25th_Decode_Ways.md

Decode Ways

https://leetcode.com/problems/decode-ways

A message containing letters from A-Z can be encoded into numbers using the following mapping:

'A' -> "1" 'B' -> "2" ... 'Z' -> "26" To decode an encoded message, all the digits must be grouped then mapped back into letters using the reverse of the mapping above (there may be multiple ways). For example, "11106" can be mapped into:

"AAJF" with the grouping (1 1 10 6) "KJF" with the grouping (11 10 6) Note that the grouping (1 11 06) is invalid because "06" cannot be mapped into 'F' since "6" is different from "06".

Given a string s containing only digits, return the number of ways to decode it.

Approach

dp

    int numDecodings(string s) {
        if (s.front() == '0')
        { // Leading zero(s) has no way to decode the number
            return 0;
        }
        int n = s.length();
        std::vector<int> dp(n + 1, 0);
        dp[0] = 1;
        for (int i = 1; i <= n; i++)
        {
            // Single digit
            if (s[i - 1] != '0')
            {
                dp[i] = dp[i - 1];
            }

            // Double digits
            if (i > 1)
            {
                //int num = std::stoi(s.substr(i - 2, 2));
                int num = (s[i - 2] - '0') * 10 + (s[i - 1] - '0'); 
                if (num >= 10 && num <= 26)
                { // Valid number   
                    dp[i] += dp[i - 2];
                }
            }
        }
        return dp.back();
    }