Now that we’ve seen an example of how quicksort works, let’s walk through the pseudocode of a quicksort function. The function itself is very simple, as shown below.

1function QUICKSORT(ARRAY, START, END)
2    # base case size <= 1
3    if START >= END then
4        return
5    end if
6    PIVOTINDEX = PARTITION(ARRAY, START, END)
7    QUICKSORT(ARRAY, START, PIVOTINDEX – 1)
8    QUICKSORT(ARRAY, PIVOTINDEX + 1, END)
9end function

This implementation of quicksort uses a simple base case on lines 3 through 5 to check if the array is either empty, or contains one element. It does so by checking if the START index is greater than or equal to the END index. If so, it can assume the array is sorted and just return it without any additional changes.

The recursive case is shown on lines 6 - 8. It simply uses a helper function called partition on line 6 to partition the array based on a pivot value. That function returns the location of the pivot value, which is stored in pivotIndex. Then, on lines 7 and 8, the quicksort function is called recursively on the two partitions of the array, before and after the pivotIndex. That’s really all there is to it!

Let’s look at one way we could implement the partition function, shown below in pseudocode.

 1function PARTITION(ARRAY, START, END)
 2    PIVOTVALUE = ARRAY[END]
 3    PIVOTINDEX = START
 4    loop INDEX from START to END
 5        if ARRAY[INDEX] <= PIVOTVALUE
 6            TEMP = ARRAY[INDEX]
 7            ARRAY[INDEX] = ARRAY[PIVOTINDEX]
 8            ARRAY[PIVOTINDEX] = TEMP
 9            PIVOTINDEX = PIVOTINDEX + 1
10        end if
11    end loop
12    return PIVOTINDEX – 1

This function begins on lines 2 and 3 by setting initial values for the pivotValue by choosing the last element in the array, and then setting the pivotIndex to 0. Then, the loop on lines 4 through 11 will look at each element in the array, determine if it is less than or equal to pivotValue, and swap that element with the element at pivotIndex if so, incrementing pivotIndex after each swap.

At the end, the value that was originally at the end of the array will be at location pivotIndex – 1, so we will return that value back to the quicksort function so it can split the array into two parts based on that value.