实用算法实现-第 7 篇Trie树

Trie,又称单词查找树,是一种树形结构，用于保存大量的字符串。它的优点是：利用字符串的公共前缀来节约存储空间。它有3个基本性质：

1. 根结点不包含字符，除根结点外每一个结点都只包含一个字符。

2. 从根结点到某一结点，路径上经过的字符连接起来，为该结点对应的字符串。

3. 每个结点的所有子结点包含的字符都不相同。

7.1    Trie树

7.1.1   实例

PKU JudgeOnline, 2513, ColoredSticks.

7.1.2   问题描述

给定一些棍子，棍子的两端涂上两种颜色。问这些棍子能不能连成一条直线，使得连在一起的两根棍子的相邻一端颜色相同。

7.1.3   输入

bluered

redviolet

cyanblue

bluemagenta

magentacyan

7.1.4   输出

Possible

7.1.5   分析

这里是个无向图的欧拉通路问题。

由于颜色种类很多，首先需要使用Trie树来查找颜色对应的编号。然后通过并查集和度数来判断欧拉通路是否存在。

7.1.6   程序

#include<stdio.h>#include<string.h>#include<iostream>using namespace std;#define maxNum500002int p[maxNum];int rank[maxNum];void makeSet(int x){p[x] = x;rank[x] = 0;}int findSet(int x){if(x != p[x]){p[x] = findSet(p[x]);}return p[x];}void link(int x, int y){if(rank[x] > rank[y]){p[y] = x;}else{p[x] = y;if(rank[x] == rank[y]){rank[y] = rank[y] + 1;}}}void unionSet(int x, int y){link(findSet(x), findSet(y));}struct trieNode {int self;//保存了是第几个加入树中，如果没有加入树中，则为int son[26];//指向儿子结点的位置};trieNode Trie[500002];int trieTop;int colorNum;int trieSearch(char *key){char *c;int son;int node;node = 0;c = key;while(*c != NULL){son = *c - 'a';if(Trie[node].son[son] == 0){return -1;}c++;node = Trie[node].son[son];}return Trie[node].self;}int trieInsert(char *key){char *c;int son;int node;node = 0;c = key;while(*c != NULL){son = *c - 'a';if(Trie[node].son[son] == 0){break;}c++;node = Trie[node].son[son];}while(*c != NULL){son = *c - 'a';Trie[node].son[son] = trieTop;trieTop++;c++;node = Trie[node].son[son];}if(Trie[node].self == 0){Trie[node].self = colorNum;}return node;}int degree[500002];int main(){int i, j;char stick[11];int oddNum;int from, to;int fail;trieTop = 1;colorNum = 0;memset(Trie, 0, sizeof(Trie));memset(degree, 0, sizeof(degree));for(i = 1; i < 500002; i++){makeSet(i);}while(scanf("%s", stick) != EOF)// && strcmp(stick, "#") != 0){from = trieSearch(stick);if(from <= 0){colorNum++;from = colorNum;trieInsert(stick);}scanf("%s", stick);to = trieSearch(stick);if(to <= 0){colorNum++;to = colorNum;trieInsert(stick);}degree[from]++;degree[to]++;if(findSet(from) != findSet(to))unionSet(from, to);}fail = 0;if(colorNum != 0){for(i = 1; i <= colorNum; i++){for(j = 1; j <= colorNum; j++){if(findSet(i) != findSet(j)){fail = 1;break;}}if(fail == 1){break;}}oddNum = 0;if(fail == 0){for(i = 1; i <= colorNum; i++){if(degree[i] % 2 != 0){oddNum++;if(oddNum > 2){fail = 1;break;}}}if(oddNum != 0&& oddNum != 2){fail = 1;}}}if(fail == 0){cout << "Possible" << endl;}else{cout << "Impossible" << endl;}return 1;}

7.2    实例

PKU JudgeOnline, 2513, Colored Sticks.

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