ArraysArrays5
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  1. 1Arrays Introduction
  2. 2Array Operations
  3. 3Array Insert Operation
  4. 4Time Complexity of Array Operations
  5. 5Space Complexity of Array Operations
StacksStacks4
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  1. 1Stacks Introduction
  2. 2Stack Operations
  3. 3Time Complexity of Stack Operations
  4. 4Space Complexity of Stack Operations
QueuesQueues4
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  1. 1Queues Introduction
  2. 2Queue Operations
  3. 3Time Complexity of Queue Operations
  4. 4Space Complexity of Queue Operations
Linked ListsLinked Lists2
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  1. 1Singly Linked List Introduction
  2. 2Doubly Linked List Introduction
TreesTrees3
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  1. 1Binary Tree Introduction
  2. 2Binary Search Tree (BST) Introduction
  3. 3Time Complexity of Binary Tree Operations
TrieTrie1
❯
  1. 1Trie Introduction

Array Insert Operation

Insertion Operation in Arrays

Insertion is an operation in arrays where a new element is added at a specific position.

Visual Example

Initial Array:

{ "array": [10, 20, 30, 40, 50], "showIndices": true }

Insert element 25 at index 2.

Desired Output

{ "array": [10, 20, 25, 30, 40, 50], "showIndices": true, "highlightIndicesGreen": [2] }

Step by step process

Given insert index is 2.

We have to shift the highlighted elements from index 2 to the right side by one position.

{ "array": [10, 20, 30, 40, 50], "showIndices": true, "highlightIndices": [2, 3, 4] }

Elements from index 2 onward are shifted one position to the right.

{ "array": [10, 20, 30, 30, 40, 50], "showIndices": true, "emptyCompIndices": [2], "highlightIndices": [3, 4, 5] }

Assign array element at index 2 with the given value 25.

{ "array": [10, 20, 25, 30, 40, 50], "showIndices": true, "highlightIndicesGreen": [2], "highlightIndices": [3, 4, 5] }

Visualization Player

Insert Operation Examples

The following examples show how to insert an element at different positions in an array, like at the beginning, in the middle, or at the end.

Array Insert Index Insert Element Output Explanation
[10, 20, 30, 40] 0 5 [5, 10, 20, 30, 40] Insert at the beginning – all elements are shifted one position to the right.
[10, 20, 30, 40] 2 25 [10, 20, 25, 30, 40] Insert at a specific index – elements from index 2 onward are shifted right.
[10, 20, 30, 40] 4 50 [10, 20, 30, 40, 50] Insert at the end – no shifting required if space is available.
[10, 20, 30, 40] 6 60 Error or undefined behavior Index 6 is out of bounds for an array of size 4. Most languages will throw an error or ignore the operation.

Step-by-Step Insertion Logic

Let’s break down the logic behind inserting an element into an array at a specified index. The array has a fixed size, so before inserting, we must ensure there’s available space. Once confirmed, we shift the elements to the right to make room for the new value.

function insertElement(array, index, value):
    if array is full:
        return error "Array is full"
    
    for i from length(array) - 1 to index:
        array[i + 1] = array[i]
    
    array[index] = value

Step-by-Step Explanation

  1. Check if the array is full: Arrays have a predefined size. If there's no space left to insert a new element, the operation cannot proceed.

    Why? Because inserting into a full array would overwrite existing data or cause memory errors in lower-level languages.

  2. Start shifting elements: To insert at a specific index, all elements from that index to the end must move one position to the right.

    Loop Direction: The loop runs backward — from the last filled element to the insertion index.

    This ensures data isn't overwritten. For example, if you moved elements left to right, you'd overwrite the data before it could be copied to the next position.

  3. Place the new value: Once space is created at the required index, place the new value there.

    After shifting, index 2 is empty, so we assign the new value (e.g., 25) to array[2].

Note:

  • This logic is applicable for static arrays where size is predefined.
  • In dynamic arrays (like Python lists), insertion can be handled more flexibly, but the underlying concept remains useful.

Key Takeaways

  • Arrays require shifting elements to insert at the beginning or in the middle.
  • Insertion at the end is efficient if space is available.
  • Be mindful of array size and shifting logic when designing algorithms.