Category: Python Coding Test

In modern society, travel provides people with various experiences and pleasures. However, planning a trip can be a challenging task. This is because several factors need to be considered, such as choosing a travel destination, coordinating dates, and managing budgets. In this course, we will address an algorithmic problem of planning a trip using Python.

Problem Definition

Implement an algorithm that recommends an appropriate travel route based on given travel destinations and distance information between them. Each destination is prioritized based on its popularity and travel time. Destinations can be visited according to the recommended priority, aiming to visit all destinations with the least distance possible.

Problem Explanation

– Input:

• List of destinations: Each destination is provided in the form of (name, popularity, location).
• Distance map: Data in the form of an adjacency matrix containing distance information between each destination.

– Output:

• List of destinations to be visited and the optimal travel route.
• Total distance required for the trip.

Problem Example

Input:
destinations = [("Seoul", 8, (37.5665, 126.978)), ("Busan", 7, (35.1796, 129.0756)), ("Jeju", 9, (33.4996, 126.5312))]
distance_map = [
    [0, 325, 450],
    [325, 0, 600],
    [450, 600, 0]
]

Output:
Travel route: ["Seoul", "Jeju", "Busan"]
Total distance: 925

Algorithm Design

To solve the problem, we will use the following approach.

• Priority Sorting: Sort the list of destinations in descending order based on popularity.
• Optimal Route Exploration: Explore all possible routes based on the sorted list.
• Distance Calculation: Calculate the total distance for each route and select the route with the least distance.

Implementation

Now, let’s implement the Python code based on the design above.

from itertools import permutations

def calculate_distance(route, distance_map):
    total_distance = 0
    for i in range(len(route) - 1):
        from_city = route[i]
        to_city = route[i + 1]
        total_distance += distance_map[from_city][to_city]
    return total_distance

def plan_trip(locations, distance_map):
    locations.sort(key=lambda x: x[1], reverse=True)  # Sort by popularity
    location_indices = {location[0]: index for index, location in enumerate(locations)}

    best_route = []
    min_distance = float('inf')

    # Explore all possible travel routes
    for perm in permutations(locations):
        route = [location[0] for location in perm]
        distance = calculate_distance(route, location_indices)
        
        if distance < min_distance:
            min_distance = distance
            best_route = route

    return best_route, min_distance

# Example execution
locations = [("Seoul", 8), ("Busan", 7), ("Jeju", 9)]
distance_map = {
    0: {0: 0, 1: 325, 2: 450},
    1: {0: 325, 1: 0, 2: 600},
    2: {0: 450, 1: 600, 2: 0},
}

best_route, total_distance = plan_trip(locations, distance_map)

print("Travel route:", best_route)
print("Total distance:", total_distance)

Code Explanation

The above code implements an algorithm to solve the travel planning problem. The plan_trip function sorts the destinations by popularity, then uses the itertools.permutations module to generate all possible combinations. The calculate_distance function calculates the total distance for each route, and the route with the shortest distance is selected.

Conclusion

Planning a trip requires considering many factors, and leveraging algorithms can help create more efficient travel plans. In this course, we explored how to find the optimal travel route by selecting travel destinations and calculating distances using Python. Developing problem-solving skills through various algorithms will also aid in your coding test preparation.

Today, I am going to write a blog post for job seekers. This tutorial will emphasize the importance of algorithms and data structures that are essential to effectively solving problems in coding tests, and I will explain how to apply them with specific examples through real problems.

1. The Necessity of Coding Tests

Many modern companies are increasingly assessing candidates’ problem-solving abilities through technical interviews. Therefore, it is important to understand the algorithms and data structures needed in practice and to develop the ability to solve problems based on them.

2. Algorithms and Data Structures: The Cornerstone

An algorithm is a set of methods by which a computer solves problems, and a data structure is a way to effectively store and manage data. These two elements are complementary to each other and are essential for solving the problems in coding tests.

3. Problem Selection: Example of an Algorithm Problem

Problem Description

Problem: Generate a password

Write a program that generates a new password by using at most two characters from the given string only once. The password can include uppercase and lowercase letters, numbers, and special characters, with a length of at least 8 and at most 16 characters.

Input

The first line contains the string to be used to generate the password.

Output

Print possible passwords, dividing them into cases that include and do not include uppercase and lowercase letters, numbers, and special characters.

Example Input

abc123@!

Example Output

abc123@!

abc123!

abc12@!

abc123

The above example shows all possible combinations of valid passwords that can be generated from the given string.

4. Problem-Solving Process

4.1. Problem Analysis

To solve the problem, we first need to analyze the given string to determine which characters are available for use. The length of the password is fixed, and the main goal is to find various combinations based on the usage of each character.

4.2. Algorithm Selection

In this problem, a backtracking algorithm can be used. During the password generation process, characters are selected, and the next character is recursively chosen based on that selection. If the selection does not meet the criteria, it is retracted, and the next character is selected.

4.3. Coding

def generate_password(s, current_password, used_chars, index): 
    if len(current_password) >= 8 and len(current_password) <= 16:
        print(current_password) 

    for i in range(index, len(s)):
        if used_chars[s[i]] < 2: 
            used_chars[s[i]] += 1 
            generate_password(s, current_password + s[i], used_chars, i + 1) 
            used_chars[s[i]] -= 1 

s = "abc123@!" 
used_chars = {char: 0 for char in s}
generate_password(s, "", used_chars, 0)

5. Code Explanation

The code above generates passwords in a recursive manner. Here is an explanation of the main parts of the code:

• generate_password: A recursive function that generates the password. It selects the next character based on the current selected password from the given string.
• used_chars: A dictionary that records how many times each character has been used. This allows for a maximum of two uses of each character.
• Condition: Prints the current password when its length is between 8 and 16 characters.

6. Time Complexity Analysis

The time complexity of this algorithm is O(n^k) in the worst case, where n is the length of the string and k is the length of the password. However, since the length of valid passwords is limited, the speed does not decrease significantly in practice.

7. Testing and Validation

After writing the code, it is important to validate the code against various input values. For example:

• Strings containing a mix of special characters, numbers, and letters
• Strings that are completely impossible to generate passwords from
• Strings containing Korean characters

8. Conclusion

The problem we reviewed today is a common type of question in coding tests, demonstrating the importance of algorithm selection. It is important to develop the ability to solve various problems through the harmony of necessary data structures and algorithms.

9. Additional Learning Resources

If you are looking for additional algorithm problem-solving resources, I recommend the following books and sites:

• Baekjoon Online Judge
• LeetCode
• Edabit
• HackerRank

10. Questions and Feedback

If you have any questions or additional feedback regarding this post, please feel free to let me know in the comments. I hope your journey to prepare for coding tests becomes easier!

Detailed guide for algorithm problem solving and understanding time complexity

Problem Description

Based on the following code, solve the problem of finding the Longest Increasing Subsequence (LIS).

Given an array of integers consisting of multiple numbers, write a function length_of_lis(nums) to determine the length of the longest increasing subsequence in this array. An increasing subsequence means that the elements of the array maintain the original order while increasing.

Input Example:

nums = [10, 9, 2, 5, 3, 7, 101, 18]

Output Example:

4  # LIS can be [2, 3, 7, 101] or [10, 18], etc.

Problem Solving Process

1. Understanding Time Complexity

To solve this problem, we must first consider the time complexity. Essentially, this problem can be solved with a time complexity of O(n^2). However, there is also a method to solve it with a time complexity of O(n log n), which can significantly improve the efficiency of the algorithm.

2. Solution Using Dynamic Programming

The dynamic programming approach to finding the longest increasing subsequence is as follows:

• Create an array dp to track the length of the LIS for each element. Initialize all values to 1 (since each element forms an increasing subsequence by itself).
• For each element, compare it with previous elements; if the current element is greater, update dp[i].
• Finally, find the maximum value in the dp array to determine the length of the LIS.

3. Code Implementation

Below is the code implemented in Python:

def length_of_lis(nums):
    if not nums:
        return 0

    dp = [1] * len(nums)  # Each element has a minimum length of 1
    for i in range(len(nums)):
        for j in range(i):
            if nums[i] > nums[j]:  # Increasing condition
                dp[i] = max(dp[i], dp[j] + 1)

    return max(dp)

4. Time Complexity Analysis

The time complexity of the above dynamic programming solution is O(n²) because there are two nested loops. However, there is also a method to solve it in O(n log n). In this method, binary search can be utilized to improve efficiency.

5. O(n log n) Approach

The O(n log n) approach uses binary search. A list is maintained to track the increasing sequence, and for each element, the appropriate position within that list is found:

import bisect

def length_of_lis(nums):
    lis = []
    for num in nums:
        pos = bisect.bisect_left(lis, num)  # Find insert position using binary search
        if pos == len(lis):
            lis.append(num)  # Add new maximum value
        else:
            lis[pos] = num  # Replace existing value
    return len(lis)

6. Running Example and Checking Results

Check if the function works properly with an example like the following:

nums = [10, 9, 2, 5, 3, 7, 101, 18]
print(length_of_lis(nums))  # Output: 4

7. Time Complexity Analysis

In the O(n log n) method, bisect.bisect_left operates in logarithmic time, so the overall time complexity is O(n log n). This provides a fast response even for large inputs, making it useful in actual coding tests.

Conclusion

This article covers the method of solving algorithm problems using Python and the concept of time complexity. Initially, the method to solve the LIS problem using dynamic programming in O(n²) was introduced, followed by improvements in efficiency using the O(n log n) method. Understanding and applying time complexity is crucial in algorithm design. I hope you continue to solve various problems and practice considering time complexity!

Hello, everyone! Today, we will take a closer look at an important concept in preparing for Python coding tests, which is time complexity. Understanding time efficiency in solving algorithm problems is essential. Therefore, this article will explain time complexity notation, how to utilize it, and how to apply it through practical problems.

1. What is Time Complexity?

Time complexity quantifies the time an algorithm takes to execute. It primarily indicates how the execution time of an algorithm varies with the input size (n). Understanding time complexity is a crucial factor in assessing the efficiency of an algorithm.

2. Notation of Time Complexity

There are several notations to represent time complexity, with the most commonly used being Big O Notation. This notation helps in understanding the worst-case execution time of an algorithm.

2.1 Big O Notation

Big O notation represents the upper bound of an algorithm and can generally be expressed in the following forms:

• O(1): Constant time
• O(log n): Logarithmic time
• O(n): Linear time
• O(n log n): Linearithmic time
• O(n²): Quadratic time
• O(2^n): Exponential time

Each notation indicates how the time required changes as the amount of data the algorithm processes increases, making it an important criterion when choosing an algorithm.

2.2 Example of Big O Notation

For example, let’s consider an algorithm that traverses the elements of an array to find a specific element. The time complexity of this algorithm is O(n). This is because the time taken to find the element increases linearly as the size of the array grows.

3. Solving Algorithm Problems

Now, let’s solve a specific algorithm problem. Here is one of the frequently asked questions.

Problem: Finding the Sum of Two Elements

Given an integer array nums and an integer target, return the indices of the two elements in nums that add up to target. Each element must be used only once, and it is guaranteed that there is exactly one solution.

Example

    Input: nums = [2, 7, 11, 15], target = 9
    Output: [0, 1]
    Explanation: nums[0] + nums[1] = 2 + 7 = 9, so return.

3.1 Problem Analysis

The key to this problem is to traverse the array and check if the sum of each element with the rest of the elements equals target. It can be solved with a time complexity of O(n²), but a more efficient solution is needed. Here, using a **hash map** allows us to solve the problem with a time complexity of O(n).

3.2 Solution Process

First, use a hash map to store each element of the array along with its index. As we traverse the array, we can check for the required values in the hash map for the current element.

Python Code Implementation

def two_sum(nums, target):
    num_map = {}
    
    for index, num in enumerate(nums):
        complement = target - num
        if complement in num_map:
            return [num_map[complement], index]
        num_map[num] = index

    return []

The code above operates by using a hash map to check the difference between the current element and target, and then returns the index of the element based on that value. It efficiently solves the problem with a time complexity of O(n).

3.3 Time Complexity Analysis

The above solution runs with two linear scans using a hash map. Therefore, the time complexity is O(n), and the additional space complexity is O(n), which is the size of the hash map.

4. Conclusion

Time complexity is a very important factor in Python coding tests. It greatly helps in evaluating the efficiency of algorithms and finding optimal solutions. I hope what we covered today helps you in solving algorithm problems. If there are parts you don’t understand or if you have additional questions, please leave a comment!

Thank you!