91. Decode Ways

题目

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.

思路

本题题目和爬梯子很相似（每次只能爬一级或两级），这是个很典型的动态规划问题。我们维护一个数组dp[i]表示从索引i开始的字符串，转码的种类。那么我们可以写出状态转移方程：

dp[i] = Integer..parseInt(s.substring(i,i+2))<=26?dp[i+1]+dp[i+2]:dp[i+1]

代码

class Solution {
public int numDecodings(String s) {
int n = s.length();
if(n==0)
return 0;
int[] nums = new int[n+1];
nums
= 1;
nums[n-1] = s.charAt(n-1)=='0'?0:1;
for(int i=n-2;i>=0;i--)
{
if(s.charAt(i)=='0') continue;
nums[i] = Integer.parseInt(s.substring(i,i+2))<=26?nums[i+1]+nums[i+2]:nums[i+1];
}
return nums[0];
}
}