2D Array Indexing

easyPROSubsetting, Slicing, IndexingNumPy IndexingNumpy

Problem Statement

Access elements and slices from a 2D NumPy array.

Background

For 2D arrays:

arr[i, j] - element at row i, column j
arr[i] or arr[i, :] - entire row i
arr[:, j] - entire column j

Your Task

Write a function index_2d(arr) that returns a dictionary with:

"element_0_0": Element at position (0, 0), as a plain Python int
"element_1_2": Element at position (1, 2), as a plain Python int
"row_0": First row as a Python list
"col_1": Second column as a Python list

Output Format

Return a dictionary with exactly these four keys.

Example

Input

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Output

{'element_0_0': 1, 'element_1_2': 6, 'row_0': [1, 2, 3], 'col_1': [2, 5, 8]}

Reasoning

arr is a $3 \times 3$ grid of integers. Positions count from zero, so position $(i, j)$ means row $i$ , column $j$ , and the top-left number sits at $(0, 0)$ .
element_0_0: row 0, column 0 holds $a_{00} = 1$ .
element_1_2: row 1 is $[4, 5, 6]$ , and its column 2 (the third entry, not the second) is $a_{12} = 6$ .
row_0: fix $i = 0$ and let $j$ run over every column: $a_{00}, a_{01}, a_{02}$ gives [1, 2, 3].
col_1: fix $j = 1$ and let $i$ run over every row: $a_{01}, a_{11}, a_{21}$ gives [2, 5, 8], the middle number of each row read top to bottom.
The two elements are single plain integers; the row and column are ordinary lists. Notice a row's length equals the number of columns and a column's length equals the number of rows: for a $2 \times 4$ input, row_0 has 4 entries but col_1 has only 2.

Constraints

Input will be a 2D array with at least 2 rows and 3 columns
Use arr[i, j] syntax for elements

Concept primerPREVIEW

1. Background Knowledge

NumPy arrays are the foundational data structure for numerical computing in Python, enabling array programming—a paradigm that treats entire arrays as single objects for efficient operations. A 2D NumPy array (ndarray with ndim=2) represents a matrix with shape (rows, cols), where indexing follows zero-based row-major order: arr[i, j] accesses element at row i, column j.

Key indexing syntax (directly from problem background):

arr[i, j] → Single element (requires exact i, j coordinates)
arr[i] or arr[i, :] → Entire row i (colon : means "all")
arr[:, j] → Entire column j

NumPy slicing returns views (not copies) by default, enabling zero-copy access for efficiency (O(1) time). Arrays must have compatible shapes per constraints (≥2 rows, ≥3 columns).

Prerequisites:

Import: import numpy as np
Array creation: np.array([[1,2,3], [4,5,6]])
Dictionary output: Python dict with exact keys as strings

2. Algorithm Approach

This is a direct indexing problem requiring four constant-time lookups:

Point queries: arr[0,0], arr[1,2] → O(1) each
Row slice: arr[0, :] → O(1) view, convert to list()
Column slice: arr[:, 1] → O(1) view, convert to list()

No iteration or search needed—pure array programming with vectorized indexing. Total algorithm: dictionary construction from four O(1) operations.

Input: arr ∈ ℝ^(m×n), m≥2, n≥3
Output: {str: scalar|list} mapping
Time: O(1) dominant (slicing) + O(n) for list conversion

3. Step-by-Step Strategy

def index_2d(arr):
 result = {} # 1. Initialize empty dict

 # 2. Element access: exact [row, col] syntax (O(1))
 result["element_0_0"] = arr[0, 0] # (0,0) → top-left
 result["element_1_2"] = arr[1, 2] # (1,2) → row1, col2

PRO

Continue the full explanation

You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.

PRO

Editor locked

The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.

solution.py

Python 3.13

Test results