POJ 1330 Nearest Common Ancestors 倍增算法的LCA

  1 /* ***********************************************
  2 Author        :kuangbin
  3 Created Time  :2013-9-5 9:45:17
  4 File Name     :F:\2013ACM练习\专题学习\LCA\POJ1330_3.cpp
  5 ************************************************ */
  6 
  7 #include <stdio.h>
  8 #include <string.h>
  9 #include <iostream>
 10 #include <algorithm>
 11 #include <vector>
 12 #include <queue>
 13 #include <set>
 14 #include <map>
 15 #include <string>
 16 #include <math.h>
 17 #include <stdlib.h>
 18 #include <time.h>
 19 using namespace std;
 20 /*
 21 * POJ 1330
 22 * LCA 在线算法
 23 */
 24 const int MAXN = 10010;
 25 const int DEG = 20;
 26 
 27 struct Edge
 28 {
 29     int to, next;
 30 }edge[MAXN * 2];
 31 int head[MAXN], tot;
 32 void addedge(int u, int v)
 33 {
 34     edge[tot].to = v;
 35     edge[tot].next = head[u];
 36     head[u] = tot++;
 37 }
 38 void init()
 39 {
 40     tot = 0;
 41     memset(head, -1, sizeof(head));
 42 }
 43 int fa[MAXN][DEG];//fa[i][j]表示结点i的第2^j个祖先
 44 int deg[MAXN];//深度数组
 45 
 46 void BFS(int root)
 47 {
 48     queue<int>que;
 49     deg[root] = 0;
 50     fa[root][0] = root;
 51     que.push(root);
 52     while (!que.empty())
 53     {
 54         int tmp = que.front();
 55         que.pop();
 56         for (int i = 1; i < DEG; i++)
 57             fa[tmp][i] = fa[fa[tmp][i - 1]][i - 1];
 58         for (int i = head[tmp]; i != -1; i = edge[i].next)
 59         {
 60             int v = edge[i].to;
 61             if (v == fa[tmp][0])continue;
 62             deg[v] = deg[tmp] + 1;
 63             fa[v][0] = tmp;
 64             que.push(v);
 65         }
 66 
 67     }
 68 }
 69 int LCA(int u, int v)
 70 {
 71     if (deg[u] > deg[v])swap(u, v);
 72     int hu = deg[u], hv = deg[v];
 73     int tu = u, tv = v;
 74     for (int det = hv - hu, i = 0; det; det >>= 1, i++)
 75     if (det & 1)
 76         tv = fa[tv][i];
 77     if (tu == tv)return tu;
 78     for (int i = DEG - 1; i >= 0; i--)
 79     {
 80         if (fa[tu][i] == fa[tv][i])
 81             continue;
 82         tu = fa[tu][i];
 83         tv = fa[tv][i];
 84     }
 85     return fa[tu][0];
 86 }
 87 bool flag[MAXN];
 88 int main()
 89 {
 90     freopen("in.txt","r",stdin);
 91     //freopen("out.txt","w",stdout);
 92     int T;
 93     int n;
 94     int u, v;
 95     scanf("%d", &T);
 96     while (T--)
 97     {
 98         scanf("%d", &n);
 99         init();
100         memset(flag, false, sizeof(flag));
101         for (int i = 1; i < n; i++)
102         {
103             scanf("%d%d", &u, &v);
104             addedge(u, v);
105             addedge(v, u);
106             flag[v] = true;
107         }
108         int root;
109         for (int i = 1; i <= n; i++)
110         if (!flag[i])
111         {
112             root = i;
113             break;
114         }
115         BFS(root);
116         scanf("%d%d", &u, &v);
117         printf("%d\n", LCA(u, v));
118     }
119     return 0;
120 }