Category: Python Coding Test

Problem Description

The problem we will deal with today is “Sum of Even and Odd Numbers.” This problem requires distinguishing between even and odd numbers in a given list and calculating their respective sums.
This problem is a good example of utilizing basic control structures and list processing techniques in Python.

Problem: Sum of Even and Odd Numbers

Given a list of integers, write a program that calculates and outputs the sum of even numbers and the sum of odd numbers in the list.

Input

The first line contains integers separated by spaces, where integers fall within the range of (-10⁶ ≤ integer ≤ 10⁶).

Output

Output the sum of even numbers and the sum of odd numbers separated by a space on the first line.

Example Input

    1 2 3 4 5 6 7 8 9 10
    

Example Output

    30 25
    

Problem Solving Process

Step 1: Understand the Problem

The first thing to do when faced with a problem is to clearly understand the requirements.
You need to be able to distinguish between even and odd numbers and sum them up. It is important to carefully examine the form of input and output at this stage.

Step 2: Plan

To solve the problem, we follow these steps:

1. Iterate through each number in the list.
2. Determine whether the current number is even or odd.
3. If it is even, add it to the even sum variable, and if it is odd, add it to the odd sum variable.
4. Finally, output the sums of even and odd numbers.

Step 3: Coding

Now, let’s write the actual code based on the above plan. While writing the code, we set the variables and the basic structure that will be used in the project.

    def sum_even_odd(numbers):
        even_sum = 0
        odd_sum = 0
        
        for num in numbers:
            if num % 2 == 0:
                even_sum += num
            else:
                odd_sum += num
                
        return even_sum, odd_sum
            
    # Input section
    input_numbers = list(map(int, input().split()))
    
    # Function call
    even_sum, odd_sum = sum_even_odd(input_numbers)
    
    # Output results
    print(even_sum, odd_sum)
    

Step 4: Debugging

After writing everything, we need to verify the accuracy of the code.
For instance, execute the code with various input values and check if the results match expectations.
It is also important to check whether there is handling for exceeding data ranges or exceptional situations.

Example of Error Occurrence

    input_numbers = list(map(int, input().split()))
    # In the above code, if a string is entered, a ValueError may occur.
    

To prevent this, we can use a try-except block:

    try:
        input_numbers = list(map(int, input().split()))
    except ValueError:
        print("Invalid input. Please enter integers only.")
    

Step 5: Optimization

The code can also be optimized. You can use list comprehension to make the code more concise. For example:

    even_sum = sum(num for num in input_numbers if num % 2 == 0)
    odd_sum = sum(num for num in input_numbers if num % 2 != 0)
    

Conclusion

Through problems like this, we learned to easily identify and sum even and odd numbers.
Additionally, by writing and debugging the code ourselves, we could enhance our problem-solving skills.
Ultimately, I want to emphasize that writing efficient and concise code is of utmost importance.
You can also cultivate debugging skills through various problems and further improve algorithmic problem-solving capabilities.

Exercise

In a manner similar to the above problem, try solving the following problem. Calculate the sum of prime numbers and the sum of non-prime numbers from the input list.

Implementing Prime Check Function

    def is_prime(n):
        if n <= 1:
            return False
        for i in range(2, int(n**0.5) + 1):
            if n % i == 0:
                return False
        return True
    

Write the Final Function

Hello! Today we will cover one of the frequently asked questions in Python coding tests, which is the problem of finding the minimum number of coins. This problem is particularly helpful in understanding algorithms and greedy problems and can be applied in various situations.

Problem Description

You have various coins, each with a finite quantity. You need to use the minimum number of coins to provide change for a given amount. Given the types of coins and the target amount as input, write a program that outputs the minimum number of coins needed.

Input Format

• In the first line, the number of coin types n (1 ≤ n ≤ 100) and the target amount k (1 ≤ k ≤ 10000) are given.
• In the second line, the values of n coins are given, separated by spaces. Each coin value is different and between 1 and 10,000.

Output Format

Output the minimum number of coins needed to make the target amount.

Example Input

    3 11
    1 2 5
    

Example Output

    3
    

Solution Approach

This problem can be solved using a greedy algorithm. A greedy algorithm is a method of solving a problem by choosing the option that seems best at the moment, aiming to find an optimal solution overall. In this case, we can start by using the highest value coins as much as possible.

Step-by-Step Approach

1. Start from the highest coin value and calculate the maximum number of that coin that can be used.
2. Subtract the value of the used coins from the remaining amount and move to the next highest coin.
3. Repeat this process until the target amount is reduced to 0.

Code Implementation

Now, let’s implement the Python code based on the above approach. We will write code to count the number of coins based on the given input.

    def min_coins(n, k, coins):
        # Sort coins in descending order.
        coins.sort(reverse=True)
        
        count = 0
        for coin in coins:
            # Calculate the maximum number of current coins that can be used.
            if k == 0:
                break
            count += k // coin  # How many of this coin can be used
            k %= coin  # Update the remaining amount
        
        return count

    # Input
    n, k = map(int, input().split())
    coins = list(map(int, input().split()))

    # Output result
    print(min_coins(n, k, coins))
    

Execution Result Analysis

The above code demonstrates the process of using the minimum number of coins based on the entered coin values and target amount. For example, if the coin types are [1, 2, 5] and the target amount is 11, the balance is reduced through the following process:

• Use 2 coins of 5: remaining 1 (count = 2)
• Use 1 coin of 1: remaining 0 (count = 3)

Time Complexity

The time complexity of this algorithm is O(n). Here, n is the number of given coins, and sorting the coin list takes O(n log n). Therefore, the overall time complexity can be considered O(n log n).

Precautions

One thing to be cautious of when finding the minimum number of coins is when there is no guarantee that coins will always exist. For example, if it is not possible to create the target amount, appropriate messages can be output through exception handling.

Conclusion

I hope this problem has helped enhance your understanding of greedy algorithms. Practice the algorithm by trying various combinations of coins and target amounts. Since this is a common problem in coding tests, it will be very beneficial to be familiar with it.

1. What is Dynamic Programming?

Dynamic Programming (DP) is an algorithmic approach to solving computational problems by breaking down complex problems into simpler subproblems. Generally, it improves performance by remembering the results of subproblems through a recursive approach (memoization technique), preventing repeated calculations.

Dynamic programming is primarily used for solving optimization problems and is effective in finding the optimal solution for a given problem. Many problems can be solved using dynamic programming, with Fibonacci sequences, the longest common subsequence, and the minimum edit distance problem being representative examples.

2. Applied Problem: Maximum Subarray Sum

Problem Description: This problem involves finding the maximum sum of a subarray within a given integer array. A subarray is formed by selecting contiguous elements from the array. For example, in the array [−2,1,−3,4,−1,2,1,−5,4], the maximum sum of a subarray is 6. (This is the sum of [4,−1,2,1].)

2.1 Problem Approach

This problem can be solved using dynamic programming. By iterating through each element of the array, we calculate the maximum sum that includes the current element. We compare the case where the current element is included and where it is not, selecting the larger value. We determine the maximum subarray sum for the current element by utilizing the maximum subarray sum of the previous elements.

3. Problem Solving Process

3.1 Define Variables

First, we will define the following variables:

• nums: Given integer array
• max_sum: Maximum subarray sum so far
• current_sum: Sum of the subarray up to the current position

3.2 Define the Recurrence Relation

The recurrence relation can be defined as follows:

current_sum = max(nums[i], current_sum + nums[i])

Where nums[i] is the current element. We will select the maximum value between the sum that includes the current element and the sum that does not. We then update max_sum each time.

3.3 Initialization and Loop

After initialization, we write a loop to iterate through each element and calculate the maximum sum of the subarray.

def max_sub_array(nums):
    max_sum = nums[0]
    current_sum = nums[0]

    for i in range(1, len(nums)):
        current_sum = max(nums[i], current_sum + nums[i])
        max_sum = max(max_sum, current_sum)

    return max_sum

In the code above, the first element of the array is set as the initial value, and the max_sub_array function is performed repeatedly starting from the second element.

3.4 Code Explanation

Let’s go through the code line by line:

• max_sum = nums[0]: Initializes the maximum subarray sum to the first element.
• current_sum = nums[0]: Initializes the current subarray sum to the first element.
• for i in range(1, len(nums)):: Iterates over the elements starting from the second element of the array.
• current_sum = max(nums[i], current_sum + nums[i]): Updates the current_sum.
• max_sum = max(max_sum, current_sum): Updates the max_sum.

3.5 Execution Result

print(max_sub_array([-2,1,-3,4,-1,2,1,-5,4])) # 6

Running the above code will output the maximum subarray sum 6.

4. Techniques of Dynamic Programming

4.1 Memoization and Bottom-Up Approach

Dynamic programming is typically divided into two main techniques:

• Memoization: A method that saves the results of subproblems to reduce unnecessary calculations. It uses recursive calls, checking for already computed results in each function call.
• Bottom-Up: A method that systematically solves smaller subproblems before progressing to larger ones. It is generally implemented using loops, which can reduce memory usage.

These techniques can be used to solve a variety of problems.

5. Conclusion

Dynamic programming is a very useful algorithmic technique for solving various optimization problems. Through the maximum subarray sum problem discussed in this lecture, we have learned the fundamental concepts of dynamic programming and methods for problem-solving. This can be applied to various algorithmic problem-solving and is a frequently covered topic in coding tests.

Additionally, I encourage you to practice various problems to deepen your understanding of dynamic programming. This will enhance your algorithmic thinking and help you achieve good results in coding tests.

Hello, everyone! Today, we will take a deep dive into the Dijkstra’s Algorithm and solve problems that are frequently asked in coding tests. Dijkstra’s Algorithm is an algorithm used to find the shortest path in a weighted graph, primarily used to solve network shortest path problems.

1. Overview of Dijkstra’s Algorithm

Dijkstra’s Algorithm, developed by Edsger Dijkstra in 1956, is a shortest path algorithm used to find the shortest path from a specific vertex to all other vertices. This algorithm does not allow negative weights and assumes that the graph is connected.

1.1 Algorithm Operating Principle

• Select a starting vertex and set its distance to 0.
• Initialize the distance of all other vertices to infinity.
• Select the vertex with the shortest distance among the vertices whose minimum distance has not yet been determined.
• Update the distances of adjacent vertices based on the selected vertex.
• Repeat until the distances of all vertices are determined.

2. Problem Description

Now let’s apply Dijkstra’s Algorithm through a real problem.

Problem: Find the Shortest Path

Write a program to find the shortest path from a specific starting vertex to all other vertices given a graph provided as input.

Input Conditions

• The first line contains the number of vertices V and the number of edges E. (1 ≤ V ≤ 20, 1 ≤ E ≤ 100)
• From the second line onwards, information about each edge is provided over E lines. Edge information is given in the form of the starting vertex A, ending vertex B, and weight C.
• The last line contains the starting vertex K.

Output Conditions

Output the shortest distance from the starting vertex K to all other vertices. If there is no path to any vertex, output INF.

3. Problem Solving Process

3.1 Graph Representation

First, we represent the graph as an adjacency list based on the given edge information. In Python, we can use a dictionary to store each vertex and the other vertices connected to it along with their weights.

from collections import defaultdict
import heapq

def create_graph(edges):
    graph = defaultdict(list)
    for A, B, C in edges:
        graph[A].append((B, C))
    return graph

3.2 Implementing Dijkstra’s Algorithm

Now we will implement Dijkstra’s Algorithm. This algorithm efficiently updates the shortest path found so far using a priority queue.

def dijkstra(graph, start, V):
    distances = {vertex: float('inf') for vertex in range(1, V + 1)}
    distances[start] = 0
    priority_queue = [(0, start)]

    while priority_queue:
        current_distance, current_vertex = heapq.heappop(priority_queue)

        if current_distance > distances[current_vertex]:
            continue

        for neighbor, weight in graph[current_vertex]:
            distance = current_distance + weight

            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(priority_queue, (distance, neighbor))

    return distances

3.3 Final Code

We compile all elements to write the final code, which also includes the input handling and result processing parts.

def main():
    V, E = map(int, input().split())
    edges = [tuple(map(int, input().split())) for _ in range(E)]
    K = int(input())

    graph = create_graph(edges)
    distances = dijkstra(graph, K, V)

    for vertex in range(1, V + 1):
        if distances[vertex] == float('inf'):
            print("INF")
        else:
            print(distances[vertex])

if __name__ == "__main__":
    main()

4. Time Complexity

The time complexity of Dijkstra’s Algorithm varies depending on the data structures used. Typically, when using a priority queue, the time complexity is O((V + E) log V), where V is the number of vertices and E is the number of edges.

5. Conclusion

In this lecture, we learned how to solve the shortest path problem using Dijkstra’s Algorithm and handled real input. This algorithm can be utilized in various fields such as networking and game development, so it’s good to have a firm grasp of it.

Practice various scenarios through additional problems. In the next lecture, we will look at another algorithm. Thank you!

Hello everyone! In this post, we will explore how to solve algorithm problems frequently encountered in coding tests using Python. The topic is ‘Building Bridges’. The ‘Building Bridges’ problem is a classic problem that actually has various variations, including important concepts related to graph theory.

Problem Description

There are several given islands. Each island is located in different positions, and we want to build bridges between the islands. At this time, bridges can only be constructed vertically or horizontally, and the bridges must stretch out in a straight line. Additionally, we need to minimize the total length of the bridges so that as many islands as possible can be connected.

Write a function that outputs the minimum total length of the bridges when the coordinates of the given islands are provided as (x, y).

def minimum_bridge_length(islands: List[Tuple[int, int]]) -> int:
    pass

Input

The number of islands N (2 ≤ N ≤ 10,000) and a list of coordinates (x, y) for each island will be provided.

Output

Return the minimum total length of the bridges as an integer.

Problem Solving Process

1. Understanding the Problem

The goal of the problem is to find the minimum total length of bridges connecting the given islands. The key to this problem is understanding how the bridge length between each pair of islands is calculated. If there are coordinates (x1, y1) and (x2, y2) for two islands, the bridge length between them can be calculated as |x1 – x2| + |y1 – y2|. In other words, it is the sum of the differences in the x-coordinates and y-coordinates of the islands.

2. Algorithm Design

We can solve the problem by considering all combinations of the islands to build bridges. However, since N can be as large as 10,000, considering all combinations would lead to an O(N^2) time complexity, which is inefficient. Instead, we can use a Minimum Spanning Tree (MST) algorithm to connect the bridges minimally.

To construct the MST, we can use either Kruskal’s or Prim’s algorithm. Here, we will use Prim’s algorithm. This algorithm starts from one vertex of the graph and builds the MST by adding the shortest edge one at a time.

3. Implementing Prim’s Algorithm

First, we prepare a list to store the coordinates of each island and a priority queue to store the connection costs. Then, starting from one island, we calculate the lengths of the bridges to all connected islands and repeat the process of adding the island with the shortest length.

import heapq
from typing import List, Tuple

def minimum_bridge_length(islands: List[Tuple[int, int]]) -> int:
    n = len(islands)
    visited = [False] * n
    min_heap = []
    
    # Start from the first island
    for i in range(1, n):
        dist = abs(islands[0][0] - islands[i][0]) + abs(islands[0][1] - islands[i][1])
        heapq.heappush(min_heap, (dist, i))
    
    visited[0] = True
    total_length = 0
    edges_used = 0
    
    while min_heap and edges_used < n - 1:
        dist, island_index = heapq.heappop(min_heap)
        
        if visited[island_index]:
            continue
        
        visited[island_index] = True
        total_length += dist
        edges_used += 1
        
        for i in range(n):
            if not visited[i]:
                new_dist = abs(islands[island_index][0] - islands[i][0]) + abs(islands[island_index][1] - islands[i][1])
                heapq.heappush(min_heap, (new_dist, i))
    
    return total_length

4. Complexity Analysis

The time complexity of this algorithm is O(E log V), where E is the number of edges and V is the number of vertices. However, since we do not consider all combinations and generate bridges based on each island, the actual performance is better.

5. Example

Now, let's solve an example using this algorithm.

islands = [(0, 0), (1, 1), (3, 1), (4, 0)]
print(minimum_bridge_length(islands))  # Output: 4

In the above example, we can connect the bridge from (0, 0) to (1, 1), from (1, 1) to (3, 1), and from (3, 1) to (4, 0). The total length of the bridges becomes 4.