Family Property

本文介绍了一个用于统计家庭成员间财产信息的算法。该算法通过输入每个家庭成员的ID、父母ID、子女数量及财产面积等数据,利用深度优先搜索(DFS)算法计算每个家庭的成员数量、平均房产数量及平均面积。

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This time, you are supposed to help us collect the data for family-owned property. Given each person's family members, and the estate(房产)info under his/her own name, we need to know the size of each family, and the average area and number of sets of their real estate.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<=1000). Then N lines follow, each gives the infomation of a person who owns estate in the format:

ID Father Mother k Child1 ... Childk M_estate Area

where ID is a unique 4-digit identification number for each person; Father and Mother are the ID's of this person's parents (if a parent has passed away, -1 will be given instead); k (0<=k<=5) is the number of children of this person; Childi's are the ID's of his/her children;M_estate is the total number of sets of the real estate under his/her name; and Area is the total area of his/her estate.

Output Specification:

For each case, first print in a line the number of families (all the people that are related directly or indirectly are considered in the same family). Then output the family info in the format:

ID M AVG_sets AVG_area

where ID is the smallest ID in the family; M is the total number of family members; AVG_sets is the average number of sets of their real estate; and AVG_area is the average area. The average numbers must be accurate up to 3 decimal places. The families must be given in descending order of their average areas, and in ascending order of the ID's if there is a tie.

Sample Input:
10
6666 5551 5552 1 7777 1 100
1234 5678 9012 1 0002 2 300
8888 -1 -1 0 1 1000
2468 0001 0004 1 2222 1 500
7777 6666 -1 0 2 300
3721 -1 -1 1 2333 2 150
9012 -1 -1 3 1236 1235 1234 1 100
1235 5678 9012 0 1 50
2222 1236 2468 2 6661 6662 1 300
2333 -1 3721 3 6661 6662 6663 1 100
Sample Output:
3
8888 1 1.000 1000.000
0001 15 0.600 100.000

5551 4 0.750 100.000

本来用并交集来写的,结果好复杂,还有bug,去网上搜了结果用 dfs 简单多了。。。

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

#define maxn 10000

struct node{
	int id;
	int num;
	double est;
	double area;
	node(int id=0, int num=0,double est=0,double area=0):id(id),num(num),est(est),area(area){}
}p[maxn];
int e[maxn],ar[maxn],f[maxn];
int id,num;
double est,area;
vector<int> t[maxn];

bool cmp(node a,node b){
if(a.area!=b.area)
		return a.area>b.area;
	return a.id<b.id;
}
void dfs(int x)
{
	id=min(id,x);
	f[x]=0;
	num++;
	est+=e[x];
	area+=ar[x];
	for(int i=0;i<t[x].size();i++){
		if(f[t[x][i]]==1)
			dfs(t[x][i]);
	}
}
int main() {
	int a;
	cin >> a;
	int total=0;
	for(int i=0;i<a;i++){
		int x,y,z;
		scanf("%d %d %d",&x,&y,&z);
		f[x]=1;
		if(y!=-1){
			f[y]=1;
			t[x].push_back(y);
			t[y].push_back(x);
		}
		if(z!=-1){
			f[z]=1;
			t[x].push_back(z);
		    t[z].push_back(x);
		}
		int b;
		scanf("%d",&b);
		for(int j=0;j<b;j++){
			scanf("%d",&z);
			f[z]=1;
			t[x].push_back(z);
		    t[z].push_back(x);
		}
		int c,d;
		scanf("%d %d",&c,&d);
		e[x]=c;
		ar[x]=d;
	}
	for(int i=0;i<10000;i++){
		if(f[i]!=1)
			continue;
		id=10000;num=0;est=0;area=0;
		dfs(i);
	    p[total++]=node(id,num,est/(double)num,area/(double)num);
	}
	sort(p,p+total,cmp);
	printf("%d\n",total);
	for (int i = 0; i < total; i++)
	    {
	        printf("%04d %d %.3lf %.3lf\n", p[i].id, p[i].num, p[i].est, p[i].area);
	    }
	return 0;
}


<think>我们正在讨论“family of facts”概念,这通常与数学教育中的基本运算(如加法和减法,或乘法和除法)相关。一个事实族指的是一组相互关联的数学事实,这些事实使用相同的数字,但以不同的方式组合。例如,在加法和减法中,对于数字3、4和7,事实族包括: 3 + 4 = 7 4 + 3 = 7 7 - 3 = 4 7 - 4 = 3 在乘法和除法中,对于数字2、5和10,事实族包括: 2 × 5 = 10 5 × 2 = 10 10 ÷ 2 = 5 10 ÷ 5 = 2 在教育环境中,事实族被用来帮助学生理解数字之间的关系和运算的可逆性。这有助于学生发展数感和心算能力。 为了准确回答,我们需要进行网络搜索,以获取关于“family of facts”的权威定义及其在教育中的使用方式。我们将重点搜索教育网站、数学教育资源和学术定义。 搜索关键词: - "family of facts definition" - "fact families in education" - "teaching fact families" - "what are fact families in math" 通过搜索,我们可以整合信息,形成清晰、详细的回答。</think>"Family of facts" (also called *fact families*) refers to a set of related arithmetic equations derived from the same set of numbers, typically focusing on inverse operations. These groups help learners understand the relationship between addition/subtraction or multiplication/division. ### Core Concept A fact family uses three numbers to create four equations: - **Addition/Subtraction Family**: For numbers $a$, $b$, and $c$ (where $c = a + b$): $$a + b = c$$ $$b + a = c$$ $$c - a = b$$ $$c - b = a$$ *Example*: Numbers 3, 5, 8 form: $3 + 5 = 8$, $5 + 3 = 8$, $8 - 3 = 5$, $8 - 5 = 3$. - **Multiplication/Division Family**: For numbers $a$, $b$, and $c$ (where $c = a \times b$): $$a \times b = c$$ $$b \times a = c$$ $$c \div a = b$$ $$c \div b = a$$ *Example*: Numbers 2, 4, 8 form: $2 \times 4 = 8$, $4 \times 2 = 8$, $8 \div 2 = 4$, $8 \div 4 = 2$. ### Educational Applications **Foundational Skill Building** Fact families introduce inverse operations, demonstrating how addition "undoes" subtraction and multiplication "undoes" division. This builds number sense and pre-algebraic thinking. **Problem-Solving Scaffolding** Students use fact families to derive missing numbers in equations. For example, knowing $7 + \_\_ = 12$ can be solved by recalling $12 - 7 = 5$ from the same family. **Visual Tools** Teachers use diagrams like *fact family triangles* or *number bonds*: ```plaintext [8] / \ [3] [5] → Equations: 3+5=8, 5+3=8, 8-3=5, 8-5=3 ``` **Curriculum Integration** - **Early Elementary (Grades 1-2)**: Focus on addition/subtraction families within 20. - **Upper Elementary (Grades 3-4)**: Extend to multiplication/division families (e.g., 6×7=42, 42÷7=6). - **Intervention**: Used to address gaps in arithmetic fluency by reinforcing core relationships. **Cognitive Benefits** - Reduces memorization burden by grouping facts. - Reinforces commutative property (e.g., $a + b = b + a$). - Supports mental math strategies (e.g., "If 9+6=15, then 15-9 must be 6"). ### Limitations and Adaptations - **Avoid overgeneralization**: Not all number sets form valid families (e.g., 3, 3, 9 works for $3×3=9$, but 3, 4, 12 does not). - **Scaffolded practice**: Begin with concrete manipulatives (counters, blocks) before abstract equations. - **Tech integration**: Digital tools like [Mathigon](https://mathigon.org/) or [Khan Academy](https://www.khanacademy.org/) offer interactive fact family exercises.
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