Category: Python Coding Test

In this article, we will enhance our understanding of arrays and lists through algorithm problems and explore various techniques useful when dealing with arrays and lists. Arrays and lists are fundamental and essential parts of data structures, frequently encountered in coding tests. This course will select one algorithm problem and explain the process of solving it step by step.

Problem Description

The following is the “Problem of finding a specific number pair in a given array.”

Problem: Two Sum

Given an integer array nums and an integer target,
write a function that returns the indices of the two numbers such that they add up to target.

For example, if nums = [2, 7, 11, 15] and target = 9,
the output should be [0, 1]. (2 + 7 = 9)

Approach to the Problem

To solve this problem, several strategies can be considered. The approaches are as follows:

1. Brute Force Method: Use two nested loops to check the sum of all pairs. This has a time complexity of O(n^2).
2. Using HashMap: Iterate through the numbers, storing the index of the current number in a hash map and checking if target - current number exists in the hash map. This has a time complexity of O(n).

Solution Method

The second method of using a hash map is more efficient, so let’s use this method to solve the problem.
First, based on the given array and the target, we will follow these steps:

Step 1: Initialization

Initialize an empty hash map and set up variables to find the sum of two numbers while iterating through the array.

Step 2: Iterate through Numbers

While checking each number in the array, first check if the complement of the current number exists in the hash map.
If it does, return that index as the result. If not, add the current number and its index to the hash map.

Step 3: Return the Result

After iterating through all the numbers, if no two numbers are found that sum up to target, it does not meet the problem’s requirements.

Code Implementation

Implementing the above approach in code would look like this:

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 []
    

Code Explanation

In the above code, the two_sum function takes two parameters nums and target.
It initializes an empty hash map called num_map and iterates through nums using the enumerate function.

For each number, it calculates the complement and searches for that value in the hash map.
If found, it returns a list containing the index of that number and the current index.
If not found after checking all, it returns an empty list.

Complexity Analysis

The time complexity of this algorithm is O(n), and the space complexity is O(n).
This is due to all numbers and indices stored in the hash map.
This method is designed to efficiently find the desired pairs in the given array.

Conclusion

Arrays and lists are fundamental elements in data processing and play a significant role in various algorithm problems.
In this course, we learned how to efficiently solve the problem of “Two Sum” by exploring array indices and utilizing hash maps.
This will help save time and resolve problems in actual coding test situations.

In the future, we will deepen our understanding of data structures such as arrays, lists, and hash maps through various algorithm problems.
With continuous practice and problem-solving, I hope to become a more skilled coder. Thank you.

One of the common problems that appears in coding tests is to find the “amount of water” that satisfies certain conditions. In this course, we will teach you how to write Python code and the importance of algorithmic thinking through this problem.

Problem Description

You need to calculate the amount of water in a single reservoir. An integer array height representing the height of the reservoir is given. The reservoir consists of blocks arranged horizontally, and the height of each block is expressed as height[i].

After it rains, you need to create a function that calculates the amount of water trapped between each block and returns the total amount of trapped water.

Input

• height: A list of positive integers. (1 ≤ height.length ≤ 2 * 10^4, 0 ≤ height[i] ≤ 10^5)

Output

• An integer representing the total amount of trapped water

Examples

Example 1

Input: height = [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6

Explanation: The amount of trapped water is 6.

Example 2

Input: height = [4,2,0,3,2,5]
Output: 9

Explanation: The amount of trapped water is 9.

Problem Solving Approach

To solve this problem, you need to understand two main points:

1. To calculate the amount of trapped water at position i, you need to know the maximum heights on both sides of position i.
2. The amount of water trapped at each position can be calculated as min(left maximum height, right maximum height) - current height.

To achieve this, we will create two arrays. One will store the maximum height from the left for each position, and the other will store the maximum height from the right.

Code Implementation

Now, let’s write the actual code based on this.

def trap(height):
    if not height:
        return 0

    n = len(height)
    left_max = [0] * n
    right_max = [0] * n

    # Calculate left maximum height
    left_max[0] = height[0]
    for i in range(1, n):
        left_max[i] = max(left_max[i - 1], height[i])

    # Calculate right maximum height
    right_max[n - 1] = height[n - 1]
    for i in range(n - 2, -1, -1):
        right_max[i] = max(right_max[i + 1], height[i])

    # Calculate the amount of trapped water
    water_trapped = 0
    for i in range(n):
        water_trapped += min(left_max[i], right_max[i]) - height[i]

    return water_trapped

# Run examples
print(trap([0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]))  # Output: 6
print(trap([4, 2, 0, 3, 2, 5]))  # Output: 9

Code Explanation

1. trap(height): This function calculates the amount of water trapped.
2. It receives the height list as input and calculates the amount of water based on it.
3. Returns 0 if the list is empty.
4. Calculates the left maximum height at each index, and calculates the right maximum height.
5. Finally, it calculates the amount of trapped water using the stored maximum heights and the current height.

Time Complexity Analysis

The time complexity of this algorithm is O(n). It takes O(n) time to create the two arrays and calculate their maximum heights, and it takes another O(n) time to measure the trapped water.

Combining all steps results in a total of O(n).

Conclusion

In this course, we have learned in depth about the problem of finding the amount of water. This problem is a representative example of algorithm problem-solving and has various variations. We hope you will also practice similar problems to improve your coding skills.

Additional Practice Problems

It is recommended to practice the following variant problems:

• Find the position where the most water gets trapped in the given height array.
• Handle the case where it doesn’t rain, i.e., when the height at all positions is the same.
• Analyze how it changes when there is water flow (i.e., when the water in each block can flow into adjacent blocks).

In this lecture, we will cover the problem of counting the number of leaf nodes in a binary tree. This problem is a common topic in many coding interviews, and understanding tree structures and recursive functions is necessary to solve it.

Problem Description

Write a function to traverse the given binary tree and calculate the number of leaf nodes. A leaf node is defined as a node that has no child nodes.

Input

• A node object representing the root of the tree, given as a Node class.

Output

• An integer value representing the number of leaf nodes.

Constraints

• The tree can have a maximum of 10⁴ nodes.

Creating and Structuring a Binary Tree

A binary tree is a data structure where each node can have at most two child nodes. Essentially, a binary tree starts from the root node and is composed of child nodes. Below is a way to define the node class for a binary tree.

class Node:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

In the code above, the Node class stores the value of each node and includes pointers that reference the left and right child nodes. Now, we can use this node structure to create a binary tree.

Counting Leaf Nodes

A leaf node is a node that has no child nodes, and to count them, we need to traverse the tree. Generally, there are three methods to traverse a binary tree: preorder, inorder, and postorder. Here, we will look at how to count leaf nodes using postorder traversal.

Postorder Traversal Algorithm

Postorder traversal is conducted through the following steps:

1. Traverse the left subtree in postorder.
2. Traverse the right subtree in postorder.
3. Visit the current node.

Using this process, we can verify whether a parent node is a leaf node. If it is a leaf node, we increase the counter to count the number of leaf nodes.

Code Implementation

def count_leaf_nodes(root):
    if root is None:
        return 0
    if root.left is None and root.right is None:
        return 1
    return count_leaf_nodes(root.left) + count_leaf_nodes(root.right)

The above count_leaf_nodes function recursively traverses the binary tree to calculate the number of leaf nodes.

Detailed Explanation of the Problem-Solving Process

Let’s take a step-by-step look at how to solve this problem.

Step 1: Basic Tree Creation

To create a binary tree, we need to define a few nodes. For example, let us consider a tree like the following.

# Create a binary tree
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.right.left = Node(6)

The code above constructs the following binary tree:

Step 2: Testing the Basic Function

Now, we can use the count_leaf_nodes function we implemented to calculate the number of leaf nodes.

leaf_count = count_leaf_nodes(root)
print(f"Number of leaf nodes: {leaf_count}")

Executing the above code will output the number of leaf nodes in the binary tree. In this case, there are 3 leaf nodes (4, 5, 6), so the output will be “Number of leaf nodes: 3”.

Time Complexity Analysis

The time complexity of the above algorithm is O(n), since it visits all nodes present in the tree. n represents the number of nodes.

Conclusion

In today’s lecture, we addressed the problem of counting leaf nodes in a binary tree. In this process, we applied recursive approaches and the concept of postorder traversal. This problem frequently appears not only in coding tests but also in practical development, so be sure to understand it thoroughly.

In the next lecture, we will explore binary trees in greater depth and cover various tree problems. Thank you.

Coding tests are now an essential requirement in the hiring processes of many companies. In particular, coding tests using Python are favored by many developers due to their simplicity and clarity. However, the importance of debugging skills in these coding tests is often overlooked. In this article, we will explore the significance of debugging through a simple algorithm problem.

Algorithm Problem: Calculate the Sum of the Digits of a Given Number

Let’s solve the following problem:

Given a non-negative integer N that is less than or equal to 10,000, write a function to calculate the sum of the digits of N. For example, if N is 1234, the return value should be 10.

Approach to Problem Solving

First, we need to clearly understand the requirements of the problem before diving into the solution. We need to think about how to separate the digits of the given N and how to sum them. We can approach it in the following steps:

1. Take the input as a numerical value.
2. Convert N to a string to separate each digit.
3. Convert each digit back to an integer and sum them all.
4. Return the result.

Function Implementation

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

def sum_of_digits(n):
    if not (0 <= n <= 10000):
        raise ValueError("N must be an integer between 0 and 10,000.")

    # Convert N to a string to separate each digit
    digits = str(n)
    # Convert each digit to an integer and calculate the total
    total = sum(int(digit) for digit in digits)
    
    return total

Debugging Process

To confirm that the implemented code works properly, let’s create some test cases. However, debugging may be necessary as there could be bugs in the code.

Test Cases

print(sum_of_digits(1234))  # Expected: 10
print(sum_of_digits(987))   # Expected: 24
print(sum_of_digits(0))     # Expected: 0
print(sum_of_digits(9999))  # Expected: 36

When running the above test cases, our first case should return the expected result. However, errors may occur in the second or third cases. Let’s look at how to debug in these situations.

Debugging Techniques

Debugging is the process of analyzing code to find and fix bugs. It involves bridging the gap between the code documented by the developer and the code that actually runs. Here are some techniques you can use for debugging:

• Use Print Statements: Print intermediate values to check the flow of the code. For example, adding print(digits) can help verify each digit.
• Use Static Analysis Tools: Tools like pylint or mypy can be used to gather statistics about the code and identify problems.
• Unit Testing: You can write continuous tests using the unittest module to verify that each function works as intended.
• Use Debugging Tools: Use debugging tools provided by your IDE to step through the program and track variable values.

Code Improvement

While it’s possible to write compact code, it is advisable to write code explicitly for the sake of readability. Additionally, it's crucial to handle exceptions relevant to each situation.

Final Code
Exception Handling and Comments Added

def sum_of_digits(n):
    """Returns the sum of the digits of the given number N."""
    if not (0 <= n <= 10000):
        raise ValueError("N must be an integer between 0 and 10,000.")

    total = sum(int(digit) for digit in str(n))
    
    return total
# Tests
for test_case in [1234, 987, 0, 9999, -1, 10001]:
    try:
        print(f"The sum of the digits of N={test_case}: {sum_of_digits(test_case)}")
    except ValueError as e:
        print(e)  # Exception handling

The Importance of Debugging

Debugging goes beyond simply fixing bugs and holds several important values:

• Enhanced Problem-Solving Skills: You can train your ability to approach complex problems logically.
• Increased Code Comprehension: It helps in understanding both your code and the code of others.
• Improved Code Quality: Continuous debugging and review can enhance the quality of the code.
• Better Collaboration Experience: Smooth communication with team members allows for better understanding and modification of the code.

Conclusion

Today, we explored the algorithm design and implementation process in coding tests as well as the importance of debugging through a simple algorithm problem. Debugging is not just about fixing errors; it provides an opportunity to grow as a developer. Hence, it is advisable not to underestimate this aspect and to actively apply it in future coding tests and projects.