How are nested loops used?

Nested loops are used in programming to perform operations on multi-dimensional data structures, such as matrices or lists of lists. They allow you to iterate through each element of a collection that contains other collections. Here are some common use cases for nested loops:

1. Matrix Operations: You can use nested loops to traverse and manipulate elements in a 2D array (matrix).

   matrix = [
       [1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]
   ]
   
   for row in matrix:
       for element in row:
           print(element, end=' ')
       print()  # New line after each row

2. Generating Patterns: Nested loops can be used to create patterns, such as stars or other shapes.

   for i in range(5):  # Number of rows
       for j in range(i + 1):  # Number of stars in each row
           print('*', end=' ')
       print()  # New line after each row

3. Combinations and Permutations: You can use nested loops to generate combinations or permutations of elements in a list.

   items = ['A', 'B', 'C']
   for i in items:
       for j in items:
           if i != j:
               print(i, j)

4. Searching and Sorting: Nested loops can be used in algorithms for searching or sorting data, such as bubble sort.

   arr = [5, 3, 8, 6, 2]
   n = len(arr)
   for i in range(n):
       for j in range(0, n-i-1):
           if arr[j] > arr[j+1]:
               arr[j], arr[j+1] = arr[j+1], arr[j]  # Swap

In summary, nested loops are powerful tools for handling complex data structures and performing repetitive tasks that require multiple levels of iteration. However, it's important to use them judiciously, as they can lead to increased time complexity.