Sorting and Unique

Sort Array

Order a 6-element list ascending by repeatedly picking the smallest remaining value. Each iteration takes min(remaining), appends it to result, and removes it from remaining. The trace shows remaining shrinking and result growing one element at a time.

By hand

Initialize remaining as a copy of values. Repeat len(values) times: find min(remaining), append it to result, remove it from remaining.

naive.py
Replay: real traced execution (multi-file project)
values = [3, 1, 4, 1, 5, 9]
remaining = list(values)
result = []
for _ in range(len(values)):
    m = min(remaining)
    result.append(m)
    remaining.remove(m)
print('RESULT:', result)

  1. values ← [3, 1, 4, 1, 5, 9]

    1values = [3, 1, 4, 1, 5, 9]2remaining = list(values)
    values this step[3, 1, 4, 1, 5, 9]values

  2. remaining ← [3, 1, 4, 1, 5, 9]

    1values = [3, 1, 4, 1, 5, 9]2remaining = list(values)3result = []
    values this step[3, 1, 4, 1, 5, 9]remaining

  3. result ← []

    2remaining = list(values)3result = []4for _ in range(len(values)):
    values this step[]result

  4. _ ← 0

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step0_

  5. m ← 1

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)
    values this step1m

  6. result ← [1]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[] → [1]result

  7. remaining ← [3, 4, 1, 5, 9]

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[3, 1, 4, 1, 5, 9] → [3, 4, 1, 5, 9]remaining

  8. _ ← 1

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step0 → 1_

  9. m = min(remaining)

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)

  10. result ← [1, 1]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[1] → [1, 1]result

  11. remaining ← [3, 4, 5, 9]

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[3, 4, 1, 5, 9] → [3, 4, 5, 9]remaining

  12. _ ← 2

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step1 → 2_

  13. m ← 3

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)
    values this step1 → 3m

  14. result ← [1, 1, 3]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[1, 1] → [1, 1, 3]result

  15. remaining ← [4, 5, 9]

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[3, 4, 5, 9] → [4, 5, 9]remaining

  16. _ ← 3

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step2 → 3_

  17. m ← 4

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)
    values this step3 → 4m

  18. result ← [1, 1, 3, 4]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[1, 1, 3] → [1, 1, 3, 4]result

  19. remaining ← [5, 9]

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[4, 5, 9] → [5, 9]remaining

  20. _ ← 4

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step3 → 4_

  21. m ← 5

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)
    values this step4 → 5m

  22. result ← [1, 1, 3, 4, 5]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[1, 1, 3, 4] → [1, 1, 3, 4, 5]result

  23. remaining ← [9]

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[5, 9] → [9]remaining

  24. _ ← 5

    3result = []4for _ in range(len(values)):5    m = min(remaining)
    values this step4 → 5_

  25. m ← 9

    4for _ in range(len(values)):5    m = min(remaining)6    result.append(m)
    values this step5 → 9m

  26. result ← [1, 1, 3, 4, 5, 9]

    5m = min(remaining)6result.append(m)7remaining.remove(m)
    values this step[1, 1, 3, 4, 5] → [1, 1, 3, 4, 5, 9]result

  27. remaining ← []

    6    result.append(m)7    remaining.remove(m)8print('RESULT:', result)
    values this step[9] → []remaining

  28. for _ in range(len(values)):

    3result = []4for _ in range(len(values)):5    m = min(remaining)

  29. stdout ← RESULT: [1, 1, 3, 4, 5, 9]

    7    remaining.remove(m)8print('RESULT:', result)
    values this stepRESULT: [1, 1, 3, 4, 5, 9]stdout

With NumPy

np.sort(a) returns a new sorted array. The original a is unchanged.

library.py 
import numpy as np

values = [3, 1, 4, 1, 5, 9]
a = np.array(values)
result = np.sort(a)
print('a: shape:', a.shape, 'dtype:', a.dtype, 'values:', a.tolist())
print('result: shape:', result.shape, 'dtype:', result.dtype, 'values:', result.tolist())
print('RESULT:', result.tolist())

a: shape: (6,) dtype: int64 values: [3, 1, 4, 1, 5, 9]
result: shape: (6,) dtype: int64 values: [1, 1, 3, 4, 5, 9]
RESULT: [1, 1, 3, 4, 5, 9]

Implementation notes

  • np.sort(a) returns a copy — a is unmodified. To sort in place use a.sort() (a method on the array), which modifies a and returns None.
  • Default sort order is ascending. For descending order use np.sort(a)[::-1] (sort first, then reverse the result).
  • This lesson teaches sort usage. The underlying algorithms (quicksort, mergesort, heapsort, timsort) are covered in the DSA track.
  • Shape, dtype, and values are shown explicitly here because ndarray.__repr__ output varies with NumPy version and print options.