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!\n");
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;
}