LeetCode - Decode Ways
Problem description
A message containing letters from A-Z is being encoded to numbers using the following mapping:
‘A’ -> 1 ‘B’ -> 2 … ‘Z’ -> 26 Given a non-empty string containing only digits, determine the total number of ways to decode it.
Example 1:
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Input: "12"
Output: 2
Explanation: It could be decoded as "AB" (1 2) or "L" (12).
Example 2:
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Input: "226"
Output: 3
Explanation: It could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).
Analysis
The first idea is to use divide and conquer, and realized that the sub-problem is related, which means we should use DP.
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class Solution {
public int numDecodings(String s) {
if(s == null || s.length() == 0) {
return 0;
}
// DP array to store the subproblem results
int[] dp = new int[s.length() + 1];
dp[0] = 1;
// Ways to decode a string of size 1 is 1. Unless the string is '0'.
// '0' doesn't have a single digit decode.
dp[1] = s.charAt(0) == '0' ? 0 : 1;
for(int i = 2; i < dp.length; i += 1) {
// Check if successful single digit decode is possible.
if(s.charAt(i-1) != '0') {
dp[i] += dp[i-1];
}
// Check if successful two digit decode is possible.
int twoDigit = Integer.valueOf(s.substring(i-2, i));
if(twoDigit >= 10 && twoDigit <= 26) {
dp[i] += dp[i-2];
}
}
return dp[s.length()];
}
}
What to improve
- for DP, the extra 1 position added to the begining is important.