1090. Highest Price in Supply Chain (25)

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本文介绍了一个供应链中产品从供应商到零售商的价格计算模型。该模型考虑了从根供应商开始，每个环节根据固定百分比增加价格的过程，并给出了计算最高零售价及其出现次数的算法实现。

A supply chain is a network of retailers（零售商）, distributors（经销商）, and suppliers（供应商）-- everyone involved in moving a product from supplier to customer.

Starting from one root supplier, everyone on the chain buys products from one's supplier in a price P and sell or distribute them in a price that is r% higher than P. It is assumed that each member in the supply chain has exactly one supplier except the root supplier, and there is no supply cycle.

Now given a supply chain, you are supposed to tell the highest price we can expect from some retailers.

Input Specification:

Each input file contains one test case. For each case, The first line contains three positive numbers: N (<=10⁵), the total number of the members in the supply chain (and hence they are numbered from 0 to N-1); P, the price given by the root supplier; and r, the percentage rate of price increment for each distributor or retailer. Then the next line contains N numbers, each number S_i is the index of the supplier for the i-th member. S_root for the root supplier is defined to be -1. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in one line the highest price we can expect from some retailers, accurate up to 2 decimal places, and the number of retailers that sell at the highest price. There must be one space between the two numbers. It is guaranteed that the price will not exceed 10¹⁰.

Sample Input:

9 1.80 1.00
1 5 4 4 -1 4 5 3 6

Sample Output:

1.85 2

#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
using namespace std;
const int maxn=100010;
vector<int> child[maxn];
double p,r;
int n,maxdepth=0,num=0;
void DFS(int index,int depth)
{
    if(child[index].size()==0)
    {
        if(depth>maxdepth)
        {
            maxdepth=depth;
            num=1;
        }
        else if(depth==maxdepth)
        {
            num++;
        }
        return;
    }
    for(int i=0;i<child[index].size();i++)
    {
        DFS(child[index][i],depth+1);
    }
}
int main()
{
    int father,root;
    scanf("%d %lf %lf",&n,&p,&r);
    r/=100;
    for(int i=0;i<n;i++)
    {
        scanf("%d",&father);
        if(father!=-1)
        {
            child[father].push_back(i);
        }
        else
        {
            root=i;
        }
    }
    DFS(root,0);
    printf("%.2f %d\n",p*pow(1+r,maxdepth),num);
    return 0;
}