Arrays & Data Collections¶

Concept Explanation¶

What is it?¶

Arrays are fundamental data structures that allow storing multiple values of the same type in a single variable. They provide efficient access to elements using indices and are essential for implementing algorithms like searching, sorting, and data processing.

Why is it important?¶

Arrays are crucial because they form the foundation for more complex data structures and algorithms. Understanding arrays enables you to handle collections of data efficiently, implement searching and sorting algorithms, and solve real-world problems involving multiple data items.

Where is it used?¶

Data Processing: Storing and processing collections of values
Searching Algorithms: Implementing linear and binary search
Sorting Algorithms: Bubble sort, selection sort, merge sort
Matrix Operations: 2D arrays for mathematical computations
Database Applications: Storing records and query results

Real-world example¶

A student management system that stores grades of multiple students in an array. You can calculate average grades, find highest/lowest scores, or search for specific student information using array operations.

Algorithm¶

Step-by-step logic (language-agnostic): 1. Start 2. Declare and initialize array 3. Read input values into array 4. Perform array operations (search, sort, count, etc.) 5. Display results 6. End

Edge Cases: - Empty arrays - Array bounds violations (index out of range) - Duplicate elements in search operations - Memory allocation issues

Implementations¶

Java (JDK 17)Python (3.10+)C (C99)Oracle (19c)

// Java implementation here

# Python implementation here

// C implementation here

-- Oracle/SQL implementation here

Explanation¶

Java: Java-specific implementation notes using array syntax and methods
Python: Python-specific implementation notes using list operations and built-in functions
C: C-specific implementation notes using pointer arithmetic and memory management
Oracle: Oracle/SQL implementation notes using collections and table operations

Complexity Analysis¶

Time Complexity: O(n) - Linear time for basic operations, O(n log n) for efficient sorting
Space Complexity: O(1) - In-place operations, O(n) for additional storage

Flowchart¶

graph TD
    A[Start] --> B[Initialize Array]
    B --> C[Read Input Values]
    C --> D[Perform Array Operations]
    D --> E[Display Results]
    E --> F[End]

Sample Dry Run¶

Step	Array State	Operation	Result	Description
Example	[1, 5, 3, 9]	Search for 5	Found at index 1	Linear search demonstration

Practice Problems¶

Easy¶

Sum of array elements
Find minimum and maximum values
Linear search implementation

Medium¶

Array reversal algorithms
Bubble sort implementation
Count specific types of elements

Hard¶

Implement binary search
Merge sort algorithm
Matrix multiplication operations

"First, solve the problem. Then, write the code." - John Johnson

8. Remove Duplicates¶

Rating: Advanced | Difficulty: Hard Remove duplicate elements from an array (or copy unique elements to a new array).

💡 Hint

Check if an element has already appeared in the part of the array you've already processed.

9. Merge Two Arrays¶

Rating: Intermediate | Difficulty: Medium Input two arrays and merge them into a third array.

💡 Hint

Copy elements of the first array, then the second array into the new one.

10. Frequency of Elements¶

Rating: Advanced | Difficulty: Hard Count the frequency (occurrences) of each element in an array.

💡 Hint

Use a nested loop or a hash map/frequency array if the range of numbers is small.

11. 2D Array - Matrix Sum¶

Rating: Intermediate | Difficulty: Medium Input two matrices of the same size and calculate their sum.

💡 Hint

result[i][j] = matrix1[i][j] + matrix2[i][j].

12. 2D Array - Transpose¶

Rating: Intermediate | Difficulty: Medium Find the transpose of a matrix (rows become columns).

💡 Hint

transpose[j][i] = original[i][j].

13. 2D Array - Diagonal Sum¶

Rating: Intermediate | Difficulty: Medium Calculate the sum of the main diagonal elements of a square matrix.

💡 Hint

Sum elements where i == j.

14. Matrix Multiplication¶

Rating: Advanced | Difficulty: Hard Multiply two matrices (Ensure columns of A == rows of B).

💡 Hint

Use three nested loops. C[i][j] += A[i][k] * B[k][j].

15. Sparse Matrix Check¶

Rating: Pro | Difficulty: Medium Check if a matrix is a Sparse Matrix (contains more zeros than non-zero elements).

💡 Hint

Count the number of zeros and compare it with (total elements / 2).

← Previous: Loops | Next Topic: Strings →