Partial sorting with np.partition() in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.partition() do in numpy?

np.partition() rearranges elements in an array so that the element at the specified index is in its sorted position, and all smaller elements are before it, while all larger elements are after it. It does not fully sort the array.

beginner

How is np.partition() different from np.sort()?

np.sort() fully sorts the entire array, while np.partition() only ensures that the element at the given index is in the correct position, with smaller elements before and larger after, but the order within those groups is not guaranteed.

beginner

What is the main use case of np.partition()?

It is useful when you want to find the k-th smallest or largest elements quickly without sorting the entire array, such as finding medians or percentiles efficiently.

intermediate

Example: What does np.partition([3, 1, 4, 1, 5], 2) return?

It returns an array where the element at index 2 is the third smallest element, and all elements before index 2 are smaller or equal, and all after are larger or equal. One possible output is [1, 1, 3, 5, 4]. The order of elements before and after index 2 is not sorted.

intermediate

Can np.partition() be used on multi-dimensional arrays?

Yes, by specifying the axis parameter, you can partition along a specific axis of a multi-dimensional array.

What does np.partition(arr, k) guarantee about the element at index k?

A It is the k-th smallest element in the array

B The array is fully sorted

C All elements are larger than the element at index k

D The array is reversed

np.partition() places the element at index k so that it is the k-th smallest element, with smaller elements before and larger elements after, but does not fully sort the array.

Which numpy function fully sorts an array?

A np.sort()

B np.argsort()

C np.partition()

D np.argpartition()

np.sort() fully sorts the array, unlike np.partition() which only partially sorts.

If you want to find the median quickly without full sorting, which function is best?

A np.sort()

B np.cumsum()

C np.partition()

D np.argmax()

np.partition() can quickly find the median by partially sorting the array around the middle index.

What happens to elements before the partition index after using np.partition()?

A They are reversed

B They are sorted in ascending order

C They are all larger than the element at the partition index

D They are all smaller or equal to the element at the partition index

Elements before the partition index are smaller or equal to the element at that index, but not necessarily sorted.

Can np.partition() be used to find the top 3 largest elements?

A No, it only finds smallest elements

B Yes, by partitioning at the correct index

C Yes, but only for 1D arrays

D No, it only sorts fully

You can use np.partition() with negative indices or by partitioning at len(arr) - 3 to find the top 3 largest elements.

Explain how np.partition() works and when you would use it instead of full sorting.

Think about finding a specific element's position without sorting everything.

Describe the difference between np.partition() and np.sort() with an example.

Consider what happens to the array after each function.

Practice

1. What does np.partition do to an array?

easy

A. It rearranges the array so the kth element is in its sorted position, with partial order around it.

B. It fully sorts the entire array in ascending order.

C. It reverses the array elements.

D. It removes duplicate elements from the array.

Solution

1. Step 1: Understand np.partition behavior

   np.partition places the kth smallest element in its correct sorted position.

2. Step 2: Recognize partial ordering

   Elements before the kth are smaller or equal, and elements after are larger or equal, but not fully sorted.

3. Final Answer:

   It rearranges the array so the kth element is in its sorted position, with partial order around it. -> Option A

4. Quick Check:

   Partial sorting = kth element fixed [OK]

Hint: Remember: np.partition fixes kth element only [OK]

Common Mistakes:

• Thinking np.partition fully sorts the array
• Assuming it reverses or removes duplicates
• Confusing np.partition with np.sort

2. Which of the following is the correct syntax to partition array arr at index 3 using np.partition?

easy

A. np.partition(arr, 3)

B. np.partition(3, arr)

C. arr.partition(3)

D. np.partition(arr, k=3)

Solution

1. Step 1: Check np.partition function signature

   The function is called as np.partition(array, kth), where kth is the index.

2. Step 2: Match syntax with options

   np.partition(arr, 3) matches the correct order: array first, then kth index.

3. Final Answer:

   np.partition(arr, 3) -> Option A

4. Quick Check:

   np.partition(array, kth) syntax [OK]

Hint: Remember: array first, kth second in np.partition() [OK]

Common Mistakes:

• Swapping arguments order
• Using method call on array (arr.partition)
• Using incorrect keyword argument like k=3

3. What is the output of the following code?

import numpy as np
arr = np.array([7, 2, 5, 3, 9])
result = np.partition(arr, 2)
print(arr)

medium

A. [2 3 5 7 9]

B. [7 2 5 3 9]

C. [2 3 5 7 9] sorted

D. [5 2 3 7 9]

Solution

1. Step 1: Identify kth element and partial sorting

   kth=2 means the element at index 2 in sorted order is placed correctly. The 3rd smallest element is 5.

2. Step 2: Rearrange array with partial order

   Elements before index 2 are smaller or equal to 5, after are larger or equal. The output is [7 2 5 3 9] because np.partition returns a new array and does not modify arr in place.

3. Final Answer:

   [7 2 5 3 9] -> Option B

4. Quick Check:

   np.partition returns a new array, original unchanged [OK]

Hint: Check kth element position, others partially ordered [OK]

Common Mistakes:

• Expecting fully sorted output
• Confusing kth index with value
• Ignoring partial order after kth

4. The code below throws an error. What is the mistake?

import numpy as np
arr = np.array([4, 1, 6, 8])
result = np.partition(arr, '2')
print(result)

medium

A. The array must be sorted before partitioning.

B. np.partition does not accept arrays as input.

C. np.partition requires a keyword argument kth=2.

D. The kth argument should be an integer, not a string.

Solution

1. Step 1: Check argument types for np.partition

   The kth argument must be an integer index, not a string.

2. Step 2: Identify error cause

   Passing '2' (string) causes a TypeError; correct is integer 2.

3. Final Answer:

   The kth argument should be an integer, not a string. -> Option D

4. Quick Check:

   kth must be int, not str [OK]

Hint: kth index must be int, not string [OK]

Common Mistakes:

• Passing kth as string instead of int
• Thinking array must be sorted first
• Using keyword argument kth which is invalid

5. You have a large dataset array data with 1 million numbers. You want to quickly find the 1000 smallest values without fully sorting. Which code snippet using np.partition is best?

hard

A. np.partition(data, 1000)[:1000]

B. np.sort(data)[:1000]

C. np.partition(data, 999)[:1000]

D. np.partition(data, -1000)[-1000:]

Solution

1. Step 1: Understand kth index for 1000 smallest

   Indices start at 0, so the 1000th smallest is at index 999.

2. Step 2: Use np.partition to get partial sorted array

   Partition at 999 puts 1000 smallest elements before index 999, so slicing [:1000] gets them.

3. Step 3: Check other options

   np.partition(data, 1000)[:1000] partitions at 1000 (off by one), C fully sorts (slow), D uses negative index (wrong for smallest).

4. Final Answer:

   np.partition(data, 999)[:1000] -> Option C

5. Quick Check:

   kth=999 for 1000 smallest [OK]

Hint: Use kth = count-1 for smallest elements [OK]

Common Mistakes:

• Using kth = 1000 instead of 999
• Using full sort instead of partition
• Using negative kth for smallest values