# Decode Ways

This is a dynamic programing problem. The cases that should be handled including:

1. '0' < str[i] <= '9'. In this case, this char can decode one letter independently.
2. i > 0, str[i - 1] == '1'. In this case, str[i - 1] along with str[i] can represent 10 to 19, which is valid encoding.
3. i > 0, str[i - 1] == '2', '0' <= str[i] <= '6'. In this case, str[i - 1] along with str[i] can represent 20 to 26, which is valid encoding.

Empty string should be handle separately.

public class DecodeWays {
public int numDecodings(String s) {
int[] dp = new int[s.length() + 1];
dp[0] = 1;

for (int i = 0; i < s.length(); i++) {
if (s.charAt(i) > '0') {
dp[i + 1] += dp[i];
}

if (i > 0 && s.charAt(i - 1) == '1') {
dp[i + 1] += dp[i - 1];
}

if (i > 0 && s.charAt(i - 1) == '2' && s.charAt(i) <= '6') {
dp[i + 1] += dp[i - 1];
}
}

dp[0] = 0;

return dp[s.length()];
}
}