# 1. Introduction

Sorting a list is a common operation in programming. Python has a built-in *sort()* function and *sorted()* function for this purpose. However, understanding how to sort a list manually without these functions can be a great way to learn about sorting algorithms and improve problem-solving skills.

## Definition

Sorting a list means arranging the elements of the list in a certain order, typically in ascending or descending sequence. We'll explore a simple sorting algorithm called the bubble sort, which repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.

# 2. Program Steps

1. Create an unsorted list of numbers.

2. Implement the bubble sort algorithm to sort the list.

3. Loop through the list, comparing each pair of adjacent items and swapping them if needed.

4. Repeat the process until the list is sorted.

5. Print the sorted list.

# 3. Code Program

```
# Step 1: Create an unsorted list of numbers
numbers = [64, 34, 25, 12, 22, 11, 90]
# Step 2: Implement bubble sort algorithm
# Loop through each element in the list
for i in range(len(numbers)):
# Nested loop to compare list elements
for j in range(0, len(numbers) - i - 1):
# Compare adjacent elements
if numbers[j] > numbers[j + 1]:
# Step 3: Swap elements if the earlier element is greater
numbers[j], numbers[j + 1] = numbers[j + 1], numbers[j]
# Step 4: Repeat until the list is sorted
# Step 5: Print the sorted list
print(f"Sorted list: {numbers}")
```

### Output:

Sorted list: [11, 12, 22, 25, 34, 64, 90]

### Explanation:

1. *numbers* is initially an unsorted list of integers.

2. The first *for* loop iterates through each element in the list by its index *i*.

3. The nested *for* loop iterates from the start of the list to the end of the unsorted section.

4. Inside the nested loop, each pair of adjacent elements are compared. The condition *if numbers[j] > numbers[j + 1]* checks if the current element is greater than the next element.

5. If the condition is true, the elements are swapped, placing the larger element after the smaller one.

6. The outer loop continues until no more swaps are needed, meaning the list is sorted.

7. The final *print* statement outputs the sorted *numbers* list, which has been arranged in ascending order by the bubble sort algorithm.

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