
}
```

## 3. Time & Space Complexity

时间复杂度O(n), 空间复杂度O(n)


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