Author: root

Coding tests are one of the essential skills required in the recent IT industry. It is necessary to deeply understand the core of the problem, rather than mechanically solving it, and to utilize the correct algorithms and data structures. In this course, we will select an algorithmic problem with the theme of helping the underprivileged and explain the process of solving that problem in detail.

Problem Description

The Helping the Underprivileged program simulates the process of gathering donations from donors to meet the amount needed by welfare organizations. Donors can contribute different amounts, and when the total amount of donations reaches a specific amount, the program must output the total amount of donations and the number of donors.

Problem Definition

Implement a program that satisfies the following conditions.

• The number of donors is N. (1 ≤ N ≤ 100)
• Each donor can contribute an amount of 1,000 or more.
• Set a target amount M. (M is a natural number of 1,000 or more)

Input

The first line contains the number of donors N and the target amount M, separated by a space.

The second line contains the amounts each donor will contribute, separated by spaces.

Output

Print the total amount of donations and the number of donors. If the total amount is greater than or equal to M, also print the message “Target Achieved”.

Problem Solving Process

Now, let’s take a step-by-step look at the algorithm to solve the above problem.

Step 1: Problem Analysis

To solve the problem, we need to calculate the total amount of donations using the number of donors and the contribution amount from each donor provided as input. Then we check this total amount against the target amount M.

Step 2: Algorithm Design

The algorithm can be designed as follows:

1. Input the number of donors N and the target amount M.
2. Input the amounts donated by N donors as a list.
3. Calculate the total amount of donations by summing all the elements in the list.
4. If the total amount of donations is greater than or equal to M, output the total amount and the number of donors, including the message “Target Achieved”.
5. If not, output only the total amount and the number of donors.

Step 3: Code Implementation

Now, let’s implement the code in Python based on the algorithm designed above.

    
def main():
    # Input the number of donors N and the target amount M
    N, M = map(int, input().split())
    
    # Input the list of amounts donated by donors
    donations = list(map(int, input().split()))
    
    # Calculate the total amount of donations
    total_donations = sum(donations)
    
    # Output the result
    print(f"Total Donations: {total_donations}, Number of Donors: {N}")
    
    # Compare with the target amount
    if total_donations >= M:
        print("Target Achieved")

if __name__ == "__main__":
    main()
    
    

Step 4: Code Explanation

The above code performs the following functions:

• On the first line, it inputs the number of donors and the target amount, converting them to integers using the map function.
• On the second line, it inputs and stores the donation amounts from each donor in a list.
• It uses the sum() function to calculate the total amount of donations and outputs this amount.
• It checks whether the total amount of donations meets or exceeds the target amount and outputs a message based on that check.

Step 5: Performance Review

The time complexity of this problem is O(N). Since the maximum number of donors is 100, this level of time complexity can be considered very efficient for coding tests. The space complexity is O(N) as a list is used to store donation amounts.

Step 6: Example and Test Cases

To increase the reliability of the code, various test cases have been prepared:

Test Case 1

Input:

    5 10000
    3000 4000 2000 5000 1500
    

Output:

    Total Donations: 15500, Number of Donors: 5
    Target Achieved
    

Test Case 2

Input:

    3 20000
    5000 6000 7000
    

Output:

    Total Donations: 18000, Number of Donors: 3
    

Through these various test cases, we can verify that the code works without issues.

Conclusion

In this course, we systematically examined the process of solving a Python algorithm problem with the theme of helping the underprivileged. I would like to emphasize the importance of accurately understanding the problem and progressively building the algorithm to solve it. This process is useful not only for coding tests but also in real development environments.

I hope you will continue to build your skills through various algorithm problems and develop your problem-solving abilities. Thank you.

I Will Become the Resident Association President – Python Coding Test Course

In this article, we will cover a famous problem called “I Will Become the Resident Association President” through an algorithm problem-solving course using Python.
This problem requires a solution using dynamic programming based on the given conditions.
We will define the problem, demonstrate the method through examples, and finally write the code to solve the problem.

Problem Description

Problem:
The resident association president is a resident living in apartment number B on the A-th floor, among N residents.
The apartment has K floors, and each floor has apartments numbered from 1 to K.
The problem is to calculate the total number of residents living in apartment B on the A-th floor.
The number of residents living in apartment B on the A-th floor varies depending on the apartment number on each floor, and the rule is as follows:

• The number of residents in apartment B on the A-th floor = The number of residents in apartment 1 on the A-th floor + The number of residents in apartment 2 on the A-th floor + … + The number of residents in apartment B on the A-th floor
• The number of residents in apartment B on the 1st floor is B.

For example, if we want to know the number of residents in apartment 4 on the 3rd floor, we need to add the number of residents from apartment 1 to apartment 4 on the 3rd floor.
The problem is to find the number of residents in apartment B on the A-th floor for the given A and B.

Input and Output Format

Input:
The first line contains the number of test cases T.
Following this, A and B will be given for each test case over T lines.

Output:
For each test case, print the number of residents in apartment B on the A-th floor.

Example

Input Example:
2
1 3
2 3

Output Example:
3
6

Problem-Solving Approach

To solve this problem, we can use a dynamic programming approach.
We can create a two-dimensional table to store the number of residents for each apartment number on each floor to solve the problem.

Step 1: Table Initialization

The number of residents on the 1st floor is always the same for each apartment number, so we initialize the table based on this.

Step 2: Set Dynamic Programming Relation

The number of residents in apartment B on each floor can be expressed as the sum of the number of residents from all apartments on the previous floor.
Therefore, the recurrence relation is as follows:

    dp[A][B] = dp[A-1][1] + dp[A-1][2] + ... + dp[A-1][B]

Step 3: Repetitive Process

Using the above recurrence relation, we calculate the values for A-th floor and apartment B through a loop.
This way, we will eventually obtain the number of residents in apartment B on the A-th floor.

Code Solution

def calculate_people(A, B):
    # Function to calculate the number of residents in apartment B on the A-th floor
    dp = [[0] * (B + 1) for _ in range(A + 1)]
    
    # Initialize the 1st floor
    for j in range(1, B + 1):
        dp[1][j] = j
    
    # Calculate number of residents using dynamic programming
    for i in range(2, A + 1): # A-th floor
        for j in range(1, B + 1): # B-th apartment
            dp[i][j] = sum(dp[i-1][k] for k in range(1, j + 1))
    
    return dp[A][B]

# Processing test cases
T = int(input())
for _ in range(T):
    A, B = map(int, input().split())
    print(calculate_people(A, B))

Conclusion

Through this problem, we explored the application of dynamic programming. We could understand how important it is to analyze the problem and design an algorithm to solve the given problem.
This approach can also help in finding more efficient solutions when solving other coding test problems.

More practice is needed to solve problems effectively. I hope you can develop an algorithmic mindset by solving a variety of problems.

Wishing you a successful coding test!

Hello! Today, we will take an in-depth look at the Merge Sort algorithm, which is frequently asked in Python coding tests. Merge Sort is one of the sorting algorithms that uses the divide and conquer method to sort data. Since sorting is a crucial process in data processing, understanding and implementing this algorithm will greatly help in coding tests as well as in actual development.

What is Merge Sort?

Merge Sort works by recursively dividing the list, sorting the divided lists, and then merging them back together. The process for Merge Sort is as follows:

1. Divide the list into halves.
2. Recursively perform merge sort on each sublist.
3. Merge the two sorted sublists into one sorted list.

The characteristic of Merge Sort is that it is a stable sort algorithm, and its time complexity is O(n log n), making it very efficient. Furthermore, it guarantees a performance of O(n log n) even in the worst case, making it useful for sorting large datasets.

Time Complexity of Merge Sort

Analyzing the time complexity of Merge Sort gives us the following results:

• When the size of the input array is n, the time required to divide the array into two parts is O(1).
• Since merge sort is called recursively on each part, the depth will be log n.
• The merging stage requires O(n) time to combine the two sublists into one.

Thus, the overall time complexity is O(n log n). Additionally, Merge Sort requires O(n) of memory space.

Implementing Merge Sort

Now let’s implement Merge Sort in Python. The code below implements Merge Sort:

def merge_sort(array):
    if len(array) <= 1:
        return array

    mid = len(array) // 2
    left_half = merge_sort(array[:mid])
    right_half = merge_sort(array[mid:])

    return merge(left_half, right_half)

def merge(left, right):
    result = []
    left_index, right_index = 0, 0

    while left_index < len(left) and right_index < len(right):
        if left[left_index] <= right[right_index]:
            result.append(left[left_index])
            left_index += 1
        else:
            result.append(right[right_index])
            right_index += 1

    result.extend(left[left_index:])
    result.extend(right[right_index:])
    
    return result

# Example usage
array = [38, 27, 43, 3, 9, 82, 10]
sorted_array = merge_sort(array)
print(sorted_array)  # [3, 9, 10, 27, 38, 43, 82]

The code above consists of two functions. The merge_sort function recursively divides the array, and the merge function merges two sorted lists. To briefly explain this code, it first returns the array if its length is 1 or less. Then, it divides the array at the midpoint and calls merge_sort on each sublist again. Finally, it merges the two sublists into one sorted list using the merge function.

Checking the Result

You can sort an input array using the merge_sort function defined above, as shown below. The output will be the sorted list.

array = [38, 27, 43, 3, 9, 82, 10]
sorted_array = merge_sort(array)
print(sorted_array)  # [3, 9, 10, 27, 38, 43, 82]

Applications of Merge Sort

Merge Sort is used in many applications that require large data processing or stability. For instance, the usefulness of Merge Sort can be found in database sorting, large-scale data analysis, and data sorting in distributed systems.

Comparison of Sorting Algorithms

Merge Sort has several pros and cons compared to Quick Sort and Insertion Sort:

• Quick Sort tends to perform faster on average, but it could have a performance of O(n2) in the worst case.
• Insertion Sort performs well on small datasets, but it is inefficient for large data processing.
• Merge Sort guarantees a performance of O(n log n) at all times, making it suitable for specific problems where stability is required.

Conclusion

In this lesson, we have delved deeply into Merge Sort. Understanding Merge Sort plays an important role in grasping the basic concepts of data sorting and serves as a foundation for learning other sorting algorithms. Knowing these algorithms will greatly assist not only in preparing for coding tests but also in actual development.

I hope this lesson helps you effectively understand and utilize Merge Sort, and next time we will explore other sorting algorithms. If you have any questions, feel free to leave a comment!

In the process of preparing for coding tests, algorithms play a very important role. In particular, graph-related algorithms are frequently used in many problems, and among them, the Bellman-Ford algorithm is very efficient in solving the shortest path problem. In this course, we will learn about the Bellman-Ford algorithm in detail and solve problems using it together.

Understanding the Bellman-Ford Algorithm

The Bellman-Ford algorithm is an algorithm that finds the shortest path from one vertex to all other vertices in a directed graph. This algorithm has the following characteristics:

• The edge weights can be negative, but there must be no negative cycles.
• The time complexity is O(VE), where V is the number of vertices and E is the number of edges.
• Unlike Dijkstra’s algorithm, it can calculate the shortest paths from multiple starting vertices.

The basic idea of the Bellman-Ford algorithm is as follows. The process of updating the shortest path for each vertex is repeated. This process is repeated V-1 times to find the shortest path. If the path is still updated after V-1 repetitions, it means that there is a negative cycle.

Algorithm Steps

The basic steps of the Bellman-Ford algorithm are as follows:

1. Initialize the distance from the starting vertex to 0 and set the distance to all other vertices to infinity.
2. Repeatedly update the shortest paths for all edges. Repeat for V-1 times.
3. Finally, if the shortest path is still updated, then a negative cycle exists.

Implementing the Algorithm

Now, let’s implement the Bellman-Ford algorithm in Python. Below is a simple implementation code for the Bellman-Ford algorithm.

def bellman_ford(graph, start):
    # Step 1: Initialization
    distance = {vertex: float('infinity') for vertex in graph}
    distance[start] = 0

    # Step 2: Iteration
    for _ in range(len(graph) - 1):
        for u, edges in graph.items():
            for v, weight in edges.items():
                if distance[u] != float('infinity') and distance[u] + weight < distance[v]:
                    distance[v] = distance[u] + weight

    # Step 3: Negative cycle check
    for u, edges in graph.items():
        for v, weight in edges.items():
            if distance[u] != float('infinity') and distance[u] + weight < distance[v]:
                print("There is a negative cycle in the graph.")
                return None

    return distance

Solving a Practical Problem

Now that we understand the Bellman-Ford algorithm, let’s solve the following problem based on it.

Problem: Finding the Shortest Path

Given the following graph, find the shortest path from A to all other vertices.

A --(1)--> B
A --(4)--> C
B --(2)--> C
C --(-5)--> D

Here, each edge is represented in the form (start vertex) --(weight)--> (end vertex). This graph explores all paths from A to reach C and D. In particular, the weight of the edge from C to D is negative. Let's solve this problem using the Bellman-Ford algorithm.

Problem Solving Process

1. Define the graph.
2. Apply the Bellman-Ford algorithm to find the shortest path.
3. Print the results.

First, let's define the graph in dictionary form:

graph = {
    'A': {'B': 1, 'C': 4},
    'B': {'C': 2},
    'C': {'D': -5},
    'D': {}
}

Now let's write code that finds the shortest path using the Bellman-Ford algorithm:

start_vertex = 'A'
shortest_paths = bellman_ford(graph, start_vertex)

if shortest_paths is not None:
    print("Shortest Path:", shortest_paths)

Result Analysis

Running the above code will yield the following shortest path results:

Shortest Path: {'A': 0, 'B': 1, 'C': 3, 'D': -2}

As a result, the shortest path from A to B is 1, the shortest path from B to C is 3, and the path from C to D is -2.

Conclusion

The Bellman-Ford algorithm is very useful and can be applied to various problems. Through this course, I hope you have enhanced your understanding of the Bellman-Ford algorithm, and that it will greatly assist you in preparing for coding tests. Practicing and utilizing such algorithms is essential.

Continuously practice solving more algorithm problems and thoroughly understand and memorize the characteristics and principles of each algorithm, as this is key to preparing for coding tests.

Hello! In this blog post, we will discuss Bubble Sort, an algorithm problem-solving course for job preparation. We will understand the concept of the bubble sort algorithm and examine how to implement it during the coding test preparation process. Through this article, I hope to deepen your understanding of bubble sort’s operation, as well as compare it with other sorting algorithms based on this knowledge.

What is Bubble Sort?

Bubble Sort is one of the sorting algorithms, the simplest method of sorting data. This algorithm compares two adjacent elements and swaps their positions if they are in the wrong order. This process is repeated until the entire array is sorted. The name ‘bubble’ comes from the way the largest elements ‘float’ to the end of the array.

The Working Principle of Bubble Sort

The basic process of bubble sort is as follows:

1. Compare the first and second elements, and swap their positions if they are not in the correct order.
2. Compare the second and third elements, and swap their positions if they are not in the correct order.
3. Proceed in this manner until the end of the array. This single pass is called a pass.
4. Repeat this process until all elements of the array have been checked.

Once sorting is completed, the entire array is sorted in ascending order. Let’s look at this process with an example.

Example

Given a number array:

[5, 1, 4, 2, 8]

We will examine the process of sorting this array using the bubble sort algorithm.

Step 1: First Pass

• [5, 1, 4, 2, 8] → Compare 5 and 1 (5 > 1) → [1, 5, 4, 2, 8]
• [1, 5, 4, 2, 8] → Compare 5 and 4 (5 > 4) → [1, 4, 5, 2, 8]
• [1, 4, 5, 2, 8] → Compare 5 and 2 (5 > 2) → [1, 4, 2, 5, 8]
• [1, 4, 2, 5, 8] → Compare 5 and 8 (5 < 8) → [1, 4, 2, 5, 8]

Step 2: Second Pass

• [1, 4, 2, 5, 8] → Compare 1 and 4 (1 < 4) → [1, 4, 2, 5, 8]
• [1, 4, 2, 5, 8] → Compare 4 and 2 (4 > 2) → [1, 2, 4, 5, 8]
• [1, 2, 4, 5, 8] → Compare 4 and 5 (4 < 5) → [1, 2, 4, 5, 8]
• [1, 2, 4, 5, 8] → Compare 5 and 8 (5 < 8) → [1, 2, 4, 5, 8]

Step 3: Third Pass

• [1, 2, 4, 5, 8] → Compare 1 and 2 (1 < 2) → [1, 2, 4, 5, 8]
• [1, 2, 4, 5, 8] → Compare 2 and 4 (2 < 4) → [1, 2, 4, 5, 8]
• [1, 2, 4, 5, 8] → Compare 4 and 5 (4 < 5) → [1, 2, 4, 5, 8]
• [1, 2, 4, 5, 8] → Compare 5 and 8 (5 < 8) → [1, 2, 4, 5, 8]

We continue this process until sorting is complete. As a result, the above array is sorted to [1, 2, 4, 5, 8].

Implementing the Bubble Sort Algorithm

Now, let’s implement the bubble sort algorithm using Python. Below is a simple bubble sort program:

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        # The last n-i elements are already sorted
        for j in range(0, n-i-1):
            # Compare two adjacent elements
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]  # Swap positions
    return arr

# Example array
numbers = [5, 1, 4, 2, 8]
sorted_numbers = bubble_sort(numbers)
print(sorted_numbers)  # Output: [1, 2, 4, 5, 8]

Time Complexity of Bubble Sort

The time complexity of bubble sort is O(n²) in the worst case. This occurs because it compares all elements. However, if an already sorted array is given, it can operate normally and may have a best-case time complexity of O(n). This is when no swaps occur during each pass.

Advantages and Disadvantages of Bubble Sort

Advantages of Bubble Sort:

• It is simple to implement and easy to understand.
• The sorted state of the array can be easily observed.

Disadvantages of Bubble Sort:

• The time complexity is O(n²), making it inefficient.
• It performs poorly compared to other sorting algorithms for large datasets.

Comparison of Bubble Sort with Other Sorting Algorithms

There are various sorting algorithms, including selection sort, insertion sort, merge sort, and quick sort, in addition to bubble sort. The characteristics of each algorithm are as follows:

1. Selection Sort: Finds the minimum (or maximum) value in the array during each iteration to sort it. Its time complexity is O(n²).
2. Insertion Sort: Sorts by placing each element in its appropriate position. It has a worst-case of O(n²) and a best-case of O(n).
3. Merge Sort: Uses a divide-and-conquer approach to sort data. Its time complexity is O(n log n).
4. Quick Sort: Sorts by partitioning the array around a pivot. On average, its time complexity is O(n log n).

Tips for Studying Algorithms

Implementing and understanding basic algorithms like bubble sort is very important. I recommend the following approaches for solving algorithm problems:

• When implementing an algorithm, try writing it out by hand first, then code it.
• Create various test cases to try out.
• Share your code with others for feedback.
• Gradually increase the difficulty by solving similar problems.

Conclusion

In this post, we provided insights into the basic concepts and implementation methods of the bubble sort algorithm, as well as comparing it with other algorithms. To improve algorithm problem-solving skills, much practice is needed, and trying various problems is essential. In the next post, we will explore other sorting algorithms and discuss their differences.

Q&A

If you have any questions about this blog post, please leave a comment. I hope this helps!