1079. Total Sales of Supply Chain (25)

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. Only the retailers will face the customers. 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 total sales from all the 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 their ID's are numbered from 0 to N-1, and the root supplier's ID is 0); P, the unit price given by the root supplier; and r, the percentage rate of price increment for each distributor or retailer. Then N lines follow, each describes a distributor or retailer in the following format:

K_i ID[1] ID[2] ... ID[K_i]

where in the i-th line, K_i is the total number of distributors or retailers who receive products from supplier i, and is then followed by the ID's of these distributors or retailers. K_j being 0 means that the j-th member is a retailer, then instead the total amount of the product will be given after K_j. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in one line the total sales we can expect from all the retailers, accurate up to 1 decimal place. It is guaranteed that the number will not exceed 10¹⁰.

Sample Input:

10 1.80 1.00
3 2 3 5
1 9
1 4
1 7
0 7
2 6 1
1 8
0 9
0 4
0 3

Sample Output:

42.4


解题思路：本题主要是利用邻接表来对供应链关系的记录，如图1所示，所给测试例子中，用一个vector来记录每个供应链中的价格分布（原价假设为0），0->2，时，2的价格变为0的1.01倍（r==0.01），当1->9时，9的价格为1的1.01倍，但由于此时1的价格未定，所以利用邻接表先存储1->9的关系，单5->1时，1的价格确定了，即可利用邻接表对和1临接的进行更新，更新9的价格为1.03：

图 1

#include<iostream>
#include<cstdio>
#include<vector>
#include<map>
using namespace std;
struct Node{
	vector<int>next;
};
vector<double>price;
map<int,int>result;
vector<Node>vt;
void update(int num,int r){
	if(vt[num].next.empty())return;
	if(result.find(num)!=result.end())return ;
	vector<int>cur=vt[num].next;
	int size=cur.size();
	for(int i=0;i<size;i++){
		price[cur[i]]=price[num]*(1+r*1.0/100);
		update(cur[i],r);
	}
}
int main(){
	int n;
	double p,r;
	scanf("%d%lf%lf",&n,&p,&r);
	price.resize(n);
	vt.resize(n);
	int i,j;
	int num;
	price[0]=p;
	for(i=0;i<n;i++){
		scanf("%d",&j);
		if(j==0){
			scanf("%d",&num);
			result.insert(make_pair(i,num));
		}else{
			while(j--){
				scanf("%d",&num);
				vt[i].next.push_back(num);
				price[num]=price[i]*(1+r*1.0/100);
				update(num,r);			
			}
		}
	}
	double sum=0;
	for(map<int,int>::iterator it=result.begin();it!=result.end();it++){
		sum=sum+price[it->first]*it->second;
	}
	printf("%.1lf
",sum);
	return 0;
}