Nested loops and multi-dimensional arrays are essential tools for solving problems that involve grid-like structures, repeated processes, or tasks that require iterating over pairs or groups of indices.

Nested Loops

A nested loop is a loop inside another loop.

Example pattern:

Multi-Dimensional Arrays

A multi-dimensional array is an array of arrays. The most common is the 2D array:

This creates a grid with 5 rows and 5 columns. You access elements using: $a[i][j]$ 2D arrays are widely used to represent:

• Matrices
• Game boards
• Grids in pathfinding

Example 1: Sum of All Elements in a 2D Array

Given a matrix $n \times m$, find the sum of all elements.

Example 2: Count How Many Positive Numbers Are in a Grid

Count the number of cells with value $> 0$.