Leetcode 题解系列(十四)
2018-01-13 01:47
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91. Decode Ways
题目要求
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.
分析
此题为动态规划,如果往一个串s后面新增加一个数字符,那么方法数应该有:1. 如果这个数不是0,那么方法数包含了原先串s的解码数量(即在原先解码出来的串s’后面添加上对应的字符ABCDEFGHIJ)
2. 如果它跟前一个数字符刚好组成一个合法的二位数(也就是介于10到26之间),那么还要在加上串s减去最后一个数字符所对应的解码数量(即是s[:-1]的解码出来的字符串加上对应的K-Z)
初始状态下:
有dp[0] = 1,dp[1] = 1
答案
class Solution { public: int numDecodings(string s) { int n = s.size(); if (s == "" || s[0] == '0') return 0; if (n == 1) return 1; vector<int> dp(n); dp[0] = 1; dp[1] = s[0] == '0' ? 0 : 1; for (int i = 2; i <= n; ++i) { dp[i] = 0; if (s[i - 1] >= '1' && s[i - 1] <= '9') { dp[i] += dp[i - 1]; } int tmp = s[i - 1] - '0' + (s[i - 2] - '0') * 10; if (tmp >= 10 && tmp <= 26) { dp[i] += dp[i - 2]; } } return dp ; } };
4000
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