Given an array of integers and a target sum, return indices of the two numbers that add up to target.

Container With Most Water

Given N non-negative integers representing vertical lines, find two lines that form a container holding the most water.

Rotate an N x N matrix by 90 degrees clockwise in-place.

If an element in an M x N matrix is 0, set its entire row and column to 0 in-place.

Linear Data StructuresBeginner LevelStudy Time: 20 mins

Array & Matrix Data Structure

An Array is a contiguous memory structure storing elements sequentially. Matrices represent 2D grids, enabling multidimensional modeling, coordinate maps, pixel manipulations, and dynamic programming lookups.

Array & Matrix Operations Visualizer

Array & Matrix visualizer initialized. Perform Insertion, Deletion, Search, or Traversal.

1D Linear Array (Contiguous Memory | Click element for O(1) direct lookup)Length: 6 / 8

2D Grid Matrix (Multi-Dimensional Coordinate Array)

10,0

20,1

30,2

41,0

51,1

61,2

72,0

82,1

92,2

Array & Matrix Index Access Step-by-Step

Sample Input:Array: [10, 20, 30, 40], Matrix: 2x2 [[1, 2], [3, 4]]

Step 1

Direct Base Address Calculation

Calculate element RAM memory offset using baseAddress + (index * elementSize).

arr[2] -> Address = 0x1000 + (2 * 4) = 0x1008 -> Output: 30

Direct memory index arithmetic achieves true O(1) constant time lookup.

Step 2

Array Element Insertion Shifting

Insert value 25 at index 1 by shifting trailing elements right.

Initial: [10, 20, 30, 40] -> Shift [20, 30, 40] -> Result: [10, 25, 20, 30, 40]

Middle insertions require O(N) shifts to preserve contiguous memory layout.

Step 3

2D Matrix Row-Major Traversal

Scan 2D matrix rows sequentially in row-major index formula: (r * cols) + c.

Row 0: matrix[0][0]=1, matrix[0][1]=2 | Row 1: matrix[1][0]=3, matrix[1][1]=4

Row-major traversal maximizes CPU cache hit rates.

Real-world analogy: Apartment Mailboxes

Contiguous

Index

Dimension

Hover over items for details

Think of mailboxes in a lobby. Each box has a sequential index number (0, 1, 2, 3). You can open any mailbox instantly if you know its index.

Contiguous= Elements sit next to each other in memory.
Index= Integer key referencing the relative position.
Dimension= Rows and columns defining the bounding space.

Operations explained

Complexity analysis

Scenario Simulator: Dataset Size (N = 500)

Presets:

N = 10N = 10,000

Complexity Curve MapArray & Matrix: O(N) Linear Time

Hover curves to inspect classes

Time Steps (N=500)

500 steps (Linear)

O(N) Linear Time

Space Footprint

O(1) / O(N) Space

Memory growth rate as N expands.

Performance Rank

Efficient Tier

Relative efficiency rating for large N.

Operation	Time Complexity	Space Complexity
Access	O(1)	O(1)
Search	O(N)	O(1)
Insert / Delete	O(N)	O(1)

Code implementations

// Access element
const val = arr[2];

// 2D grid matrix traversal
for(let r=0; r<rows; r++) {
  for(let c=0; c<cols; c++) {
    console.log(matrix[r][c]);
  }
}

Real-world applications

Case 01

Pixel Storage

Models screen pixel buffers and digital image filters.

Case 02

Database Indices

Caches database search records in contiguous arrays.

Case 03

Dynamic Tables

Provides memoization states for knapsack and grid solvers.

Interview questions

Topic Knowledge Test & Assessment

10 Questions Assessment