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DSA Arrays

Arrays are one of the most fundamental data structures in computer science. They provide a way to store multiple elements in a single, ordered collection.

Think of an array like a row of lockers in a hallway: each locker has a number (index) and holds a value.

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🔹 What is an Array?

• An array is a collection of elements stored at contiguous memory locations.
• Each element can be accessed directly using its index.
• Arrays make it easy to perform operations such as searching, sorting, and iteration.

📌 Why use arrays?

• Easy to access elements by index (constant time, O(1)).
• Compact and memory-friendly compared to some other data structures.
• Widely supported across programming languages.

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🔹 Arrays in Python, Java, and C

Python Example:

my_array = [10, 25, 7, 14, 32]
print(my_array[0])   # Output: 10

👉 In Python, arrays are represented by lists.

Java Example:

int[] myArray = {10, 25, 7, 14, 32};
System.out.println(myArray[0]);  // Output: 10

C Example:

#include <stdio.h>

int main() {
    int myArray[] = {10, 25, 7, 14, 32};
    printf("%d", myArray[0]);   // Output: 10
    return 0;
}

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🔹 Array Indexing

• Arrays are zero-indexed in most programming languages.
• This means the first element is at index 0, the second at index 1, and so on.

For example:

Array: [10, 25, 7, 14, 32]
Index:   0   1   2   3   4

So, my_array[2] will give you 7.

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🔹 Algorithm: Find the Minimum Value in an Array

Let’s write our first algorithm using arrays!

Goal: Find the smallest number in an array.

Step-by-step logic:

1. Start with the first element and assume it’s the smallest.
2. Go through the array, one element at a time.
3. If you find a smaller element, update your “minimum”.
4. At the end, you’ll have the lowest value.

Pseudocode:

minVal = array[0]
for each element in array:
    if element < minVal:
        minVal = element
return minVal

Python Implementation:

my_array = [10, 25, 7, 14, 32]
minVal = my_array[0]

for value in my_array:
    if value < minVal:
        minVal = value

print("Lowest value:", minVal)

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🔹 Time Complexity Analysis

• This algorithm must check every element once.
• If the array has n elements, the loop runs n times.
• Therefore, the time complexity is O(n).

👉 If the array has:

• 5 elements → 5 comparisons
• 100 elements → 100 comparisons
• 1,000,000 elements → 1,000,000 comparisons

📊 The relationship is linear: double the input size, double the work.

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🔹 Space Complexity

• We only used one extra variable (minVal).
• This means the space complexity is O(1) (constant space).

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✅ Key Takeaways

• Arrays are ordered collections with indexed access.
• They allow fast lookups (O(1)), but some operations (like finding the minimum) require scanning the entire array.
• Understanding arrays is the first step to mastering more complex data structures.

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