POJ 1655 Balancing Act&&POJ 3107 Godfather(树的重心)

树的重心的定义是： 一个点的所有子树中节点数最大的子树节点数最小。

这句话可能说起来比较绕，但是其实想想他的字面意思也就是找到最平衡的那个点。

POJ 1655

题目大意： 直接给你一棵树，让你求树的重心，如果有多个，找出编号最小的那个，并输出他的子树当中最大的节点数。

思路：利用dfs求出每个点的所有孩子数目，然后在dfs一下求出树的重心。

用途：树的重心在树分治的点分治中有重要作用。具体可以看上篇树分治的题目http://www.cnblogs.com/Howe-Young/p/4776852.html

代码：

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 42000;
const int inf = 0x3f3f3f3f;
int tot, head[maxn];
struct Edge {
    int to, next;
}edge[maxn];
int siz[maxn];
void init()
{
    tot = 0;
    memset(head, -1, sizeof(head));
}
void addedge(int u, int v)
{
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;
}
int dfs_size(int u, int fa)
{
    siz[u] = 1;
    for (int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == fa) continue;
        siz[u] += dfs_size(v, u);
    }
    return siz[u];
}
int minn;
void dfs_balance(int u, int fa, int totnum, int &root)
{
    int maxx = totnum - siz[u];
    for (int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == fa) continue;
        dfs_balance(v, u, totnum, root);
        maxx = max(maxx, siz[v]);
    }
    if (maxx < minn || maxx == minn && root > u)
    {
        minn = maxx;
        root = u;
    }
}
void solve()
{
    int totnum = dfs_size(1, 0);
    minn = inf;
    int root;
    dfs_balance(1, 0, totnum, root);
    printf("%d %d
", root, minn);
}
int main()
{
    int T, n;
    scanf("%d", &T);
    while (T--)
    {
        init();
        scanf("%d", &n);
        int u, v;
        for (int i = 1; i < n; i++)
        {
            scanf("%d %d", &u, &v);
            addedge(u, v);
            addedge(v, u);
        }
        solve();
    }
    return 0;
} 

POJ 3107
题目大意： 还是给出一棵树，让求它的所有的重心。

思路：基本上和上一个题目一样，就是多了所有的重心。在求所有的重心的时候如果找到了最小的比之前的都小，那么现在就它一个，如果相等的话，就继续往上加，因为还没找到比他还小的

代码：

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 110000;
const int inf = 0x3f3f3f3f;
int tot, head[maxn];
struct Edge {
    int to, next;
}edge[maxn];
int siz[maxn];
int res[maxn], index;
void init()
{
    tot = 0;
    memset(head, -1, sizeof(head));
}
void addedge(int u, int v)
{
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;
}
int dfs_size(int u, int fa)
{
    siz[u] = 1;
    for (int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == fa) continue;
        siz[u] += dfs_size(v, u);
    }
    return siz[u];
}
int minn;
void dfs_balance(int u, int fa, int totnum)
{
    int maxx = totnum - siz[u];
    for (int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if (v == fa) continue;
        dfs_balance(v, u, totnum);
        maxx = max(maxx, siz[v]);
    }
    if (maxx < minn)
    {
        minn = maxx;
        index = 0;
        res[index++] = u;
    }
    else if (maxx == minn)
    {
        res[index++] = u;
    }
}
void solve()
{
    int totnum = dfs_size(1, 0);
    minn = inf;
    dfs_balance(1, 0, totnum);
    sort(res, res + index);
    for (int i = 0; i < index; i++)
        printf("%d ", res[i]);
    puts("");
}
int main()
{
    int n;
    while (~scanf("%d", &n))
    {
        init();
        int u, v;
        for (int i = 1; i < n; i++)
        {
            scanf("%d %d", &u, &v);
            addedge(u, v);
            addedge(v, u);
        }
        solve();
    }
    return 0;
}