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.
Solution:
Use Dynamic Programming method to solve the problem, for positition i, we can get that
if substring(i-1,i) is a valid string, the number of ways decoding from the beginning to position i equals the number of ways decoding from the beginning to position i-1;
if substring(i-2,i) is a valid string, the number of ways decoding from the beginning to position i equals the number of ways decoding from the beginning to position i-2;
1 public class Solution { 2 public int numDecodings(String s) { 3 if(s==null||s.length()==0) 4 return 0; 5 int[] dp=new int[s.length()+1]; 6 dp[0]=1; 7 if(isValid(s.substring(0,1))){ 8 dp[1]=1; 9 }else{ 10 dp[1]=0; 11 } 12 for(int i=2;i<=s.length();++i){ 13 if(isValid(s.substring(i-1, i))) 14 dp[i]=dp[i-1]; 15 if(isValid(s.substring(i-2, i))){ 16 dp[i]+=dp[i-2]; 17 } 18 19 } 20 return dp[s.length()]; 21 } 22 private boolean isValid(String s) { 23 // TODO Auto-generated method stub 24 int N=s.length(); 25 if(N==1){ 26 return(s.charAt(0)>=‘1‘&&s.charAt(0)<=‘9‘); 27 }else if(N==2){ 28 return((s.charAt(0)==‘1‘&&s.charAt(1)>=‘0‘&&s.charAt(1)<=‘9‘)|| 29 (s.charAt(0)==‘2‘&&s.charAt(1)>=‘0‘&&s.charAt(1)<=‘6‘)); 30 } 31 return false; 32 } 33 }
原文：http://www.cnblogs.com/Phoebe815/p/4261399.html