Hello, everyone! In this post, we will discuss a C++ algorithm problem called “Gift Exchange.” This problem focuses particularly on testing sequential thinking and algorithm design skills.
Problem Description
The gift exchange problem models the process of passing gifts among a group of people. You need to solve the problem with the following conditions.
- There are n people.
- Each person has one gift.
- Any two people can exchange gifts with each other.
Your goal is to find an optimal way to pass the gifts so that everyone receives at least one gift.
Input Format
The first line contains the number of people n, and the next n lines provide the information about the gifts each person has.
Output Format
Output the minimum gift exchange method such that everyone receives at least one gift.
Approach
To solve this problem, you need an understanding of the basics of graph theory and search algorithms like BFS or DFS. The strategy to solve the problem is as follows:
- Model the problem in the form of a graph.
- Use BFS or DFS to explore the gift exchange paths.
- Find the minimum path at each node (person) to exchange gifts.
C++ Code Implementation
Now, let’s solve the problem with C++ code. The code below is an example that implements gift exchange among people based on the given conditions.
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
struct Person {
int id;
vector<int> gifts;
};
// Graph structure for gift exchange
void giftExchange(vector<Person> &people) {
queue<int> q;
vector<bool> received(people.size(), false);
// Find people who have not received gifts and add them to the queue
for (int i = 0; i < people.size(); ++i) {
if (people[i].gifts.empty()) {
q.push(i);
}
}
while (!q.empty()) {
int current = q.front();
q.pop();
for (int giftRecipient : people[current].gifts) {
if (!received[giftRecipient]) {
cout << "Person " << current << " has delivered a gift to person " << giftRecipient << "!" << endl;
received[giftRecipient] = true;
// After delivering the gift, add the current person back to the queue
q.push(giftRecipient);
}
}
}
}
int main() {
int n;
cout << "Please enter the number of people: ";
cin >> n;
vector<Person> people(n);
for (int i = 0; i < n; ++i) {
people[i].id = i;
int m;
cout << "Please enter the number of gifts person " << i << " will give: ";
cin >> m;
for (int j = 0; j < m; ++j) {
int giftRecipient;
cout << "Please enter the ID of the person who will receive the gift from person " << i << ": ";
cin >> giftRecipient;
people[i].gifts.push_back(giftRecipient);
}
}
giftExchange(people);
return 0;
}
Code Explanation
The code above implements a C++ program to solve the gift exchange problem. Each person has a list of their gifts, and a queue is used to simulate the exchange process. Starting with those who have never received gifts, the simulation proceeds to properly exchange gifts for each person.
Code Analysis
Let’s analyze the code step by step:
- Structure Definition: The
struct Person
stores the ID of a person and the information about the gifts they will give. - Queue Initialization: Finds those who have not received gifts and adds them to the queue.
- Loop: Extracts each person from the queue one by one and processes the gift exchange.
Key Concept Explanation
This problem helps to understand the following algorithmic concepts:
- BFS Search: Simulates the gift exchange process using the Breadth-First Search (BFS) algorithm.
- Graph Modeling: Models the relationships between people and gift exchange in the form of a graph for efficient problem-solving.
Considerations After Solving the Problem
After solving the problem, consider asking yourself the following questions:
- What is the time complexity of this algorithm?
- Were there any alternative approaches?
- What other problems could be modified or derived from this problem?
Conclusion
Preparing for coding tests is important as it helps you experience various problems and improve your algorithm design skills. I hope you could learn graph exploration using DFS and BFS through the “Gift Exchange” problem. Don’t neglect practicing writing efficient code by effectively utilizing the features of the C++ language!
Next time, I will bring another interesting problem. Thank you!