Sorting and Unique

Argsort

Produce the index ordering that would sort a 6-element list. The naive version builds (value, index) pairs, sorts them, then extracts the indices — keeping the sort structure visible without a nested loop. The trace shows pairs growing, then reordering in one step, then order filling with the extracted indices.

By hand

Build a list of [value, index] pairs. Sort the pairs (Python sorts lists lexicographically, so they sort by value then by index). Extract the second element of each sorted pair into order.

naive.py 
values = [3, 1, 4, 2, 5, 0]
pairs = []
for i in range(len(values)):
    pairs.append([values[i], i])
pairs.sort()
order = []
for p in pairs:
    order.append(p[1])
print('RESULT:', order)

With NumPy

np.argsort(a) returns an array of integer indices such that a[indices] gives a in ascending order.

library.py 
import numpy as np

values = [3, 1, 4, 2, 5, 0]
a = np.array(values)
result = np.argsort(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, 2, 5, 0]
result: shape: (6,) dtype: int64 values: [5, 1, 3, 0, 2, 4]
RESULT: [5, 1, 3, 0, 2, 4]

Implementation notes

  • Verify: a[[5, 1, 3, 0, 2, 4]] = [0, 1, 2, 3, 4, 5] — applying the argsort indices to a yields the sorted values (see fancy-index for index-array selection).
  • Argsort is useful to reorder a parallel array: if names and scores share the same positional index, argsort(scores) gives the index order to sort names by score without losing alignment.
  • For the rank-assignment pattern (each element gets its sorted rank) see rank-assign in the python-data-basics book.
  • Shape, dtype, and values are shown explicitly here because ndarray.__repr__ output varies with NumPy version and print options.