Sort and Search

easyPROMiscNumPy UtilitiesNumpy

Problem Statement

Sort NumPy arrays and find elements.

Background

np.sort(arr): Returns sorted copy
np.argsort(arr): Returns indices that would sort the array
np.where(condition): Find indices where condition is True
np.argmax(), np.argmin(): Index of max/min element

Your Task

Write a function sort_and_search(arr) that returns a dictionary with:

"sorted": Sorted array as list
"argsort": Indices that would sort the array, as a list
"argmax": Index of maximum value, as a plain integer
"argmin": Index of minimum value (first occurrence), as a plain integer

Output Format

Return a dictionary with exactly these four keys.

Example

Input

[3, 1, 4, 1, 5, 9, 2, 6]

Output

{'sorted': [1, 1, 2, 3, 4, 5, 6, 9], 'argsort': [1, 3, 6, 0, 2, 4, 7, 5], 'argmax': 5, 'argmin': 1}

Reasoning

Input: arr is a 1D array of 8 values, indexed $0$ to $7$ : $a = (3, 1, 4, 1, 5, 9, 2, 6)$ .
Sorted: the same 8 values in ascending order, [1, 1, 2, 3, 4, 5, 6, 9]. Both 1s stay.
Argsort: instead of values, list the positions they came from, in sorted order. The smallest value 1 sits at positions 1 and 3, then 2 is at 6, 3 at 0, 4 at 2, 5 at 4, 6 at 7 and 9 at 5, giving [1, 3, 6, 0, 2, 4, 7, 5]. Reading $a$ at those positions gives the sorted list.
Argmax / argmin: the largest value, 9, is at position 5, and the smallest, 1, first appears at position 1, so argmax is 5 and argmin is 1.
Notice that with ties, position 1 beats position 3 for the minimum: it is the first occurrence that counts. Here the maximum 9 is unique, so the last entry of argsort is the argmax position 5, and in this sample its first entry, 1, is also the argmin position.

Constraints

Use np.sort(), np.argsort(), np.argmax(), np.argmin()
Array will have at least 1 element

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Sort and Search: Comprehensive Background

1. Background Knowledge

NumPy Array Operations

NumPy is Python's fundamental library for numerical computing, providing efficient array operations that are orders of magnitude faster than native Python lists. NumPy arrays enable vectorized operations—applying functions to entire arrays without explicit loops—which improves both performance and code readability.

Core Sorting Concepts

Sorting is arranging elements in a specific order (ascending or descending). The key insight is that different sorting operations serve different purposes:

np.sort(arr): Returns a new sorted array without modifying the original
np.argsort(arr): Returns the indices that would sort the array—crucial for tracking element positions
np.argmax() / np.argmin(): Find the index of the maximum/minimum value, not the value itself

Why Indices Matter

When you call np.argsort(), you get indices that represent the permutation needed to sort the array. For example, if argsort() returns [1, 3, 6, 0, 2, 4, 7, 5], this means: "take element at index 1 first, then index 3, then index 6," etc., to get a sorted sequence.

2. Algorithm Approach

Sorting Algorithms in NumPy

NumPy's sort() uses Quicksort by default (with fallback to Heapsort for worst-case scenarios), achieving average-case performance of $O(n \log n)$ . The underlying implementation is highly optimized in C, making it significantly faster than Python-level sorting.

Index-Based Sorting

np.argsort() performs the same sorting operation but returns indices instead of values. This is essential when you need to:

Track which original positions elements came from
Apply the same permutation to multiple arrays
Maintain relationships between sorted data and metadata

Extrema Finding

np.argmax() and np.argmin() scan the array once in $O(n)$ time to find the index of the maximum/minimum element. These are more efficient than sorting when you only need one extremum.

3. Step-by-Step Strategy

Step 1: Sort the array

sorted_arr = np.sort(arr)

Convert to list for the dictionary output using .tolist().

Step 2: Get sorting indices

indices = np.argsort(arr)

These indices tell you the original positions of elements in sorted order.

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solution.py

Python 3.13

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