91 Decode Ways

91. Decode Ways

1. Question

A message containing letters fromA-Zis 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

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)