Python: Sort a list of elements using Cycle sort

Last update on April 23 2025 12:50:13 (UTC/GMT +8 hours)

16. Cycle Sort

Write a Python program to sort a list of elements using Cycle sort.
Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.

Sample Solution:

Python Code:

# License: https://bit.ly/2V5W81t 
def cycleSort(vector):
    "Sort a vector in place and return the number of writes."
    writes = 0
 
    # Loop through the vector to find cycles to rotate.
    for cycleStart, item in enumerate(vector):
 
        # Find where to put the item.
        pos = cycleStart
        for item2 in vector[cycleStart + 1:]:
            if item2 < item:
                pos += 1
 
        # If the item is already there, this is not a cycle.
        if pos == cycleStart:
            continue
 
        # Otherwise, put the item there or right after any duplicates.
        while item == vector[pos]:
            pos += 1
        vector[pos], item = item, vector[pos]
        writes += 1
 
        # Rotate the rest of the cycle.
        while pos != cycleStart:
 
            # Find where to put the item.
            pos = cycleStart
            for item2 in vector[cycleStart + 1:]:
                if item2 < item:
                    pos += 1
 
            # Put the item there or right after any duplicates.
            while item == vector[pos]:
                pos += 1
            vector[pos], item = item, vector[pos]
            writes += 1
 
    return writes
 
 
if __name__ == '__main__':
    x = [0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
    xcopy = x[::]
    writes = cycleSort(xcopy)
    if xcopy != sorted(x):
        print('Wrong order!')
    else:
        print('%r\nIs correctly sorted using cycleSort to'
              '\n%r\nUsing %i writes.' % (x, xcopy, writes))

Sample Output:

[0, 1, 2, 2, 2, 2, 1, 9, 3.5, 5, 8, 4, 7, 0, 6]
Is correctly sorted using cycleSort to
[0, 0, 1, 1, 2, 2, 2, 2, 3.5, 4, 5, 6, 7, 8, 9]
Using 10 writes.

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to implement cycle sort and print the number of writes made to sort the array.
Write a Python script to use cycle sort on a list of unique integers and then verify that the algorithm minimizes data movement.
Write a Python program to implement cycle sort and output the cycles detected during the sorting process.
Write a Python function to perform cycle sort on a list and then compare the result with Python’s built-in sorted() function.

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