问题描述:
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.
示例:
Given encoded message "12"
, it could be decoded as "AB"
(1 2) or "L"
(12).
The number of ways decoding "12"
is 2.
问题分析:
根据题意可知,这是一道动态规划题。dp是状态转移数组,对于s[i - 1] 和 s[i]的不同取值,dp的对应转换过程也不相同。
过程详见代码:
class Solution {
public:
int numDecodings(string s) {
int len = s.length();
if (!len || s[0] == '0') return 0;
vector<int> dp(len + 1, 0);
dp[1] = 1;
dp[0] = 1;
for (int i = 1; i < len; i++)
{
int t = (s[i - 1] - '0') * 10 + s[i] - '0';
if(!t || t > 26 && t % 10 == 0) return 0;
else if(t < 10 || t > 26) dp[i + 1] = dp[i];
else if(t == 10 || t == 20) dp[i + 1] = dp[i - 1];
else dp[i + 1] = dp[i] + dp[i - 1];
}
return dp[len];
}
};
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