Decode Ways

Q:

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

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

Given an encoded message containing digits, determine the total number of ways to decode it.

For example,
Given encoded message "12", it could be decoded as "AB" (1 2) or "L" (12).

The number of ways decoding "12" is 2.

A: 一维动态规划

    int numDecodings(string s) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(s.empty()||s[0]=='0')
            return 0;
        vector<int> dp(s.size()+1);
        
        dp[0] = 1;
        dp[1] = 1;
        for(int i=2;i<=s.size();i++)
        {
            if(s[i-1]=='0')
            {
                if(s[i-2]<='2'&&s[i-2]>'0')
                    dp[i] = dp[i-2];   
                else
                    return 0;
            }else
            {                
                if(s[i-2]=='0'||s[i-2]>'2'||(s[i-2]=='2'&&s[i-1]>'6'))
                    dp[i] = dp[i-1];
                else
                    dp[i] = dp[i-1]+dp[i-2];            
            }

        }
        
        return dp[s.size()];
    }

　　更简洁的作法：

    int numDecodings(string s) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(s.empty())
            return 0;
        int n = s.size();
        vector<int> dp(n+1);
        
        dp[0] = 1;
        for(int i=1;i<=n;i++)
        {
            int c1=0,c2=0; //分别考虑dp[i-1]和dp[i-2]
            if(s[i-1]!='0')
                c1 = dp[i-1];
            if(i>=2&&(s[i-2]=='1'||s[i-2]=='2'&&s[i-1]<='6'))
                c2 = dp[i-2];
            dp[i] = c1+c2;
        }
        
        return dp[n];
        
    }