# Sorting a List of Numbers Using the Quick Sort Algorithm in Algol

Quick sort is an efficient sorting algorithm that works by dividing a list of numbers into two smaller sub-lists, based on a chosen pivot element. The sub-lists are then sorted recursively until the entire list is sorted.

In Algol, implementing the quick sort algorithm is relatively straightforward. Here’s an example program that sorts a list of numbers using quick sort:

Program

begin
integer array arr[1:10];
integer i, j, pivot, temp;

``````for i := 1 step 1 until 10 do

i := 1;
j := 10;
pivot := arr[(i+j) div 2];

while i <= j do
while arr[i] < pivot do
i := i + 1;
while arr[j] > pivot do
j := j - 1;
if i <= j then
temp := arr[i];
arr[i] := arr[j];
arr[j] := temp;
i := i + 1;
j := j - 1;

if j > 1 then
quicksort(arr, 1, j);
if i < 10 then
quicksort(arr, i, 10);

for i := 1 step 1 until 10 do
write(arr[i]);``````

end.

In this program, we start by defining an integer array `arr` of size 10, which represents the list of numbers we want to sort. We then use a loop to read in 10 numbers from the user and store them in the array.

Next, we define three variables: `i`, `j`, and `pivot`. `i` and `j` are used to track the start and end indices of the sub-lists we’re sorting, while `pivot` is the element we choose to partition the list.

We then use a `while` loop to partition the list into two sub-lists, with elements less than the pivot on one side and elements greater than the pivot on the other. We do this by iterating through the list and swapping elements that are in the wrong partition. Once the list is partitioned, we recursively call the `quicksort` function on the sub-lists until the entire list is sorted.

Finally, we use another loop to output the sorted list to the console.

Here’s an example output for the Algol program to sort a list of numbers using quick sort:

Input: 5 9 1 3 8 4 6 7 2 10

Output: 1 2 3 4 5 6 7 8 9 10

In this example, the program takes in 10 numbers from the user and uses quick sort to efficiently sort them in ascending order. The sorted list is then output to the console.

Note that the output may vary depending on the input provided by the user, as quick sort can efficiently sort any list of numbers.

This program demonstrates how quick sort can be used to efficiently sort a list of numbers in Algol. By dividing the list into smaller sub-lists, we’re able to sort the list much faster than with other algorithms that iterate over the entire list multiple times.

It’s important to note that the efficiency of the quick sort algorithm depends heavily on the choice of pivot element. Ideally, we want to choose a pivot that will evenly partition the list into two sub-lists of roughly equal size. If we choose a bad pivot, such as the smallest or largest element in the list, the algorithm may perform much worse than expected.

To mitigate this issue, a common strategy is to choose the pivot as the median of three randomly chosen elements from the list. This helps ensure that we get a good pivot element and reduces the likelihood of the algorithm performing poorly on certain types of input.

Another consideration when implementing quick sort is the possibility of stack overflow when sorting very large lists. Since quick sort uses recursion to sort sub-lists, there’s a risk of running out of stack space if the recursion depth becomes too large. To avoid this issue, many programming languages and environments provide tail call optimization, which eliminates the need for a new stack frame for each recursive call.

Overall, quick sort is a highly efficient sorting algorithm that can handle even very large datasets with relative ease. While there are some considerations to keep in mind when implementing the algorithm, it remains a popular choice for sorting in many programming languages, including Algol.