LCA：最近公共祖先问题
解决方法：
1. 采用链式前行星存图，可以优化空间占用和遍历速度
2. Tarjan离线可以一次性处理所有的请求，时间复杂度为O(n+q)
下面简单介绍下Tarjan离线求LCA：
首先dfs遍历树，当某个结点左右子树都遍历完成后，处理所有与它有关的请求，然后将其利用并查集合并到父结点上。详见图解、
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代码(POJ 1330)：
1 #include<cstdio> 2 #include<cstdlib> 3 #include<cstring> 4 #include<cmath> 5 #include<algorithm> 6 #include<queue> 7 #include<stack> 8 #include<deque> 9 #include<map> 10 #include<iostream> 11 using namespace std; 12 typedef long long LL; 13 const double pi=acos(-1.0); 14 const double e=exp(1); 15 const int N = 10100; 16 17 #define lson i << 1, l, m 18 #define rson i << 1 | 1, m + 1, r 19 int cnt,ans; 20 int a,b,n; 21 int root; 22 int head[N]; //指向结点i的第一条边 23 int is_root[N]; 24 int father[N]; // 并查集的boss结点 25 int vis[N]; 26 27 struct edge 28 { 29 int to; 30 int next; 31 } edge[N]; 32 33 int seek(int ss) 34 { 35 int mid; 36 int head = ss; 37 while(ss != father[ss]) 38 ss = father[ss]; 39 40 while(head != ss) 41 { 42 mid = father[head]; 43 father[head] = ss; 44 head = mid; 45 } 46 return ss; 47 } 48 49 void join(int xx, int yy) 50 { 51 int one = seek(xx); 52 int two = seek(yy); 53 if(one != two) 54 father[two] = one; //注意把谁变成谁的上级 55 } 56 57 void add(int x, int y) 58 { 59 edge[cnt].to = y; 60 edge[cnt].next = head[x]; 61 head[x] = cnt++; 62 } 63 64 void init() 65 { 66 int i, p, j; 67 int x, y; 68 cnt = 0; 69 memset(head, -1, sizeof(head)); 70 memset(is_root, 0, sizeof(is_root)); 71 memset(vis, 0, sizeof(vis)); 72 scanf("%d", &n); 73 for(i = 0; i <= n; i++) //并查集预处理 74 father[i] = i; 75 for(i = 1; i < n; i++) 76 { 77 scanf("%d%d", &x, &y); 78 add(x, y); //加边 79 is_root[y] = 1; 80 } 81 for(i = 1; i <= n; i++) 82 if(is_root[i] == 0) 83 root = i; 84 } 85 86 void LCA(int u) 87 { 88 int i, p, j; 89 for(i = head[u]; i != -1; i = edge[i].next) 90 { 91 int v = edge[i].to; 92 LCA(v); 93 join(u, v); 94 vis[v] = 1; 95 } 96 97 if(u == a && vis[b] == 1) 98 ans = seek(b); 99 if(u == b && vis[a] == 1) 100 ans = seek(a); 101 102 return ; 103 } 104 105 void solve() 106 { 107 scanf("%d%d", &a, &b); 108 LCA(root); 109 } 110 111 int main() 112 { 113 int t, m, i, p, j; 114 scanf("%d", &t); 115 for(i = 1; i <= t; i++) 116 { 117 init(); // 链式前向星建图 118 solve(); // Tarjan求LCA 119 120 printf("%d ", ans); 121 } 122 return 0; 123 }