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Decode Ways
A message containing letters from A-Z is being encoded to numbers using the following mapping:
‘A‘ -> 1‘B‘ -> 2...‘Z‘ -> 26Given 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.
思路：使用DP求解该题。num[i]记录s的前i个字符的解码方案数。若s[i-1]不为‘0‘，则可由num[i-1]通过s[i-1]达到num[i]；若s(i-2:i-1)（即s.substr(i-2,2)）小于等于‘26’，则可由num[i-2]通过s(i-2:i-1)达到num[i]。
1 class Solution { 2 public: 3 int numDecodings( string s ) { 4 if( s.empty() || s[0] == ‘0‘ ) { return 0; } 5 vector<int> num( s.length()+1, 0 ); 6 num[0] = 1; num[1] = 1; 7 for( int i = 2; i <= (int)s.length(); ++i ) { 8 if( s[i-1] != ‘0‘ ) { num[i] = num[i-1]; } 9 if( s[i-2] == ‘1‘ || ( s[i-2] == ‘2‘ && s[i-1] <= ‘6‘ ) ) { num[i] += num[i-2]; }10 }11 return num.back();12 }13 };
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