1090. Highest Price in Supply Chain (25)【树】——PAT (Advanced Level) Practise

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本文介绍了一种计算供应链中零售商能期望的最高价格的方法。通过构建树形结构并进行搜索，确定从根供应商到最终零售商的价格增长过程。输入包含供应链成员数量、初始价格及价格增长率。

题目信息

1090. Highest Price in Supply Chain (25)

时间限制200 ms
内存限制65536 kB
代码长度限制16000 B
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 (<=10^5), 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 Si is the index of the supplier for the i-th member. Sroot 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

解题思路

建树搜索

AC代码

#include <cstdio>
#include <vector>
#include <cmath>
using namespace std;
int fa[100005];
vector<int> sroot, child[100005];
int maxLevel = -1, maxNum;

void dfs(int root, int lv){
    if (lv > maxLevel){
        maxLevel = lv;
        maxNum = 1;
    }else if (lv == maxLevel){
        ++maxNum;
    }
    for (int i = 0; i < child[root].size(); ++i){
        dfs(child[root][i], lv + 1);
    }
}
int main()
{
    int n, t;
    double p, r;
    scanf("%d%lf%lf", &n, &p, &r);
    for (int i = 0; i < n; ++i){
        scanf("%d", &t);
        fa[i] = t;
        if (t == -1){
            sroot.push_back(i);
        }else{
            child[t].push_back(i);
        }
    }
    int mx = 0;
    for (int i = 0; i < sroot.size(); ++i){
        dfs(sroot[i], 0);
    }
    printf("%.2f %d\n", p * pow(1+r/100, maxLevel), maxNum);
    return 0;
}