Author: root

Python Coding Test Course, Gift Delivery

Problem Description

One day, a special event for gift delivery was held in a village. The purpose of this event is to deliver gifts among different people. There are n participants, and each participant must deliver exactly one gift. However, there are constraints on whom they can deliver gifts to.

Each participant has a list or array that indicates who they can deliver their gifts to. Considering these constraints, we need to determine whether all participants can deliver gifts, meaning whether every participant can receive a gift.

Input Format

The first line contains the number of participants n. The next line contains a list that represents the possible recipients for each of the n participants. Each element of the list expresses the index of the participant that the corresponding participant can deliver their gift to.

Output Format

If all participants can receive gifts, print ‘YES’; otherwise, print ‘NO’.

Example Input

5
1 2 3 4 0

Example Output

YES

Solution Method

This problem can be viewed similarly to the “cycle detection” problem in graph theory. Each participant can be represented as a node, and the relationships of whom they can give gifts to can be expressed as edges, forming a directed graph. All nodes must be visited at least once, and if the graph has only one cycle, we can return ‘YES’.

Step-by-Step Solution Process

1. Constructing the Graph

Based on the provided information, we construct the graph in list form. Each participant’s designated recipient is represented by their index in the list.

2. Using DFS or BFS

We can traverse the graph using DFS (Depth First Search) or BFS (Breadth First Search). The goal is to determine whether all participants can receive a gift. This involves checking each node for visit status while traversing the graph.

3. Cycle Detection

We check if a cycle exists that allows every participant to give and receive gifts. This cycle must include all nodes, and if there is exactly one cycle, everyone will be able to receive a gift.

4. Implementation

Based on the above methods, we implement a Python code:

def can_give_gifts(n, connections):
    visited = [False] * n
    count = 0

    def dfs(v):
        nonlocal count
        visited[v] = True
        count += 1
        next_giver = connections[v]
        if not visited[next_giver]:
            dfs(next_giver)

    for i in range(n):
        if not visited[i]:
            count = 0
            dfs(i)
            if count < n:
                return "NO"

    return "YES"

# Test
n = 5
connections = [1, 2, 3, 4, 0]
print(can_give_gifts(n, connections))

Code Explanation

The code above is an algorithm to verify gift delivery. The 'can_give_gifts' function takes the number of participants n and the list of possible gift receivers connections as arguments. A visited list is set up to check each participant's visit status. DFS is used to visit each participant, increasing the count. If all participants are visited, it returns 'YES'; otherwise, it returns 'NO'.

Comprehensive Example

Let's examine this algorithm in action through the following example:

6
1 2 3 4 5 0

Expected Output

YES

Conclusion

This problem is a common type encountered in Python coding tests. It helps in understanding graph concepts and the method of solving problems through cycle detection. By practicing various types of problems, you can enhance your insights into algorithms.

Python Coding Test Course, Insertion Sort

Introduction

Algorithms are one of the most important topics in coding interviews. The ability to understand and implement algorithms is essential for programming and software development. In this course, we will study the Insertion Sort algorithm in depth and increase our understanding through relevant problems.

What is Insertion Sort?

Insertion Sort is a simple sorting algorithm that divides a given data set into a sorted list and an unsorted list, then takes data one by one from the unsorted list and inserts it into the correct position in the sorted list. This algorithm is intuitive and has the advantage of being easy to implement.

How Insertion Sort Works

Insertion Sort works through the following steps:

  1. Starting from the second element, each element is compared to the current element (C).
  2. If the current element (C) is smaller than the previous element (A) of the sorted list, the current element (C) is inserted into the correct position in the sorted list.
  3. This process is repeated until the end of the array is reached, ultimately yielding a sorted array.

Time Complexity of Insertion Sort

The time complexity of Insertion Sort is O(n^2) in the worst case, O(n) in the best case, and O(n^2) on average. It is generally efficient when the data is nearly sorted. However, its performance can degrade when the data is distributed randomly.

Problem: Implement Insertion Sort

Let’s solve the following problem.


Problem: Sort the given list of integers using Insertion Sort.

Input: [5, 2, 9, 1, 5, 6]
Output: [1, 2, 5, 5, 6, 9]

Solution Process

To solve the problem above, we will implement the Insertion Sort algorithm. Below is the code that implements Insertion Sort using Python.


def insertion_sort(arr):
    # Start from the second element of the list
    for i in range(1, len(arr)):
        key = arr[i]  # Current element
        j = i - 1  # Previous index of the current element

        # Find the correct position in the sorted list
        while j >= 0 and key < arr[j]:
            arr[j + 1] = arr[j]  # Move the element to the right
            j -= 1  # Decrease the index
        
        arr[j + 1] = key  # Insert the current element in the correct position
    return arr

# Example list
example_list = [5, 2, 9, 1, 5, 6]
sorted_list = insertion_sort(example_list)
print(sorted_list)

Explanation of the Code

The code above has the following structure:

  1. def insertion_sort(arr): - Defines the Insertion Sort function.
  2. for i in range(1, len(arr)): - Begins the iteration from the second element.
  3. key = arr[i] - Stores the current element.
  4. while j >= 0 and key < arr[j]: - Looks for an element in the sorted list that is larger than the current element.
  5. arr[j + 1] = arr[j] - Moves the element to the right to make space.
  6. arr[j + 1] = key - Inserts the current element in the correct position.
  7. Finally, it returns the sorted array.

Advantages and Disadvantages of Insertion Sort

Advantages

  • It is simple and intuitive to implement.
  • It is particularly efficient when the data is nearly sorted.
  • As an in-place sorting algorithm, it uses little additional space.

Disadvantages

  • Its time complexity of O(n^2) does not offer good performance in absolute terms.
  • It is inefficient when the data is distributed randomly.

Conclusion

In this course, we learned about the Insertion Sort algorithm. Insertion Sort is a simple yet useful sorting algorithm that can often appear in coding tests. Understanding the principles of the algorithm and practicing its rigorous implementation is important to solve given problems. In the next course, we will cover another sorting algorithm.

References

Python Coding Test Course, Dictionary Search

Problem Description

A person wants to find a word in a dictionary. This dictionary contains words sorted in alphabetical order. Write a program to find the first occurrence of a given word in the dictionary.

The input consists of a sorted list of words and the word to be searched. If the word does not exist in the dictionary, return -1.

Input Format

  • List of words: words (in list form, each word as a string)
  • The word to search for: target (string)

Output Format

Return the index of the word to be searched (0-based index). If the word does not exist, return -1.

Example

    Input: 
    words = ["apple", "banana", "cherry", "date", "fig", "grape"]
    target = "cherry"

    Output: 2

Approach to the Problem

This problem can be solved using the Binary Search algorithm. Binary search is an efficient algorithm for finding a specific value in sorted data, with a time complexity of O(log n).

Overview of the Binary Search Algorithm

Binary search proceeds as follows:

  1. Find the middle element of the list.
  2. Check if the middle element matches the value being searched for.
  3. If it matches, return the index of the middle element.
  4. If it does not match, continue searching in the left part if the value to be searched is smaller than the middle element, or in the right part if it is larger.
  5. Repeat this process until the condition is satisfied.

Implementation

Here we will implement the binary search algorithm using Python. Below is the dictionary-finding function using binary search.

def binary_search(words, target):
    left, right = 0, len(words) - 1

    while left <= right:
        mid = (left + right) // 2
        if words[mid] == target:
            return mid
        elif words[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

Code Explanation

The above binary_search function operates as follows:

  1. Use left and right variables to set the search range. The initial values are 0 and len(words) - 1, respectively.
  2. Using the while left <= right loop, repeat until the search range is valid.
  3. Calculate the middle index mid (through integer division).
  4. If words[mid] is equal to target, return mid to return the index.
  5. If not, update left to mid + 1 if words[mid] is less than target, or update right to mid - 1 if it is larger.
  6. If the search ends without finding the target word, return -1.

Test Cases

Let’s add a few cases to test the functionality of the code.

if __name__ == "__main__":
    words = ["apple", "banana", "cherry", "date", "fig", "grape"]
    target = "cherry"
    result = binary_search(words, target)
    print(f"'{target}' is at index {result}.")  # Output: 'cherry' is at index 2.

    target = "orange"
    result = binary_search(words, target)
    print(f"'{target}' is at index {result}.")  # Output: 'orange' is at index -1.

Conclusion

In this lesson, we solved the problem of finding a specific word in a given dictionary using Python’s binary search algorithm. This algorithm is useful for quickly finding values in a sorted list and can be applied to various problems. Understanding and utilizing binary search is highly beneficial for coding tests and real programming tasks.

References

Python Coding Test Course, Finding Building Order

Problem Description

This is a problem to find the appropriate order to reconstruct buildings given the heights of buildings on a long street. Each building is represented by an array of heights, and based on that array, we need to determine the order in which those buildings were erected.

For example, if the heights of the buildings are [3, 1, 4, 1, 5], the order in which they should be built, starting from the tallest building, is as follows.

  • Building 1: Height 5
  • Building 2: Height 4
  • Building 3: Height 3
  • Building 4: Height 1
  • Building 5: Height 1

Input

An integer array heights will be given. Each element represents the height of a building.

Output

You must output the order in which the buildings should be erected in the form of a list of indices.

Example

Input: heights = [3, 1, 4, 1, 5]
Output: [4, 3, 0, 1, 2]

Solution Process

To solve this problem, we need to sort the building indices based on their height information. Below are the steps of the solution process.

Step 1: Input

First, we need to take the heights of the given buildings as input. We can declare a heights array or receive input through a function.

Step 2: Create Height-Index Pairs

Create a list of pairs containing each building’s height and index. In Python, we can easily create a list that includes indices using the enumerate function.

building_pairs = list(enumerate(heights))

Step 3: Sorting

Now we need to sort the list of buildings based on height. We can sort the list in descending order of heights using the sorted function. In this case, we specify the height as the key argument for sorting.

sorted_buildings = sorted(building_pairs, key=lambda x: x[1], reverse=True)

Step 4: Extracting Results

From the sorted list, extract the indices to create a result list. This can be easily done using list comprehension.

result = [index for index, height in sorted_buildings]

Step 5: Output the Result

Finally, we need to print the order of the buildings. All the related codes can be integrated and provided in the form of a function.

Final Code

def building_order(heights):
    building_pairs = list(enumerate(heights))
    sorted_buildings = sorted(building_pairs, key=lambda x: x[1], reverse=True)
    result = [index for index, height in sorted_buildings]
    return result

# Example usage
heights = [3, 1, 4, 1, 5]
print(building_order(heights))

Result Check

Running the code above will output [4, 3, 0, 1, 2], which represents the correct order based on the provided building heights.

Result Analysis

The indices were paired and sorted according to the heights in the array, thereby effectively deriving the order of building construction.

Python Coding Test Course, Creating Blu-ray

Problem Description

The company is trying to develop a new Blu-ray disc production system. Each Blu-ray disc has a specific size, and it must be optimized to store the maximum amount of data. Based on the given capacity of the Blu-ray and the sizes of each file, write a program that can fit as many files as possible onto the Blu-ray.

Problem Definition: Given N files, each with a positive integer size, and a given capacity C of the Blu-ray, write a program to calculate the maximum number of files that can fit without exceeding the Blu-ray’s capacity.

Input Format:
The first line contains the capacity C of the Blu-ray (1 ≤ C ≤ 10000) and the number of files N (1 ≤ N ≤ 100).
The second line contains the sizes of N files (1 ≤ file size ≤ 1000).

Output Format:
Print the maximum number of files that can fit on the Blu-ray.

Problem Analysis

This problem involves finding the maximum number of files that can be combined without exceeding the capacity C of the Blu-ray. To maximize the number of files that can fit on the Blu-ray, the files must be sorted appropriately in advance, and a suitable search method must be used to solve the problem.

The basic strategy to solve the problem is as follows:

  • Sort the file sizes in ascending order.
  • Sequentially add the sorted files until the total size exceeds the capacity C of the Blu-ray.
  • If it exceeds the capacity, stop adding files and return the count of files added so far.

Problem Solving Process

Let’s look at the process of solving the problem step by step.

Step 1: Input

First, we get the capacity of the Blu-ray, the number of files, and the sizes of the files. Input takes place via standard input. We can use Python’s input() function to receive the data.

Step 2: Data Sorting

Sort the input file sizes in ascending order. This is necessary to ensure we add the smallest files first. Python’s sorted() function can easily sort the data.

Step 3: Add Files and Sum Sizes

While iterating through the sorted file list, check if adding the current file would exceed the total capacity C of the Blu-ray. If it does not exceed, add the current file to the Blu-ray and count the number of files.

Step 4: Output Result

After iterating through all the files, output the final count of files that can fit on the Blu-ray.

Step 5: Complete Code


def maximum_files_in_blu_ray(capacity, files):
    # Sort file sizes
    files.sort()
    count = 0
    total_size = 0

    for file in files:
        if total_size + file <= capacity:
            total_size += file
            count += 1
        else:
            break

    return count

# Get input
capacity, n = map(int, input().split())
files = list(map(int, input().split()))

# Call function and output result
result = maximum_files_in_blu_ray(capacity, files)
print(result)

Example Input and Output

Example 1

Input:

10 5
1 2 3 4 5

Output:

4

Example 2

Input:

7 4
1 2 3 4

Output:

3

Result Analysis

By using the above code, we can fit the optimal number of files according to the size of the given Blu-ray. This problem serves as a fundamental example of a greedy algorithm, presenting one method that satisfies the problem's conditions.

Conclusion

In this lecture, we have learned about basic list manipulation, sorting, and searching in Python through the Blu-ray making problem. These fundamental problem-solving techniques can be very useful in actual coding tests or algorithm problems. Keep improving your skills through a variety of challenges.