poj 1470 Closest Common Ancestors （LCA）

最新推荐文章于 2020-04-21 16:31:35 发布

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本文深入探讨了在树形结构中寻找两个节点的最近公共祖先的算法实现。通过使用深度优先搜索(DFS)，文章详细解释了如何遍历树并标记节点以确定最近公共祖先的过程。此外，还提供了一个具体的代码示例，帮助读者更好地理解算法的工作原理。

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Write a program that takes as input a rooted tree and a list of pairs of vertices. For each pair (u,v) the program determines the closest common ancestor of u and v in the tree. The closest common ancestor of two nodes u and v is the node w that is an ancestor of both u and v and has the greatest depth in the tree. A node can be its own ancestor (for example in Figure 1 the ancestors of node 2 are 2 and 5)

Input

The data set, which is read from a the std input, starts with the tree description, in the form:

nr_of_vertices
vertex:(nr_of_successors) successor1 successor2 ... successorn
...
where vertices are represented as integers from 1 to n ( n <= 900 ). The tree description is followed by a list of pairs of vertices, in the form:
nr_of_pairs
(u v) (x y) ...

The input file contents several data sets (at least one).
Note that white-spaces (tabs, spaces and line breaks) can be used freely in the input.

Output

For each common ancestor the program prints the ancestor and the number of pair for which it is an ancestor. The results are printed on the standard output on separate lines, in to the ascending order of the vertices, in the format: ancestor:times
For example, for the following tree:

Sample Input

5
5:(3) 1 4 2
1:(0)
4:(0)
2:(1) 3
3:(0)
6
(1 5) (1 4) (4 2)
      (2 3)
(1 3) (4 3)

Sample Output

2:1
5:5

Hint

Huge input, scanf is recommended.

题意：给出一棵树，给出两个点，求最近公共祖先。

思路：最简单的方法dfs。遍历一遍第一个点的父亲，并标记他们，第二个点最先遇到有标记的父亲就是最近公共祖先。

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
struct path
{
    int to,nextt;
} A[900*900+10];
int n,m,x,y,tot,root,pan;
int head[910],in[910],fa[910],f[910],ans[910];
void add(int x,int y)
{
    A[tot].to=y;
    A[tot].nextt=head[x];
    head[x]=tot++;
}
void init()
{
    tot=0;
    memset(head,-1,sizeof(head));
    memset(in,0,sizeof(in));
    for(int i=1;i<=n;i++)
        fa[i]=i;
    memset(ans,0,sizeof(ans));
}
void dfs(int u,int pre)
{
    int tem;
    for(int i=head[u]; i!=-1; i=A[i].nextt)
    {
        tem=A[i].to;
        dfs(tem,u);
        fa[tem]=u;
    }
}
int solve(int u,int v)
{
    memset(f,0,sizeof(f));
    do
    {
        f[u]=1;
        u=fa[u];
    }while(u!=root);
    f[root]=1;
    while(!f[v])
    {
        v=fa[v];
    }
    return v;
}
int main()
{
    while(~scanf("%d",&n))
    {
        init();
        for(int i=1; i<=n; i++)
        {
            scanf("%d:(%d)",&x,&m);
            while(m--)
            {
                scanf("%d",&y);
                add(x,y);
                in[y]++;
            }
        }
        scanf("%d",&m);
        root;
        for(int i=1; i<=n; i++)
        {
            if(in[i]==0)
            {
                root=i;
                break;
            }
        }
        dfs(root,-1);
        while(m)
        {
            while(getchar()=='(')
            {
                scanf("%d %d)",&x,&y);
                pan=solve(x,y);
                ans[pan]++;
                m--;
            }
        }
        for(int i=1; i<=n; i++)
        {
            if(ans[i])
            {
                printf("%d:%d\n",i,ans[i]);
            }
        }
    }
}