Category: Python Coding Test

For many developers preparing for coding tests, the average calculation problem has become a simple yet essential foundational problem.
This problem provides a great opportunity to solidify basic programming concepts through the process of calculating the average from a data set.

Problem Description

Calculate the average from the given list of integers.
The list consists of integers ranging from 1 to 100, and its length ranges from 1 to 1000.
The average should be rounded to one decimal point.

Input

• The first line contains an integer n (1 ≤ n ≤ 1000). n is the length of the list.
• The second line contains n integers. Each integer is between 1 and 100.

Output

Output the average of the list rounded to one decimal point.

Example

Input:
5
10 20 30 40 50
Output:
30.0

Problem Solving Process

1. Problem Analysis

To solve this problem, you can follow these steps:

1. Receive integers from the list.
2. Calculate the total sum of the list.
3. Divide the total sum by the length of the list (n) to calculate the average.
4. Round the calculated average to one decimal point.

2. Algorithm Design

Based on the above steps, let’s design the algorithm.
1. Get n from the user.
2. Input n integers and store them in the list.
3. Calculate the sum of the list.
4. Divide the sum by n to calculate the average.
5. Output the average.

3. Python Code Implementation

Now we will implement the above algorithm in Python code.
The code is as follows:

def calculate_average():
    # Get the length from the user
    n = int(input("Enter the length of the list: "))
    # Create the list
    numbers = list(map(int, input("Enter integers (separated by spaces): ").split()))
    
    # Validity check
    if len(numbers) != n:
        print("The number of inputted integers does not match the length of the list.")
        return
    
    # Average calculation
    total = sum(numbers)
    average = total / n
    
    # Round to one decimal place
    average_rounded = round(average, 1)
    
    # Output the result
    print(f"Average of the list: {average_rounded}")

# Function call
calculate_average()
    

4. Code Explanation

1. Getting Input: Get `n` and then input `n` integers to store them in the list `numbers`.

2. Validity Check: Check if the number of inputted integers matches `n`.
If not, output an error message and exit the function.

3. Calculate Sum and Average: Calculate the sum of the list and then calculate the average.

4. Rounding: Use the `round()` function to round the average to one decimal point.

5. Output: Finally, output the calculated average.

5. Exception Handling and Additional Considerations

– The program should handle cases where the input values do not meet the conditions.
For example, if the length of the list and the number of inputted integers differ, an error message should be displayed.

– Additionally, since the `input()` function returns a string, it needs to be converted to integers.
Here we used the `map(int, …)` function to convert all elements of the list into integers.

6. Additional Problem: Improve the Average Calculation Function

After solving the above problem, several improvements can be added.
For instance, the function could provide guidance messages to the user when receiving input.
Providing user-appropriate feedback enhances the user experience.

Conclusion

In this post, we covered the problem of calculating the average from a list.
Such foundational problems help us understand the basic syntax of Python and data processing methods.
Building basic problem-solving skills is essential before tackling more complex problems.
Keep progressing through algorithms and data handling skills step by step using Python.

Thank you!

Author: [Author Name]

Date: [Date]

Problem Definition

This is a problem of finding a list of cities that can be reached exactly at a specific distance K based on the given city and road information.
Each city is represented by a number, and the distance information between two cities is provided in the form of bidirectional roads.
The goal is to find cities that are K distance away.

For example, given N cities and M roads, and a starting city, we need to output the cities that are K distance away.

Input

• N: Number of cities (1 ≤ N ≤ 300,000)
• M: Number of roads (1 ≤ M ≤ 1,000,000)
• K: Distance information (0 ≤ K ≤ 300,000)
• X: Starting city number (1 ≤ X ≤ N)
• Road information: A, B (road from A to B)

Output

Output the numbers of cities that are exactly K distance away in ascending order. If there are no such cities, output -1.

Example

                
                Input:
                4 4 2 1
                1 2
                1 3
                2 3
                2 4

                Output:
                4
                
                

Explanation: When starting from city 1, city 4 is the only city at distance 2.

Algorithm Approach

This problem can be solved using graph search algorithms.
We will construct a graph that represents cities as nodes and roads as edges.
We will use the BFS (Breadth-First Search) algorithm to find cities that are K distance away from the starting city X.
BFS is useful for finding the shortest path and works efficiently even in large graphs, making it suitable for this problem.

Problem Solving Process

1. Graph Creation

First, we will create a graph from the road information.
We will represent the graph using a list and use a dictionary where each city is a key and the connected cities are the values.

2. Implementing BFS

We will use a queue for implementing BFS.
We add the starting city to the queue and keep track of visited cities.
For each city, we explore the cities that are K distance away.

3. Handling Output

After the BFS search, we will either sort and output the city numbers that match the K distance or output -1 if there are no cities.

Python Code

                
                from collections import deque

                def find_cities_with_distance(n, m, k, x, roads):
                    # Create the graph
                    graph = [[] for _ in range(n + 1)]
                    for a, b in roads:
                        graph[a].append(b)
                    
                    # Initialize BFS
                    distance = [-1] * (n + 1)
                    distance[x] = 0
                    queue = deque([x])
                    
                    while queue:
                        city = queue.popleft()
                        for neighbor in graph[city]:
                            if distance[neighbor] == -1:  # Unvisited city
                                distance[neighbor] = distance[city] + 1
                                queue.append(neighbor)
                    
                    # Generate results
                    result = [i for i in range(1, n + 1) if distance[i] == k]
                    return result if result else [-1]
                
                # Test case
                n = 4
                m = 4
                k = 2
                x = 1
                roads = [(1, 2), (1, 3), (2, 3), (2, 4)]
                print(find_cities_with_distance(n, m, k, x, roads))
                
            

This code uses BFS to find the cities that can be reached at a specific distance K. The graph is represented using an adjacency list and the connectivity between nodes is defined based on the edge information.

Conclusion

The “Finding Cities at a Specific Distance” problem can be efficiently solved using graph search algorithms, particularly BFS.
Through this problem, we can enhance our understanding of the basic principles of BFS, how to construct graphs, and shortest path searches.
This will serve as a stepping stone from basics to more complex graph problems.

Trees are one of the most important data structures in computer science. In particular, trees are useful for representing hierarchical relationships and are used in various algorithmic problems. This lecture will cover the problem of finding the diameter of a tree.
The diameter refers to the longest path between two nodes in the tree. This problem can be solved using DFS (Depth First Search) or BFS (Breadth First Search) algorithms.

Problem Description

Each node in the given non-empty tree is represented by an integer. Solve the problem of finding the length of the longest path between two nodes in the tree.
The input consists of the number of nodes in the tree N and N-1 edge information. The edge information is provided in a way that connects two nodes.
Specifically, the input will be given in the following format:

    N
    a1 b1
    a2 b2
    ...
    a(N-1) b(N-1)
    

Here, a and b represent the two connected nodes, respectively.

Input Example

    5
    1 2
    1 3
    2 4
    2 5
    

Output Example

    3
    

In this case, the diameter of the tree is between node 4 and node 5, with the path being 4 → 2 → 1 → 3 or 4 → 2 → 5.
Therefore, the output is 3.

Solution

To find the diameter of the tree, we can use DFS or BFS algorithms.
The general approach is as follows:

1. In the first step, perform DFS from an arbitrary node to find the farthest node.
   Let’s call this node X.
2. In the second step, perform DFS again from node X to find the farthest node, Y.
   The path between X and Y will be the diameter of the tree.

Through this process, the time complexity will be O(N), implemented by recursively calling DFS.

Python Code Implementation

Now, based on the logic above, let’s implement the code to find the diameter of the tree in Python.
Check the details of each step with the code provided below.

from collections import defaultdict

def dfs(graph, node, visited):
    visited.add(node)
    max_distance = 0
    farthest_node = node

    for neighbor in graph[node]:
        if neighbor not in visited:
            distance, next_node = dfs(graph, neighbor, visited)
            distance += 1
            
            if distance > max_distance:
                max_distance = distance
                farthest_node = next_node

    return max_distance, farthest_node

def tree_diameter(edges, n):
    graph = defaultdict(list)
    
    for a, b in edges:
        graph[a].append(b)
        graph[b].append(a)

    # Step 1: start DFS from an arbitrary node (1)
    visited = set()
    _, farthest_node = dfs(graph, 1, visited)

    # Step 2: start DFS from the farthest node found
    visited.clear()
    diameter, _ = dfs(graph, farthest_node, visited)

    return diameter

# Input reading part
n = int(input())
edges = [tuple(map(int, input().split())) for _ in range(n-1)]
print(tree_diameter(edges, n))

    

Code Explanation

The above code is structured in the following way:

• collections.defaultdict is used to create the graph in the form of an adjacency list.
  This represents the connectivity between nodes.
• dfs function performs depth-first search and calculates the distance to each node.
  It returns the farthest node and distance.
• tree_diameter function coordinates the overall process and calculates the diameter through two DFS calls.
• In the last part, it takes input from the user and calls the tree_diameter function to output the result.

Performance Analysis

The presented algorithm has a time complexity of O(N).
This is possible because it visits all nodes in the tree once through DFS.
Therefore, it can efficiently calculate the diameter even for very large trees.

Conclusion

In this lecture, we explored the diameter of trees.
We were able to efficiently solve the problem using a DFS approach.
Trees are utilized in various problems, so it is beneficial to thoroughly understand the contents of this lecture.
If you have additional questions or need practice problems, please leave a comment.

Hello! In this post, we will tackle an algorithm problem involving tree-structured data. Through the problem “Finding the Parent of a Tree”, we will understand trees and enhance our Python programming skills. The tree structure is one of the essential concepts in computer science and is widely applied in various fields such as databases, file systems, and website structures.

Problem Description

Problem: Write a function to find the parent node of a given vertex. A tree is a nonlinear data structure composed of nodes and edges, where each node can have zero or more child nodes. The input will provide the number of nodes and the parent node information for each node. We need to create a function that returns the parent node of a specific node.

Input Format:
– The first line contains the number of nodes N (1 ≤ N ≤ 100,000).
– The next N-1 lines each contain two integers A and B, indicating that A is the parent of B.

Output Format: Output the parent node number of a specific node.

Solution Approach

To solve this problem, we must first be able to form the tree structure based on the given information. We will follow the steps below to resolve the issue.

Step 1: Choose Data Structure

We will use a dictionary to implement the tree. We will use the node number as the key and the corresponding parent node as the value. This way, we can efficiently store the given relationships and quickly find the parent node.

Step 2: Process Input Data

We will read the input data and create the tree structure. We will take the number of nodes as input and add parent-child relationships over N-1 lines. This will allow us to construct the entire tree.

Step 3: Find Parent Node

To find the parent node of a specific node, we can directly query the dictionary we created earlier for that node’s parent. This can be done in constant time (`O(1)`).

Step 4: Write Function

Based on the above discussions, let’s write a Python function. Below is the code for solving the problem:

def find_parent(n, edges, query_node):
    # Dictionary to store parent node information
    parent = {}
    
    # Creating the dictionary based on the given relationships
    for a, b in edges:
        parent[b] = a
        
    # Return the parent node when requested for a specific node
    return parent.get(query_node, None)

# Example input
n = 7  # Number of nodes
edges = [(1, 2), (1, 3), (2, 4), (2, 5), (3, 6), (3, 7)]  # Parent-child relationships
query_node = 4  # Node to find the parent of

# Find parent node
print(find_parent(n, edges, query_node))

Complete Code

def find_parent(n, edges, query_node):
    parent = {}
    
    # Storing relationships in a dictionary
    for a, b in edges:
        parent[b] = a
    
    return parent.get(query_node, None)

if __name__ == "__main__":
    n = int(input("Enter the number of nodes: "))
    edges = []
    for _ in range(n - 1):
        a, b = map(int, input("Enter the parent and child relationship (e.g., 'A B'): ").split())
        edges.append((a, b))
    
    query_node = int(input("Enter the node number for which you want to find the parent: "))
    result = find_parent(n, edges, query_node)
    
    if result is not None:
        print(f"The parent of node {query_node} is {result}.")
    else:
        print(f"The parent of node {query_node} cannot be found.")

Analysis of the Solution Process

The above code solves the problem in the following structure:

• Efficiently stores parent node information using a dictionary.
• Forms the tree structure based on the given relationships.
• Allows for quick lookup of parent nodes for specific nodes.

Complexity Analysis

– Time Complexity: `O(N)` \- Stores parent node relationships proportional to the number of nodes (N).
– Space Complexity: `O(N)` \- Uses a dictionary to store node information.

Conclusion

In this post, we learned about a basic algorithm related to tree structures through the problem of “Finding the Parent of a Tree.” Trees are increasingly used in data science and software development as an efficient way to explore and store data. I believe this problem has provided a great foundation for understanding trees. In the next post, we will tackle more complex tree problems. Thank you!

This article will discuss the concept of tree data structures and algorithm problems based on this structure, providing a detailed explanation of the process to solve them.

What is a tree?

A tree is a type of non-linear data structure used to represent hierarchical relationships. A tree has the following characteristics:

• A tree consists of a collection of nodes.
• There is one root node, and the remaining nodes form subtrees based on this root node.
• Each node can have zero or more child nodes.
• A tree does not have cycles.

What types of trees are there?

Trees can be divided into various types based on their structure and rules. Here are several major types of trees:

• Binary Tree: A tree where each node has a maximum of two child nodes.
• Complete Binary Tree: A tree where every level has the maximum number of nodes.
• Balanced Binary Tree: A binary tree where the height difference is minimized.
• Binary Search Tree (BST): A tree where all values in the left subtree are smaller than the parent and all values in the right subtree are larger than the parent.
• AVL Tree: A type of balanced binary search tree.

Algorithm Problem: Maximum Depth of a Binary Tree

Let’s solve the following problem.

Problem: Given a binary tree, write a function to determine the maximum depth of the tree. The depth of the tree is the number of nodes along the longest path from the root node down to the farthest leaf node.

For example, given the following tree:

            3
           / \
          9  20
            /  \
           15   7
        

The maximum depth of this tree is 3.

Approach to Problem Solving

To solve this problem, we can traverse the nodes of the tree and calculate the depth of each node. There are various ways to calculate depth, but using Depth-First Search (DFS) makes the solution straightforward. A recursive approach can make the code concise.

Python Code Implementation

Below is the Python code to solve the given problem:

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def maxDepth(root):
    if not root:
        return 0
    else:
        left_depth = maxDepth(root.left)
        right_depth = maxDepth(root.right)
        return max(left_depth, right_depth) + 1

        

The above code takes the root node of a binary tree as input and returns the maximum depth. By using a recursive function, if the current node is not empty, it calculates the maximum depth of the left and right subtrees and adds 1 to the larger depth before returning it.

Example of Code Execution

Below is an example of creating a tree and calculating its maximum depth:

root = TreeNode(3)
root.left = TreeNode(9)
root.right = TreeNode(20)
root.right.left = TreeNode(15)
root.right.right = TreeNode(7)

print(maxDepth(root))  # Output: 3

        

When executing the above code, the result obtained is that the maximum depth of the given binary tree is 3.

Advanced Learning: Other Tree Traversal Methods

In addition to DFS, there is the Breadth-First Search (BFS) method for tree traversal. BFS uses a queue to explore nodes in level order. Below is a method for calculating maximum depth using BFS.

from collections import deque

def maxDepthBFS(root):
    if not root:
        return 0
    queue = deque([root])
    depth = 0
    while queue:
        depth += 1
        level_size = len(queue)
        for _ in range(level_size):
            node = queue.popleft()
            if node.left:
                queue.append(node.left)
            if node.right:
                queue.append(node.right)
    return depth

        

Using the BFS approach, by iterating through each level to traverse nodes, we can efficiently calculate the overall depth.

Importance of Solving Tree Problems

Tree problems are frequently featured in coding tests. As trees are complex data structures, understanding them is essential to solving difficult problems. Through tree problems, one can learn various problem-solving strategies, including recursion, BFS, DFS, and backtracking. Therefore, it is crucial to practice tree problems thoroughly to prepare for coding tests conducted by companies.

Conclusion

In this article, we explored the concept of binary trees and an algorithm problem to calculate maximum depth, examining both Depth-First Search and Breadth-First Search approaches. Tree problems form the foundation of algorithm questions and are an important topic frequently tested in actual coding interviews. Thus, it is essential to solve a variety of related problems to gain experience.

We hope you can gain diverse experiences by solving tree-related problems and enhance your algorithm understanding. Continue to study various data structures and algorithms in depth.