CF321C Ciel the Commander | 树的重心

Solution

Thinking 1

对于一个已经确定了根的数，当前根的等级一定是最高的。

Thinking 2

考虑近似链的情况，所以每次根都要取当前重心，来保证等级总个数最小。

# include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
int n;
vector <int> g[N];
int root = 0,siz[N],max_siz[N],S;
bool del[N],isd[N];
char ans[N];
int total = 0;

void find_root(int x,int fa)
{
    siz[x] = 1,max_siz[x] = 0;
    for(int i = 0; i < (int)g[x].size(); i++)
    {
        int v = g[x][i];
        if(v == fa || del[v]) continue;
        find_root(v,x);
        siz[x] += siz[v];
        if(siz[v] > max_siz[x]) max_siz[x] = siz[v];
    }
    max_siz[x] = max(max_siz[x], S - max_siz[x]);
    if(max_siz[x] < max_siz[root]) root = x;
    return;
}       

void dfs(int x,int d)
{
    del[x] = 1;
    ans[x] = char(int('A') + d),isd[x] = 1;
    total = max(total,d);
    if(ans[x] > 'Z') 
    {
        printf("Impossible!
");
        exit(0);
    }
    for(int i = 0; i < g[x].size(); i++)
    {
        int v = g[x][i];
        if(del[v]) continue;
        max_siz[root = 0] = S = siz[v];
        find_root(v,0);
        find_root(root,0);
        dfs(root,d + 1);
    }
    return;
}

int main(void)
{
    scanf("%d",&n);
    for(int i = 1; i < n; i++)
    {
        int u,v;
        scanf("%d%d",&u,&v);
        g[v].push_back(u),g[u].push_back(v);
    }
    max_siz[root = 0] = S = n;
    find_root(1,0);find_root(root,0);
    dfs(root,0);
    for(int i = 1; i <= n; i++)
    {
        if(!isd[i]) ans[i] = char(int('A') + total);
    }
    for(int i = 1; i <= n; i++) 
    {
        cout << ans[i] << ' ';
    }
    return 0;
}