1-indexed Array

A 1-indexed array is an array where the index starts at 1 rather than the typical 0. For example, the first element is at index 1, second element at index 2, and so on. The last index is equal to the array length.

1-indexed arrays can be useful in some scenarios:

  • When mapping to real-world collections that use natural counting.

  • Interfacing with languages like Matlab and Fortran that use 1-based indexing.

  • Modeling structures like pagination where pages start at page 1.

  • Solving algorithm problems defined using 1-based indexing.

However, 0-based indexing is more common in most languages and avoids off-by-one errors.

Example in Java:

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int[] arr = new int[5]; 

// Initialize 1-indexed array
arr[1] = 10; 
arr[2] = 20;

System.out.println(arr[3]); // 0 (default init)

Example in C++:

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vector<int> arr(5);

// 1-indexed assignment  
arr[1] = 5;
arr[4] = 10;

cout << arr[2]; // 0

Example in Python:

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arr = [0] * 5 

# 1-indexed populate
arr[1] = 11  
arr[3] = 20

print(arr[4]) # 0

So in summary, 1-indexed arrays start their index at 1 rather than 0, but need special handling in languages designed for 0-based indexing.

Concept: 1-Indexed Array

A 1-indexed array is an array data structure where the indices start from 1 instead of the more common 0. In most programming languages, arrays are 0-indexed by default, meaning the first element is at index 0. However, in a 1-indexed array, the first element is at index 1, the second at index 2, and so on.

Code Explanation: Java

Here’s how you can create and access a 1-indexed array in Java:

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// Creating a 1-indexed array of size 5
int[] arr = new int[6];

// Assigning values to the array
arr[1] = 10;
arr[2] = 20;
arr[3] = 30;
arr[4] = 40;
arr[5] = 50;

// Accessing elements
int elementAtIndex3 = arr[3]; // Retrieves the value 30

Code Explanation: C++ Creating and using a 1-indexed array in C++ is quite similar:

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// Creating a 1-indexed array of size 5
int arr[6];

// Assigning values to the array
arr[1] = 10;
arr[2] = 20;
arr[3] = 30;
arr[4] = 40;
arr[5] = 50;

// Accessing elements
int elementAtIndex2 = arr[2]; // Retrieves the value 20

Code Explanation: Python Python doesn’t directly support 1-indexed arrays, but you can achieve a similar effect using a list:

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# Creating a 1-indexed "array" using a list
arr = [0, 10, 20, 30, 40, 50]

# Accessing elements
element_at_index4 = arr[4]  # Retrieves the value 40

Using 1-indexed arrays can be confusing since most programming languages use 0-indexing. It’s important to be consistent with the indexing style to avoid confusion, especially when working on collaborative projects or learning from community resources.

Key Takeaways:

  • A 1-indexed array starts its indices from 1 instead of 0.
  • Java and C++ allow you to create and access 1-indexed arrays directly.
  • In Python, you can simulate 1-indexing using a list, though it’s not the conventional approach.
  • Consistency in indexing style is crucial to avoid confusion in your code and collaboration.