目录

CF600E-Lomsat gelral

CF600E-Lomsat gelral

题目:

题目描述:

You are given a rooted tree with root in vertex $ 1 $ . Each vertex is coloured in some colour.

Let’s call colour $ c $ dominating in the subtree of vertex $ v $ if there are no other colours that appear in the subtree of vertex $ v $ more times than colour $ c $ . So it’s possible that two or more colours will be dominating in the subtree of some vertex.

The subtree of vertex $ v $ is the vertex $ v $ and all other vertices that contains vertex $ v $ in each path to the root.

For each vertex $ v $ find the sum of all dominating colours in the subtree of vertex $ v $ .

输入格式:

The first line contains integer $ n $ ( $ 1<=n<=10^{5} $ ) — the number of vertices in the tree.

The second line contains $ n $ integers $ c_{i} $ ( $ 1<=c_{i}<=n $ ), $ c_{i} $ — the colour of the $ i $ -th vertex.

Each of the next $ n-1 $ lines contains two integers $ x_{j},y_{j} $ ( $ 1<=x_{j},y_{j}<=n $ ) — the edge of the tree. The first vertex is the root of the tree.

输出格式:

Print $ n $ integers — the sums of dominating colours for each vertex.

样例:

样例输入1:

1
2
3
4
5
4
1 2 3 4
1 2
2 3
2 4

样例输出1:

1
10 9 3 4

样例输入2:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13

样例输出2:

1
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3

思路:

一道dsu on tree的简单例题 用一个通桶统计一遍答案即可

实现:

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
// Problem: CF600E Lomsat gelral
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/CF600E
// Memory Limit: 250 MB
// Time Limit: 2000 ms
// Author: Ybw051114
//
// Powered by CP Editor (https://cpeditor.org)

#include "ybwhead/ios.h"
#define int long long
const int maxn = 1e5 + 10;
struct edge
{
    int v, nxt;
} e[maxn << 1];
int head[maxn], tot, ans[maxn], siz[maxn], c[maxn], wson[maxn];
int a[maxn], n;
int mx, sum;
void __ADD(int u, int v)
{
    e[++tot] = {v, head[u]};
    head[u] = tot;
}
void add(int u, int v)
{
    __ADD(u, v), __ADD(v, u);
}
void dfs(int u, int fa)
{
    siz[u] = 1;
    for (int i = head[u]; i; i = e[i].nxt)
    {
        int v = e[i].v;
        if (v == fa)
            continue;
        dfs(v, u);
        siz[u] += siz[v];
        if (siz[wson[u]] < siz[v])
            wson[u] = v;
    }
}
void add(int u, int fa, int rt)
{
    c[a[u]]++;
    if (c[a[u]] == mx)
        sum += a[u];
    if (c[a[u]] > mx)
        sum = a[u], mx = c[a[u]];
    for (int i = head[u]; i; i = e[i].nxt)
    {
        int v = e[i].v;
        if (v == fa)
            continue;
        add(v, u, rt);
    }
}
void del(int u, int fa)
{
    c[a[u]]--;
    mx = sum = 0;
    for (int i = head[u]; i; i = e[i].nxt)
    {
        int v = e[i].v;
        if (v == fa)
            continue;
        del(v, u);
    }
}
void solve(int u, int fa)
{
    for (int i = head[u]; i; i = e[i].nxt)
    {
        int v = e[i].v;
        if (v == fa || v == wson[u])
            continue;

        solve(v, u);
        del(v, u);
    }
    if (wson[u])
        solve(wson[u], u);
    // cerr << mx << " " << sum << endl;
    c[a[u]]++;
    if (c[a[u]] == mx)
        sum += a[u];
    if (c[a[u]] > mx)
        sum = a[u], mx = c[a[u]];
    for (int i = head[u]; i; i = e[i].nxt)
    {
        int v = e[i].v;
        if (v == fa || v == wson[u])
            continue;
        add(v, u, u);
    }
    ans[u] = sum;
}
signed main()
{
    yin >> n;
    for (int i = 1; i <= n; ++i)
    {
        yin >> a[i];
    }
    for (int i = 1; i < n; i++)
    {
        int x, y;
        yin >> x >> y;
        add(x, y);
    }
    dfs(1, 0);
    solve(1, 0);
    for (int i = 1; i <= n; i++)
        yout << ans[i] << " ";
    return 0;
}