Description
A rooted tree is a well-known data structure in computer science and engineering. An example is shown below:
In the figure, each node is labeled with an integer from {1, 2,...,16}. Node 8 is the root of the tree. Node x is an ancestor of node y if node x is in the path between the root and node y. For example, node 4 is an ancestor of node 16. Node 10 is also an ancestor of node 16. As a matter of fact, nodes 8, 4, 10, and 16 are the ancestors of node 16. Remember that a node is an ancestor of itself. Nodes 8, 4, 6, and 7 are the ancestors of node 7. A node x is called a common ancestor of two different nodes y and z if node x is an ancestor of node y and an ancestor of node z. Thus, nodes 8 and 4 are the common ancestors of nodes 16 and 7. A node x is called the nearest common ancestor of nodes y and z if x is a common ancestor of y and z and nearest to y and z among their common ancestors. Hence, the nearest common ancestor of nodes 16 and 7 is node 4. Node 4 is nearer to nodes 16 and 7 than node 8 is.
For other examples, the nearest common ancestor of nodes 2 and 3 is node 10, the nearest common ancestor of nodes 6 and 13 is node 8, and the nearest common ancestor of nodes 4 and 12 is node 4. In the last example, if y is an ancestor of z, then the nearest common ancestor of y and z is y.
Write a program that finds the nearest common ancestor of two distinct nodes in a tree.
In the figure, each node is labeled with an integer from {1, 2,...,16}. Node 8 is the root of the tree. Node x is an ancestor of node y if node x is in the path between the root and node y. For example, node 4 is an ancestor of node 16. Node 10 is also an ancestor of node 16. As a matter of fact, nodes 8, 4, 10, and 16 are the ancestors of node 16. Remember that a node is an ancestor of itself. Nodes 8, 4, 6, and 7 are the ancestors of node 7. A node x is called a common ancestor of two different nodes y and z if node x is an ancestor of node y and an ancestor of node z. Thus, nodes 8 and 4 are the common ancestors of nodes 16 and 7. A node x is called the nearest common ancestor of nodes y and z if x is a common ancestor of y and z and nearest to y and z among their common ancestors. Hence, the nearest common ancestor of nodes 16 and 7 is node 4. Node 4 is nearer to nodes 16 and 7 than node 8 is.
For other examples, the nearest common ancestor of nodes 2 and 3 is node 10, the nearest common ancestor of nodes 6 and 13 is node 8, and the nearest common ancestor of nodes 4 and 12 is node 4. In the last example, if y is an ancestor of z, then the nearest common ancestor of y and z is y.
Write a program that finds the nearest common ancestor of two distinct nodes in a tree.
Input
The input consists of T test cases. The number of test cases (T)
is given in the first line of the input file. Each test case starts with
a line containing an integer N , the number of nodes in a tree,
2<=N<=10,000. The nodes are labeled with integers 1, 2,..., N.
Each of the next N -1 lines contains a pair of integers that represent
an edge --the first integer is the parent node of the second integer.
Note that a tree with N nodes has exactly N - 1 edges. The last line of
each test case contains two distinct integers whose nearest common
ancestor is to be computed.
Output
Print exactly one line for each test case. The line should contain the integer that is the nearest common ancestor.
Sample Input
2 16 1 14 8 5 10 16 5 9 4 6 8 4 4 10 1 13 6 15 10 11 6 7 10 2 16 3 8 1 16 12 16 7 5 2 3 3 4 3 1 1 5 3 5
Sample Output
4 3 【分析】这题就是求最近公共祖先，让我对Tarjan有了一个新的认识。先找到根节点，一直往下深搜，
找到子节点，若该节点就是要求的点且另一个点已经被访问过，则另一个点所在并查集的根节点即为最近公共祖先。
#include <iostream> #include <cstring> #include <cstdio> #include <cstring> #include <algorithm> #include <cmath> #include <time.h> #include <string> #include <map> #include <stack> #include <vector> #include <set> #include <queue> #define inf 0x3f3f3f3f #define mod 1000000007 typedef long long ll; using namespace std; const int N = 100005; int fa[N],node1,node2,ret; bool root[N],visit[N]; vector<int>child[N]; int Find(int x) { if(x==fa[x]) return x; return fa[x]=Find(fa[x]); } void Union(int x,int y) { x=Find(x); y=Find(y); fa[y]=x; } void Tarjan(int root) { fa[root]=root;visit[root]=true; for(int i=0;i<child[root].size();i++) { Tarjan(child[root][i]); Union(root,child[root][i]); } if(root==node1&&visit[node2]) { ret=fa[Find(node2)]; return ; } if(root==node2&&visit[node1]) { ret=fa[Find(node1)]; return ; } } int main() { int T,n,i; scanf("%d",&T); while(T--) { memset(visit,false,sizeof(visit)); scanf("%d",&n); for(i=1;i<=n;i++) { root[i]=true; child[i].clear(); } for(i=1;i<=n-1;i++) { int a,b; scanf("%d%d",&a,&b); child[a].push_back(b); root[b]=false;//寻找root } scanf("%d%d",&node1,&node2); for(i=1;i<=n;i++) if(root[i]) { Tarjan(i); break; } printf("%d ",ret); } }