SGU - 195 New Year Bonus Grant （ 贪心

New Year Bonus Grant

题目描述

All programmers of Mocrosoft software company are organized in a strict subordination hierarchy. Every programmer has exactly one chief, except Bill Hates who is also the head of the company and has no chief.

Due to the celebration of the new 2003 year, chief accountant of Mocrosoft decided to pay a New Year Bonus Grant of 1000 dollars to some programmers. However being extremely concerned of the company wealth she would like to designate the least possible amount of money for these grants. On the other hand she didn’t want to be accused of being too greedy or of giving preferences to some programmers. To do this, she developed the following scheme of grants appointment:

Each programmer may either assign a grant to one of his subordinates or have a grant assigned to him by his chief or none of the above.
No programmer can simultaneously receive a grant and assign a grant to one of his subordinates.
No programmer can assign a grant to more than one of his subordinates

The scheme seemed to be designed perfectly — nobody would like to assign a grant to anybody since in this case he himself would not receive money. But programmers somehow discovered the plan of chief accountant and decided to make a trick to get the most money possible and share them fairly afterwards. The idea was to make such grant assignments that the total amount of grant money received is maximum possible.

You were selected to write the program which will find the optimal grants appointment.

输入

The first line of the input file contains integer N — the number of programmers in Mocrosoft company (2 ≤ N ≤ 500 000). Each programmer is assigned his unique identifier — integer number ranging from 1 to N. Bill Hates has number 1 and each programmer has the number greater then the number of his chief. The second line of the input file contains N-1 integers, i-th of which being the number of the chief of the worker whose number is (i + 1).

输出

On the first line of the output file print the maximum possible amount of money workers can get. On the second line output the numbers of programmers that will receive grant in ascending order.

样例

Input
4 
1 1 2 

Output
2000 
3 4 

题意

挺简单的一道题 就是体面太长了，，，
问题抽象为树的染色问题，我们可以知道 染色条件是
节点如果染色， 那么所有和他的父节点，兄弟节点，子节点都不能染色
节点不染色，那么就可以将且仅可以将自己的一个子节点染色
求的是染色节点尽可能个的多 那么 我们可以从叶子节点 不端向上更新，这样做的优点就是可以不考虑自己兄弟节点的情况，这个是一个贪心的过程

AC代码

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <cstdio>
using namespace std;

#define LL long long
#define CLR(a,b) memset(a,(b),sizeof(a))
#define ls st<<1
#define rs st<<1|1

const int MAXN = 1e6+10;
int fa[MAXN];
bool vis[MAXN];
int sum[MAXN];
int main() {
    int n;
    ios::sync_with_stdio(false);
    cin >> n;
    for(int i = 2; i <= n; i++) {
        cin >> fa[i];
    }
    int k = 0;
    for(int i = n; i >= 2; i--) {
        if(!vis[i] && !vis[fa[i]]) {
            vis[i] = true;
            vis[fa[i]] = true;
            sum[k++] = i;
        }
    }
    cout << k*1000 << endl;
    for(int i = k-1; i >= 1; i--) {
        cout << sum[i] << " ";
    }
    cout << sum[0] << endl;

return 0;
}