PAT 1021

1021. Deepest Root (25)

A graph which is connected and acyclic can be considered a tree. The height of the tree depends on the selected root. Now you are supposed to find the root that results in a highest tree. Such a root is called the deepest root.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=10000) which is the number of nodes, and hence the nodes are numbered from 1 to N. Then N-1 lines follow, each describes an edge by given the two adjacent nodes' numbers.

Output Specification:

For each test case, print each of the deepest roots in a line. If such a root is not unique, print them in increasing order of their numbers. In case that the given graph is not a tree, print "Error: K components" where K is the number of connected components in the graph.

Sample Input 1:

51 21 31 42 5

Sample Output 1:

345

Sample Input 2:

51 31 42 53 4

Sample Output 2:

Error: 2 components
首先说说算法的思路：先用并查集判断树是否是联通；然后任选一个结点做bfs，则得到最低层的叶结点一定是Deepest Root，接下去在从已选出的Deepest Root中任选一点，在做一次dfs，然后在
将最底层的叶结点加入Deepest Root。此题在时间和空间上都有限制，如果暴力解决的话会超时，如果用邻接矩阵存树的话会超内存，所以采用链表存树。
代码

  1 #include <stdio.h>  2 #include <string.h>  3 #include <stdlib.h>  4   5 #define NUM 10001  6 typedef struct linkNode{  7     int a;  8     linkNode *next;  9 }linkNode; 10  11 linkNode *map[NUM]; 12 int unionSet[NUM]; 13 int level[NUM]; 14 int queue[NUM]; 15 int deepestRoot[NUM]; 16  17 int findRoot(int); 18 int bfs(int); 19 void destroyMap(int); 20  21 int main() 22 { 23     int N,i; 24     int s,e; 25     int k; 26     linkNode *p; 27     while(scanf("%d",&N) != EOF){ 28         memset(unionSet,0,sizeof(unionSet)); 29         memset(map,0,sizeof(map)); 30         k = 0; 31         for(i=1;i<N;++i){ 32             scanf("%d%d",&s,&e); 33             int sR = findRoot(s); 34             int eR = findRoot(e); 35             if(sR != eR){ 36                 unionSet[sR] = eR; 37                 ++k; 38                 p = (linkNode*) malloc(sizeof(linkNode)); 39                 p->a = e; 40                 p->next = NULL; 41                 if(map[s]){ 42                     p->next = map[s]; 43                     map[s] = p; 44                 } 45                 else 46                     map[s] = p; 47                 p = (linkNode*) malloc(sizeof(linkNode)); 48                 p->a = s; 49                 p->next = NULL; 50                 if(map[e]){ 51                     p->next = map[e]; 52                     map[e] = p; 53                 } 54                 else 55                     map[e] = p; 56             } 57         } 58         if(k < N - 1){ 59             printf("Error: %d components\n",N-k); 60             destroyMap(N); 61             continue; 62         } 63         memset(deepestRoot,0,sizeof(deepestRoot)); 64         int maxLevel = bfs(1); 65         int maxLevel_i; 66         for(i=1;i<=N;++i){ 67             if(level[i] == maxLevel){ 68                 deepestRoot[i] = 1; 69                 maxLevel_i = i; 70             } 71         } 72         maxLevel = bfs(maxLevel_i); 73         for(i=1;i<=N;++i){ 74             if(level[i] == maxLevel) 75                 deepestRoot[i] = 1; 76         } 77         for(i=1;i<=N;++i){ 78             if(deepestRoot[i]) 79                 printf("%d\n",i); 80         } 81         destroyMap(N); 82     } 83     return 0; 84 } 85  86 int findRoot(int s) 87 { 88     while(unionSet[s]) 89         s = unionSet[s]; 90     return s; 91 } 92  93  94 int bfs(int s) 95 { 96     memset(level,-1,sizeof(level)); 97     int base = 0,top = 0; 98     int levelNum = 1,endLevel = 1; 99     int t,i;100     linkNode *p;101     queue[top++] = s;102     while(top > base){103         t = queue[base++];104         level[t] = levelNum;105         p = map[t];106         while(p){107             if(level[p->a] == -1){108                 queue[top++] = p->a;109             }110             p = p->next;111         }112         if(endLevel == base){113             endLevel = top;114             ++levelNum;115         }116     }117     return levelNum - 1;118 }119 120 void destroyMap(int n)121 {122     linkNode *p,*q;123     int i;124     for(i=1;i<=n;++i){125         p = map[i];126         while(p){127             q = p->next;128             free(p);129             p = q;130         }131     }132 }