Category: Swift Coding Test

Swift Coding Test Course, Exploring Geometry

Introduction

Hello! In this tutorial, we will learn how to solve geometric algorithm problems using Swift. Geometric problems are one of the frequently asked topics in coding tests, and the ability to solve problems related to points, lines, and surfaces in a coordinate system is crucial. In this article, we will present fundamental concepts of geometry, along with algorithmic problems that utilize these concepts, and we will explain the process of solving those problems in detail.

Basics of Geometry

Geometry is a branch of mathematics that studies shapes and the relationships between those shapes. The geometric objects mainly dealt with in algorithm problems include points, lines, triangles, and polygons. Various problems can be solved by utilizing the properties of these geometric figures. For example, calculating the distance between two points, whether lines intersect, and determining the perimeter and area of polygons are key aspects of geometric problems.

Problem Description

The problem at hand is to calculate the area of a polygon. You will need to write an algorithm that calculates the area of a polygon formed by connecting N given points.

Problem

Given N points, write an algorithm to calculate the area of the polygon formed by connecting these points. The points are provided in a two-dimensional plane, and their coordinates are expressed as integers.

Input

  • The first line contains an integer N (3 ≤ N ≤ 10^6).
  • In the next N lines, the X and Y coordinates of each point are given as integers.

Output

Print the area of the polygon rounded to the second decimal place.

Problem Solving Process

To design an algorithm for solving the problem, one must first understand how to calculate the area of a polygon. Generally, the most widely known method for calculating the area of a polygon is the ‘Shoelace Theorem’ (or ‘Surveyor’s Formula’). This method uses the following formula:

Shoelace Theorem

Given points (x1, y1), (x2, y2), …, (xN, yN), the area of the polygon can be calculated as follows:

= ( ∑ ( x _ i · y _ i+1 ) – ∑ ( y _ i · x _ i+1 ) ) 2

To put this very simply, you take the absolute value of the sum obtained by applying the above formula to all the points of the polygon, and divide by 2 to get the area. Now, let’s implement this in Swift.

Swift Implementation

            
                import Foundation

                struct Point {
                    var x: Int
                    var y: Int
                }

                func polygonArea(points: [Point]) -> Double {
                    var area = 0
                    let n = points.count

                    for i in 0..

With the above code, we have implemented the functionality to calculate the area of a polygon. We use structs to represent the coordinates of the points, and the polygonArea function calculates the area for the given list of points. Finally, we handle the input of these points and output the area in the main function.

Conclusion

Through this tutorial, we have learned about geometric problems and the algorithms for solving them. We wrote a program to calculate the area of a polygon using Swift, which is a very useful technique in coding tests. There are various variations of geometric problems, so it is important to have a thorough understanding of the basic concepts and to practice. Keep challenging yourself with various geometric problems to build your skills!

© 2023 Swift Coding Test Course

Swift Coding Test Course, Radix Sort

Hello! Today, we will discuss the Radix Sort algorithm using Swift. Radix Sort is an efficient algorithm that sorts by grouping similar numbers together, primarily used for sorting a set of integers.

Overview of Radix Sort

Radix Sort is a comparison-based sorting algorithm that sorts numbers or strings by breaking them into digits. Radix Sort works as follows:

  • It decomposes the given number into specific digit places.
  • It sorts starting from the least significant digit (LSB).
  • It repeats this process for higher digit places.

Radix Sort is a stable sorting algorithm, and its average and worst-case time complexity is O(nk), where n is the number of elements and k is the maximum number of digits.

Problem Description

Now let’s solve the following problem using Radix Sort.

Problem:

Sort the following integer array in ascending order using the Radix Sort algorithm:

[170, 45, 75, 90, 802, 24, 2, 66]

Solution

To solve the problem, we will implement the Radix Sort algorithm step by step. We will write the code using pre-defined functions and structures in Swift.

Step 1: Separating by Digit Places

As the first step of Radix Sort, we separate based on each digit place. To perform this task, we will create a function to extract digits according to their place value.

func getDigit(number: Int, digitIndex: Int) -> Int {
    return (number / Int(pow(10.0, Double(digitIndex)))) % 10
}

Step 2: Implementing the Radix Sort Algorithm

Now let’s implement the complete Radix Sort algorithm. We need to create an array to group by digit places and sort accordingly.

func radixSort(array: [Int]) -> [Int] {
    let maxNumber = array.max() ?? 0
    let maxDigits = String(maxNumber).count
    
    var sortedArray = array
    
    for digitIndex in 0..
func countingSort(array: [Int], digitIndex: Int) -> [Int] {
    let countArraySize = 10
    var countArray = [Int](repeating: 0, count: countArraySize)
    var outputArray = [Int](repeating: 0, count: array.count)
    
    for number in array {
        let digit = getDigit(number: number, digitIndex: digitIndex)
        countArray[digit] += 1
    }
    
    for index in 1..

Step 3: Outputting the Result

Now let's output the results using the Radix Sort algorithm. We will call the functions we implemented above to sort the given array.

let unsortedArray = [170, 45, 75, 90, 802, 24, 2, 66]
let sortedArray = radixSort(array: unsortedArray)

print("Sorted array: \(sortedArray)")

Conclusion

Radix Sort is an effective method for grouping and sorting data based on specific digit places. We were able to sort an integer array in ascending order using this algorithm. By implementing Radix Sort in Swift, we gained an understanding of the principles of the algorithm and how to systematically solve problems.

References

  • Introduction to Algorithms - Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
  • GeeksforGeeks Radix Sort article
  • Swift official documentation

Swift Coding Test Course, Representation of Graphs

1. Introduction

Understanding algorithms and data structures is crucial in the field of software development. One of the problems that frequently appears in coding tests is related to graphs. A graph is a data structure composed of nodes (vertices) and edges, allowing data to be represented in various forms. In this course, we will deepen our understanding through algorithm problems related to graph representation.

2. Graph Representation

There are mainly two ways to represent a graph.

  • Adjacency Matrix: A two-dimensional array is used to represent the presence or absence of edges for all vertices in the graph. This method is useful when the number of vertices is small. The size of the array is O(V^2).
  • Adjacency List: This method stores the connected vertices as a list for each vertex. It is memory efficient and suitable for graphs with fewer edges. The time complexity of this method is O(V + E).

3. Problem Description

We will apply the graph representation methods through the following problem.

Problem: Friend Network

You are managing a network of N friends. Friend relationships are bidirectional, meaning if two friends are directly connected, they are friends with each other. Represent the friend relationship as a graph and write a program to check if two specific friends belong to the same friend group. A friend group includes all friends that are indirectly connected.

Input Format:

N (number of friends)
M (number of friend relationships)
For M lines, two friends A and B (1 ≤ A, B ≤ N) are given.

Output Format:

Print "YES" if A and B are in the same friend group, otherwise print "NO".

4. Problem Solving Process

4.1. Graph Creation

First, we need to create a graph based on the given friend relationships. We will implement this using an adjacency list. Here is a simple Swift code for graph creation.


import Foundation

// Adjacency list for graph representation
var graph: [Int: [Int]] = [:]

// Function to add friend relations
func addFriendRelation(friendA: Int, friendB: Int) {
    graph[friendA, default: []].append(friendB)
    graph[friendB, default: []].append(friendA)
}

// Function to create graph
func createGraph(N: Int, relations: [(Int, Int)]) {
    for (A, B) in relations {
        addFriendRelation(friendA: A, friendB: B)
    }
}

The above code creates a dictionary where each friend is a key and the value is the list of connected friends.

4.2. Finding Friend Groups

Now we can use one of the graph traversal algorithms to check if two friends belong to the same group. We can use Depth-First Search (DFS) or Breadth-First Search (BFS), and we will choose DFS here. DFS allows us to explore all related friends.


func dfs(start: Int, visited: inout Set) {
    visited.insert(start)
    for friend in graph[start, default: []] {
        if !visited.contains(friend) {
            dfs(start: friend, visited: &visited)
        }
    }
}

// Function to check if two friends are in the same group
func areInSameGroup(friendA: Int, friendB: Int) -> Bool {
    var visited = Set()
    dfs(start: friendA, visited: &visited)
    return visited.contains(friendB)
}

4.3. Entire Process

Now let’s integrate the entire process to solve the problem. Here is the code to read input, create the graph, and check the relationship of two friends.


let N = Int(readLine()!)! // Number of friends
let M = Int(readLine()!)! // Number of friend relationships

var relations = [(Int, Int)]()

for _ in 0..

The above code implements the logic to represent and verify friend relationships through the overall flow.

5. Conclusion

In this course, we explored how to represent graphs and how to use basic DFS algorithms to solve problems. Graphs are useful data structures that can be applied to various problems, and it is essential to become familiar with them through sufficient practice. Since such problems often appear in coding tests, I encourage you to improve your skills by solving problems multiple times.

© 2023 Swift Coding Test Course. All Rights Reserved.

Swift Coding Test Course, Greedy Algorithm

The greedy algorithm is a method that always makes the optimal choice in the process of solving a problem, functioning as an algorithm that selects the best option based on the current state in real-time. In this course, we will help you understand the basic concepts and examples of the greedy algorithm.

Problem: Coin Change

This problem involves finding the minimum number of coins needed to give change for a given amount, given the types of coins available in the store.

Problem Description:

  • Input: Types of coins and the amount to be given as change.
  • Output: Minimum number of coins

Example Input:

Types of coins: 1, 3, 4
Amount: 6

Example Output:

2 (3 + 3)

Problem Solving Process

1. Problem Analysis

The key to this problem is expressing the amount to be given as change using the minimum number of coins based on the types of coins available. The approach of selecting the largest coin first is efficient.

2. Approach

The basic approach to solving this is as follows:

  1. Sort the given types of coins in ascending order.
  2. Use as many of the largest coin as possible.
  3. Repeat the above process for the remaining amount.
  4. Continue this process until the amount to be given as change is 0.

3. Algorithm Implementation (Swift)


func minCoins(coins: [Int], amount: Int) -> Int {
    var remainingAmount = amount
    var coinCount = 0
    var sortedCoins = coins.sorted(by: { $0 > $1 }) // Sort in descending order
    
    for coin in sortedCoins {
        while remainingAmount >= coin {
            remainingAmount -= coin
            coinCount += 1
        }
    }
    return remainingAmount == 0 ? coinCount : -1 // Return -1 if unable to give exact change
}

// Example usage
let coins = [1, 3, 4]
let amount = 6
let result = minCoins(coins: coins, amount: amount)
print("Minimum number of coins: \(result)")

The above code solves the problem by sorting the given types of coins in ascending order and then deducting from the amount using as many of the largest coins as possible while counting the number of coins used.

Result Analysis

The time complexity of this algorithm is O(n log n). (n is the number of coin types) This problem is a typical example of the greedy algorithm, which guarantees an optimal solution when the types of coins increase monotonically or follow a specific pattern.

However, the greedy algorithm does not guarantee an optimal solution in all situations, so caution is needed. For example, while it can find an optimal solution with coin types {1, 3, 4}, the result may change if the types of coins are extended to {1, 3, 4, 6}.

Through this article, I hope to enhance a basic understanding of the greedy algorithm and broaden its potential applications in practice.

Swift Coding Test Course, Finding the Sum of Intervals 3

In this lecture, we will learn how to solve the range sum problem using Swift.

Problem Description

Let’s consider the following problem.

An array A consisting of N integers and M queries are given. Each query is provided as two integers i and j, and we need to calculate the sum from A[i] to A[j].

The size of the array N and the number of queries M are as follows:

  • 1 ≤ N, M ≤ 100,000
  • -10,000 ≤ A[i] ≤ 10,000
  • 1 ≤ i ≤ j ≤ N

Input Example

The input format is as follows:

        5 3
        1 2 3 4 5
        1 3
        2 4
        1 5

In the above input, the first line represents the size of the array N and the number of queries M. The second line contains the elements of the array A. The subsequent M lines represent each query.

Output Example

The sum for each of the queries from the input should be output.

        6
        9
        15

Problem Solving Method

A efficient way to solve this problem is to use prefix sums. That is, by calculating the prefix sums of array A in advance, we can determine the sum of each query in constant time.

Step 1: Calculate Prefix Sums

Create a prefix sum array prefixSum such that prefixSum[i] stores the sum of the first element of array A up to the i-th element.

    let N = 5
    let A = [1, 2, 3, 4, 5]
    var prefixSum = [Int](repeating: 0, count: N + 1)

    for i in 1...N {
        prefixSum[i] = prefixSum[i - 1] + A[i - 1]
    }

Step 2: Process Queries

When processing the queries, use prefixSum[j] - prefixSum[i - 1] to obtain the sum from i to j. This allows the time complexity for each query to be O(1).

    let queries = [(1, 3), (2, 4), (1, 5)]
    for query in queries {
        let i = query.0
        let j = query.1
        let result = prefixSum[j] - prefixSum[i - 1]
        print(result)
    }

Complete Code

Combining the above explanations, the complete code is as follows.

    let firstLine = readLine()!.split(separator: " ").map { Int($0)! }
    let N = firstLine[0] // Size of the array
    let M = firstLine[1] // Number of queries

    let A = readLine()!.split(separator: " ").map { Int($0)! }
    var prefixSum = [Int](repeating: 0, count: N + 1)

    for i in 1...N {
        prefixSum[i] = prefixSum[i - 1] + A[i - 1]
    }

    for _ in 0..

Time Complexity


The time complexity of this algorithm is O(N + M). Here, N is the size of array A, and M is the number of queries. This is due to the O(N) for summing all elements of A and O(M) for processing M queries combined.


Conclusion


In this lecture, we learned how to use prefix sums to solve the range sum problem. This method can significantly improve performance. I encourage you to apply this technique when solving similar problems in the future.