Shortest Prefixes 字典树 (前缀树) 入门题题解

旧城等待， 2021-08-27 19:47 448阅读 0赞

### Shortest Prefixes 题解 ###

*  （1）题目
 *  （2）题解

# （1）题目 #

Shortest Prefixes

A prefix of a string is a substring starting at the beginning of the given string. The prefixes of “carbon” are: “c”, “ca”, “car”, “carb”, “carbo”, and “carbon”. Note that the empty string is not considered a prefix in this problem, but every non-empty string is considered to be a prefix of itself. In everyday language, we tend to abbreviate words by prefixes. For example, “carbohydrate” is commonly abbreviated by “carb”. In this problem, given a set of words, you will find for each word the shortest prefix that uniquely identifies the word it represents.

In the sample input below, “carbohydrate” can be abbreviated to “carboh”, but it cannot be abbreviated to “carbo” (or anything shorter) because there are other words in the list that begin with “carbo”.

An exact match will override a prefix match. For example, the prefix “car” matches the given word “car” exactly. Therefore, it is understood without ambiguity that “car” is an abbreviation for “car” , not for “carriage” or any of the other words in the list that begins with “car”.  
Input  
The input contains at least two, but no more than 1000 lines. Each line contains one word consisting of 1 to 20 lower case letters.  
Output  
The output contains the same number of lines as the input. Each line of the output contains the word from the corresponding line of the input, followed by one blank space, and the shortest prefix that uniquely (without ambiguity) identifies this word.  
Sample Input  
carbohydrate  
cart  
carburetor  
caramel  
caribou  
carbonic  
cartilage  
carbon  
carriage  
carton  
car  
carbonate  
Sample Output  
carbohydrate carboh  
cart cart  
carburetor carbu  
caramel cara  
caribou cari  
carbonic carboni  
cartilage carti  
carbon carbon  
carriage carr  
carton carto  
car car  
carbonate carbona

# （2）题解 #

这道题的题意是 输出最短的前缀唯一地(没有歧义)标识这个单词。字典树的入门题，只需要在原来的模板上改动一些即可。解题思路是 输出在字典中有相同的前缀+1个字符来唯一识别这个单词。  
字典树（前缀树）的模板：  
https://blog.csdn.net/u011787119/article/details/46991691  
代码如下：

#include<cstdio>
    #include<iostream>
    #include<cstring>
    using namespace std;
    const int maxn = 26;
    char s[1010][30];
    struct Trie
    { 
    	Trie *Next[maxn];
    	int cnt;
    	Trie()
    	{ 
    		cnt = 1;
    		memset(Next, NULL, sizeof(Next));
    	}
    }*root;
    void insert(char *str)
    { 
    	int len = strlen(str);
    	Trie *p = root, *q;
    	for (int i = 0; i < len; i++)
    	{ 
    		int id = str[i] - 'a';
    		if (p->Next[id] == NULL)
    		{ 
    			q = new Trie();
    			p->Next[id] = q;
    			p = p->Next[id];
    		}
    		else
    		{ 
    			p=p->Next[id];
    			(p->cnt)++;
    		}
    	}
    }
    void find(char *str)
    { 
    	int len = strlen(str);
    	Trie *p = root;
    	for (int i = 0; i < len; i++)
    	{ 
    		int id = str[i] - 'a';
    		p = p->Next[id];
    		if (p->cnt > 1)  ///输出这些字符串相同的前缀
    		{ 
    			printf("%c", str[i]);
    		}
    		else   ///当p->cnt==1时，多输出一个字符来唯一的标识这个字符串（本题的关键） 
    		{ 
    			printf("%c", str[i]);
    			return;
    		}
    	}
    }
    int main()
    { 
    	root = new Trie();
    	int n = 0;  //模仿别人的博客来进行输入
    	while (scanf("%s", s[n])!=EOF)
    	{ 
    		insert(s[n]);
    		n++;
    	}
    	for (int i = 0; i < n; i++)
    	{ 
    		printf("%s ", s[i]);
    		find(s[i]);
    		printf("\n");
    	}
    	return 0;
    }

这道题参考的这篇博客  
链接: [https://blog.csdn.net/caduca/article/details/43531875][https_blog.csdn.net_caduca_article_details_43531875].

[https_blog.csdn.net_caduca_article_details_43531875]: https://blog.csdn.net/caduca/article/details/43531875