POJ2513【并查集+字典树+欧拉】

/*Colored Sticks Time Limit : 10000/5000ms (Java/Other)   Memory Limit : 256000/128000K (Java/Other)Total Submission(s) : 0   Accepted Submission(s) : 0Problem DescriptionYou are given a bunch of wooden sticks. Each endpoint of each stick is colored with some color. Is it possible to align the sticks in a straight line such that the colors of the endpoints that touch are of the same color?  InputInput is a sequence of lines, each line contains two words, separated by spaces, giving the colors of the endpoints of one stick. A word is a sequence of lowercase letters no longer than 10 characters. There is no more than 250000 sticks. OutputIf the sticks can be aligned in the desired way, output a single line saying Possible, otherwise output Impossible.Sample Inputblue redred violetcyan blueblue magentamagenta cyanSample OutputPossible SourcePKU*/#include<stdio.h>#include<string.h>#include<stdlib.h>typedef struct Tree{bool flag;int id;Tree * next[27];}Tree;Tree root;int colorid, colornum, f[500010], color[500010];int getid(char *s){Tree *p = &root, *q;int i, j, k;k = strlen(s);for(i = 0; i < k; ++i){j = s[i] - 'a';//idif(p->next[j] == NULL){q = (Tree *)malloc(sizeof(root));q->flag = false;for(int l = 0; l < 26; ++l)q->next[l] = NULL;p->next[j] = q;}p = p->next[j];if(i == k-1)break;}if(!p->flag){p->flag = true;p->id = ++colorid;}return p->id;}int find(int x){if(x != f[x])f[x] = find(f[x]);return f[x];}bool merge(int x, int y){x = find(x);y = find(y);if(x != y){f[x] = y;return true;}return false;}int main(){char s1[11], s2[11];int i, j, k;for(i = 1; i <= 500001; ++i)f[i] = i;colorid = 0;colornum = 0;memset(color, 0, sizeof(color));for(i = 0; i < 26; ++i)//字典树根节点初始化 root.next[i] = NULL;while(scanf("%s%s", s1, s2) != EOF){i = getid(s1);j = getid(s2);color[i]++;//保存度数 color[j]++;if(merge(i, j))//如果合并成功 colornum++;}if(colorid == 0){printf("Possible\n");return 0;}if(colornum != colorid-1)//如果不连通 {printf("Impossible\n");}else//连通 {j = 0;for(i = 1; i <= colorid; ++i){if(color[i] & 1)//记录奇数度数个数 j++;}if(j == 1 || j >= 3)printf("Impossible\n");elseprintf("Possible\n");}return 0;}

题意：给出一个筷子，筷子的两端都涂有一种颜色，现在给出n根两端都涂有颜色的筷子，当2根筷子的一端具有同种颜色时，两根筷子可以连成一条直线，问这n根筷子是否能连成一条直线。

思路：本题可以将颜色看做是一个节点，筷子看做是边，则题目的要求就类似于，给出n个节点，和m条边，问是否能一笔画走完每一条边一次。这就是欧拉回路，所以根据定义，若是所有的颜色的边的个数全为偶数，或是只有2个颜色的边数为奇数，则可以一笔画走完。现在就要开始模拟这种思想。但是这里还有一个难点就是怎么给颜色字符串编号的问题，如果按照常规的方法必定超时，所以这里又要用到字典树，对颜色进行编号，可以大大提高效率。对每种颜色进行编号的同时可以进行边数的统计，以及并查集的操作，最后用来判断这n种颜色是否能够连通，并且边数是否符合要求，最终判定是否是欧拉回路。

体会：第一做这种综合性的题目，难度好大0.0