Author: root

DFS (Depth-First Search) and BFS (Breadth-First Search), which frequently appear in coding tests, are fundamental methodologies for graph and tree traversal. In this course, we will implement these two algorithms in Swift and solve the problems using them.

1. Overview of DFS and BFS

DFS (Depth-First Search) explores one path to the end before exploring the next one. It uses a stack and can also be called recursively.

BFS (Breadth-First Search) explores adjacent nodes starting from the initial node and then explores the nodes at the next depth. It is mainly implemented using a queue.

2. Problem: Counting Connected Components

We will tackle the problem of counting the number of connected components in a given undirected graph. The graph consists of vertices and edges, and the goal is to find the number of connected vertices.

Problem Definition

Integer n (1 ≤ n ≤ 1000): Number of vertices
List edges: A tuple (a, b) representing the two vertices connected by each edge.

Return the number of connected components.

Input Example

n = 5
edges = [(1, 2), (2, 3), (4, 5)]

Output Example

2

3. Algorithm Explanation

Both DFS and BFS methods can be used to solve this problem. Here, we will solve it using DFS. The following steps will be taken:

• Convert the graph into an adjacency list format.
• Create an array to check whether a vertex has been visited.
• For each vertex, if there are unvisited vertices, execute DFS and mark all connected vertices as visited within the called DFS.
• Each time DFS is called, increment the number of connected components by one.

4. Swift Implementation

Let’s implement the problem in Swift.

import Foundation

var graph = [[Int]]()
var visited: [Bool] = []
var connectedComponents = 0

// Define the DFS function
func dfs(node: Int) {
    visited[node] = true
    
    for neighbor in graph[node] {
        if !visited[neighbor] {
            dfs(node: neighbor)
        }
    }
}

// Main function
func connectedComponentsCount(n: Int, edges: [(Int, Int)]) -> Int {
    graph = Array(repeating: [Int](), count: n + 1)
    visited = Array(repeating: false, count: n + 1)
    
    // Create the graph
    for edge in edges {
        let (a, b) = edge
        graph[a].append(b)
        graph[b].append(a)
    }
    
    for i in 1...n {
        if !visited[i] {
            dfs(node: i)
            connectedComponents += 1 // New connected component discovered
        }
    }
    
    return connectedComponents
}

// Example usage
let n = 5
let edges = [(1, 2), (2, 3), (4, 5)]
let result = connectedComponentsCount(n: n, edges: edges)
print("Number of connected components: \(result)") // Output: Number of connected components: 2

5. Algorithm Analysis

The algorithm above explores the graph using DFS, resulting in a time complexity of O(V + E). Here, V is the number of vertices and E is the number of edges. This is because the algorithm visits each vertex once and checks each edge once as well.

6. Conclusion

In this course, we introduced an algorithm to count the number of connected components using DFS. Both DFS and BFS are important techniques for graph traversal, so it is crucial to understand the characteristics and implementation methods of each algorithm thoroughly and practice them. In the next course, we will tackle a similar problem using BFS.

7. References

• GeeksforGeeks
• Apple Swift Documentation
• Tutorial Horizon

Hello, everyone! Today we will tackle an algorithm problem implemented in Swift. The topic is an algorithmic problem that arises in the ‘DDR (Dance Dance Revolution)’ game. This problem will be very useful for improving your understanding of Swift programming and algorithms. Let’s explain the problem first and then solve it together.

Problem Description

The problem is as follows:

Example Input

5 3
1 2 3 4 5

Example Output

3

Solution Process

Now let’s approach the problem step by step. Follow the processes below to understand the solution method.

Step 1: Input Handling

First, we need to read the number of arrows, the time limit, and the activation times of the arrows given in the input. The input data will be stored in an array. For example, in Swift, you can do the following:

import Foundation

// Input handling
let input = readLine()!.split(separator: " ").map { Int($0)! }
let n = input[0]  // Total number of arrows
let t = input[1]  // Given time (seconds)
let arrows = readLine()!.split(separator: " ").map { Int($0)! } // Arrow activation times

Step 2: Understanding the Problem

The task is to find out how many arrows can be stepped on within the given time ‘t’. In other words, we need to count the number of arrows in the arrow arrangement array from 1 to t seconds.

Step 3: Sorting the Array and Validating

After receiving the input, we need to sort the arrow activation time array. This will simplify the counting based on valid time.

let sortedArrows = arrows.sorted()

Step 4: Writing the Counting Logic

Now we simply need to count the number of arrows that satisfy the conditions. The method for counting how many arrows correspond to the given time ‘t’ is very straightforward. We can increment the count each time we encounter an arrow that is less than or equal to t while traversing the array.

var count = 0
for arrow in sortedArrows {
    if arrow <= t {
        count += 1
    } else {
        break // No need to check further
    }
}

Step 5: Output the Result

After checking all the arrows, we print the count to the console.

print(count)

Complete Code

By integrating all the above steps, we can write a program as follows:

import Foundation

// Input handling
let input = readLine()!.split(separator: " ").map { Int($0)! }
let n = input[0]  // Total number of arrows
let t = input[1]  // Given time (seconds)
let arrows = readLine()!.split(separator: " ").map { Int($0)! } // Arrow activation times

// Sorting the arrows
let sortedArrows = arrows.sorted()

// Count variable
var count = 0
for arrow in sortedArrows {
    if arrow <= t {
        count += 1
    } else {
        break
    }
}

// Output the result
print(count)

Conclusion

Thus, we have solved the DDR arrow counting problem using Swift. Algorithm problems can initially seem difficult, but it is important to organize the problem well and approach it step by step. Keep practicing various problems and enhance your Swift programming skills! Thank you!

Hello! In this article, we will cover a useful algorithm problem for preparing for coding tests, which is calculating the ATM withdrawal time. Through this problem, we will go step by step in solving it using arrays, sorting, and basic mathematical reasoning.

Problem Description

There are people lined up to withdraw money from an ATM. Each person knows the time (in seconds) it takes to use the ATM. Everyone will use the ATM in order of their line up. You need to write a program to calculate the total time taken for everyone to use the ATM.

In other words, when given an input like the following:

• Input: [3, 1, 4, 3, 2]
• Output: 32

If the first person takes 3 seconds, the second person takes 1 second, the third takes 4 seconds, and so on, the total time taken for everyone to use the ATM would be 3 + (3 + 1) + (3 + 1 + 4) + (3 + 1 + 4 + 3) + (3 + 1 + 4 + 3 + 2) = 32 seconds.

Approach to the Problem

To solve this problem, you can follow these steps:

1. Sort the times taken in ascending order.
2. Accumulate each person’s withdrawal time to calculate the total withdrawal time.

Implementation Steps

Step 1: Define and Sort Input

First, let’s sort the given times so that the fastest withdrawal times come first. To do this, we can use Swift’s sort() method.

let withdrawalTimes = [3, 1, 4, 3, 2]
let sortedTimes = withdrawalTimes.sorted()

Step 2: Calculate Total Time

Now, let’s use the sorted array to calculate the cumulative time based on each person’s withdrawal order.

var totalTime = 0
var accumulatedTime = 0

for time in sortedTimes {
    accumulatedTime += time
    totalTime += accumulatedTime
}

Step 3: Complete Code

Combining all the steps, the Swift program can be written as follows:

func calculateTotalWithdrawalTime(withdrawalTimes: [Int]) -> Int {
    let sortedTimes = withdrawalTimes.sorted()
    var totalTime = 0
    var accumulatedTime = 0

    for time in sortedTimes {
        accumulatedTime += time
        totalTime += accumulatedTime
    }
    
    return totalTime
}

let times = [3, 1, 4, 3, 2]
let total = calculateTotalWithdrawalTime(withdrawalTimes: times)
print("Total withdrawal time: \(total) seconds")

Code Explanation

The above code first receives a list of withdrawal times and sorts it, then uses a for loop to accumulate each user’s time and calculate the total time. Let’s take a closer look at each step.

• calculateTotalWithdrawalTime(withdrawalTimes: [Int]) -> Int: A function that takes withdrawal times as input and returns the total time taken.
• let sortedTimes = withdrawalTimes.sorted(): Sorts the array in ascending order using Swift’s sort feature.
• accumulatedTime += time: Accumulates each person’s withdrawal time for calculation.
• totalTime += accumulatedTime: Adds the accumulated time to the total time.

Results Confirmation

When the above code is executed, it will output that the total withdrawal time for the given times [3, 1, 4, 3, 2] is 32 seconds.

This method allows for sufficient testing with various inputs. For example:

let testTimes = [2, 5, 3, 1, 4]
let testTotal = calculateTotalWithdrawalTime(withdrawalTimes: testTimes)
print("Test withdrawal time: \(testTotal) seconds")

This will produce results corresponding to the test case.

Conclusion

In this article, we explored the process of solving the ATM withdrawal time calculation problem. This problem is a great example for practicing the basics of handling arrays, sorting, and calculating cumulative sums. Implementing the problem in Swift has deepened my understanding of the algorithm. It’s important to practice various problems of this level while preparing for coding tests.

I hope this has been helpful in your coding test preparations. If you have additional questions or problems, feel free to leave them in the comments!