leetcode题解:91.Decode Ways(解码方式数量)

题目描述：

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

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

Given 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).

• 正向解法：

public int numDecodings(String s) {
        int n = s.length();
        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = s.charAt(0) == '0' ? 0 : 1;
        for(int i = 2; i <= n; i++){
            if(s.charAt(i - 1) != '0'){
                dp[i] += dp[i - 1];
            }
            if(s.charAt(i - 2) == '0'){
                continue;
            }
        
            if(s.charAt(i - 2) == '1' || s.charAt(i - 2) == '2' && s.charAt(i - 1) <= '6'){
                dp[i] += dp[i - 2];
            }
        }
        return dp[n];
    }

• 逆向解法

 public int numDecodings(String s) {
        int n = s.length();
        int[] dp = new int[n + 1];
        dp[n] = 1;
        dp[n - 1] = s.charAt(n - 1) == '0' ? 0 : 1;
        for(int i = n - 2; i >= 0; i--){
            if(s.charAt(i) == '1' || s.charAt(i) == '2' && s.charAt(i + 1) <= '6'){
                dp[i] += dp[i + 2];
            }
            if(s.charAt(i) == '0')
                continue;
            else
                dp[i] += dp[i + 1];
        }
        return dp[0];
    }