Leetcode 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.

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解题思路：

典型的dynamic programming

判断dp[i-1] , dp[i-2] 是否有效

recurrence formula: dp[i] += dp[i-1] if(s(i-1, i) is valid (1-9))  + dp[i-2] (if s(i-2, i)) is valid( 10-26))

base case: dp[0] =1, dp[1] = 1(s(0) is valid) or 0 (s(0) is not valid)

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Java code:

public class Solution {
    public int numDecodings(String s) {
        if(s == null || s.length() == 0 || s.equals("0")){
            return 0;
        }
        int[] dp = new int[s.length()+1];
        //base case: dp[0] dp[1]
        dp[0] = 1;
        if(isValid(s.substring(0,1))){
            dp[1] = 1;
        }else {
            dp[1] = 0;
        }
        for(int i = 2; i<= s.length(); i++){
            if(isValid(s.substring(i-1, i))){
                dp[i] += dp[i-1];
            }
            if(isValid(s.substring(i-2,i))){
                dp[i] += dp[i-2];
            }
        }
        return dp[s.length()];
    }
    
    public boolean isValid(String s){
        if(s.charAt(0) == '0') {
            return false;
        }
        int value = Integer.parseInt(s); // Integer.parseInt: translate string to int
        return value >=1 && value <= 26;
    }
}

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Reference:

1. http://www.programcreek.com/2014/06/leetcode-decode-ways-java/

2. http://www.cnblogs.com/springfor/p/3896162.html