Finding Missing and Repeated Values

Problem Link 🔗

Problem Statement

The problem "Find Missing and Repeated Values" requires us to analyze a n x n grid containing numbers ranging from 1 to n^2. Each number appears exactly once, except for one number that appears twice, while another number is missing from the sequence.

Example

Input:

grid = [[1,3],[2,2]]

Output:

[2,4]

Explanation:

The number 2 is repeated, while 4 is missing. Therefore, the output is [2, 4].

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Algorithm

To solve this problem, follow these steps:

1. Iterate through the 2D array and convert it into a 1D array.

2. Iterate through the 1D array and find the occurrences of each element.

3. Iterate through the occurrences array and determine the missing and repeated values.

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Approach

To solve this problem efficiently, we break it down into two main steps:

1. Flatten the grid: Since the input is a 2D list, we first convert it into a 1D list for easier processing.

2. Identify the repeated and missing values: We count the occurrences of each number and determine which one appears twice and which one is missing.

Let's now walk through the code implementation step by step.

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Code Implementation and Explanation

Step 1: Flatten the Grid

The function get_combined_array() converts a 2D grid into a 1D array.

def get_combined_array(input_arr):
    combined_array = []
    for mainIndex in range(len(input_arr)):
        for subIndex in range(len(input_arr[mainIndex])):
            combined_array.append(input_arr[mainIndex][subIndex])

    return combined_array

Explanation:

• We initialize an empty list combined_array to store the flattened values.

• We iterate over the 2D list using two nested loops:

  • The outer loop iterates through each row.

  • The inner loop iterates through each element in that row.

• Each value is appended to combined_array.

Step 2: Find the Missing and Repeated Values

The function find_missing_and_repeated_values() takes the flattened array as input and identifies the repeated and missing numbers.

def find_missing_and_repeated_values(combined_array):
    n = len(combined_array)
    num_count = {}

    for num in combined_array:
        num_count[num] = num_count.get(num, 0) + 1

    repeated_value = missing_value = 0

    for num in range(1, n + 1):
        if num_count.get(num, 0) == 2:
            repeated_value = num
        elif num not in num_count:
            missing_value = num

    return [repeated_value, missing_value]

Explanation:

• We determine the length of combined_array, which represents n^2.

• We create a dictionary num_count to store the frequency of each number.

• We iterate through combined_array, updating the dictionary with the count of each number.

• Next, we loop through the numbers from 1 to n:

  • If a number appears twice, we assign it to repeated_value.

  • If a number is missing, we assign it to missing_value.

• Finally, we return [repeated_value, missing_value].

Step 3: Running the Code

The if __name__ == "__main__" block initializes the grid and executes the functions.

if __name__ == "__main__":
    grid = [[9,1,7],[8,9,2],[3,4,6]]
    combined_array = get_combined_array(grid)
    result = find_missing_and_repeated_values(combined_array)
    print(f"Final result: {result}")

Explanation:

• We define a sample 2D grid.

• We call get_combined_array(grid) to flatten the 2D list into a 1D list.

• We call find_missing_and_repeated_values(combined_array) to identify the missing and repeated numbers.

• The result is printed to the console.

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Complexity Analysis

Time Complexity

• Flattening the 2D array takes O(n^2).

• Counting occurrences takes O(n^2).

• Checking for missing/repeated values takes O(n^2).

Thus, the overall time complexity is O(n^2).

Space Complexity

• combined_array stores all n^2 elements → O(n^2).

• num_count dictionary stores at most n^2 elements → O(n^2).

• Other variables take constant space → O(1).

Thus, the overall space complexity is O(n^2).

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Topics Covered in This Solution

1. 2D Array Manipulation: Converting a grid into a 1D list.

2. Hashing (Dictionary in Python): Counting occurrences of elements efficiently.

3. Iterative Approach: Using loops to process elements systematically.

This approach is simple and easy to understand, making it suitable for beginners solving similar problems involving missing and repeated numbers.

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Thank You!

Thank you for reading!
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Happy Coding!
Darshit Anjaria