LCA（最近公共祖先）——LCA倍增法

一、前人种树

博客：最近公共祖先 LCA 倍增法

博客：浅谈倍增法求LCA

二、沙场练兵

题目：POJ 1330 Nearest Common Ancestors

代码：

const int MAXN = 10010; 
const int DEG = 20; 
 
struct Edge 
{ 
  int to,next; 
}edge[MAXN*2]; 
int head[MAXN],tot; 
void addedge(int u,int v) 
{ 
  edge[tot].to = v; 
  edge[tot].next = head[u]; 
  head[u] = tot++; 
} 
void init() 
{ 
  tot = 0; 
  memset(head,-1,sizeof(head)); 
} 
int fa[MAXN][DEG];//fa[i][j]表示结点i的第2^j个祖先 
int deg[MAXN];//深度数组 
 
void BFS(int root) 
{ 
  queue<int>que; 
  deg[root] = 0; 
  fa[root][0] = root; 
  que.push(root); 
  while(!que.empty()) 
  { 
    int tmp = que.front(); 
    que.pop(); 
    for(int i = 1;i < DEG;i++) 
      fa[tmp][i] = fa[fa[tmp][i-1]][i-1]; 
    for(int i = head[tmp]; i != -1;i = edge[i].next) 
    { 
      int v = edge[i].to; 
      if(v == fa[tmp][0])continue; 
      deg[v] = deg[tmp] + 1; 
      fa[v][0] = tmp; 
      que.push(v); 
    } 
 
  } 
} 
int LCA(int u,int v) 
{ 
  if(deg[u] > deg[v])swap(u,v); 
  int hu = deg[u], hv = deg[v]; 
  int tu = u, tv = v; 
  for(int det = hv-hu, i = 0; det ;det>>=1, i++) 
    if(det&1) 
      tv = fa[tv][i]; 
  if(tu == tv)return tu; 
  for(int i = DEG-1; i >= 0; i--) 
  { 
    if(fa[tu][i] == fa[tv][i]) 
      continue; 
    tu = fa[tu][i]; 
    tv = fa[tv][i]; 
  } 
  return fa[tu][0]; 
} 
bool flag[MAXN]; 
int main() 
{ 
    int T; 
  int n; 
  int u,v; 
  scanf("%d",&T); 
  while(T--) 
  { 
    scanf("%d",&n); 
    init(); 
    memset(flag,false,sizeof(flag)); 
    for(int i = 1;i < n;i++) 
    { 
      scanf("%d%d",&u,&v); 
      addedge(u,v); 
      addedge(v,u); 
      flag[v] = true; 
    } 
    int root; 
    for(int i = 1;i <= n;i++) 
      if(!flag[i]) 
      { 
        root = i; 
        break; 
      } 
    BFS(root); 
    scanf("%d%d",&u,&v); 
    printf("%d
",LCA(u,v)); 
  } 
    return 0; 
}