### leetcode Question 26: Decode Ways

Decode Ways

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.

Analysis:
The key to this problem is : num(current) = num(current-1) + num(current-2).
Be careful with the conditions of above equation:
if the current char =='0'
if the current char and previous char >26
if the previous char =='0'

### Updated 201309:

This can be think as a simple DP problem, res[i]= res[i-1] if s[i] is valid +  res[i-2] if s[i-1:i] is valid.

### Code (Updated 201309):

class Solution {
public:
bool valid(string s){
if (s.size()==0){return false;}
if (s[0]=='0'){return false;}
if (s.size()==2){
if (s[0]>'2' || (s[0]=='2'&& s[1]>'6')){return false;}
}
return true;
}

int numDecodings(string s) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
if (s.empty()){return 0;}
vector<int> res(s.size(),0);
if (s[0]!='0'){res[0]=1;} // set res[0]
if (s.size()==1){return res[0];}
if (valid(s.substr(0,2))){res[1]++;} //set res[1]
if (s[0]!='0' && s[1]!='0'){res[1]++;} //set res[1]

//DP
for (int i=2;i<s.size();i++){
if (s[i]!='0'){res[i]+=res[i-1];}
if (valid(s.substr(i-1,2))){
res[i]+=res[i-2];
}
}

return res[s.size()-1];
}

};


The source code:

class Solution {
public:
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;}

int t1=1; //num from 0 to current-1
int t2=1; //num from 0 to current-2
for (int i=1; i<s.size();i++){
int tc=0; //num from 0 to current
if ((s[i]=='0')){
int d1 = (s[i-1]-'0');
if( (d1<3)&&(d1>0) ){tc=t2;}
}
if (s[i]!='0'){
if (s[i-1]=='0'){tc = t1;}
else{
int d2 = (s[i-1]-'0')*10+(s[i]-'0');
if (d2<=26) {tc = t1+t2;}
else{tc =t1;}
}
}
t2=t1;
t1=tc;
}
return t1;
}
};