np.unravel_index() for multi-dim positions in NumPy - Time & Space Complexity

Time Complexity: np.unravel_index() for multi-dim positions

O(n * d)

Understanding Time Complexity

We want to understand how the time needed to find multi-dimensional positions grows when using np.unravel_index().

Specifically, how does the work change as the input size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

indices = np.array([5, 23, 45, 67])
shape = (4, 5, 6)
positions = np.unravel_index(indices, shape)
print(positions)

This code converts flat indices into multi-dimensional positions based on the given shape.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: For each index, the function calculates its position by dividing and taking remainders for each dimension.
• How many times: This happens once per index and once per dimension in the shape.

How Execution Grows With Input

As the number of indices or the number of dimensions grows, the work increases proportionally.

Input Size (n = number of indices)	Dimensions (d)	Approx. Operations
10	3	About 30 (10 * 3)
100	3	About 300 (100 * 3)
1000	3	About 3000 (1000 * 3)

Pattern observation: The total work grows linearly with both the number of indices and the number of dimensions.

Final Time Complexity

Time Complexity: O(n * d)

This means the time grows in direct proportion to the number of indices and the number of dimensions.

Common Mistake

[X] Wrong: "The time to convert indices does not depend on the number of dimensions."

[OK] Correct: Each dimension requires a division and remainder operation, so more dimensions mean more work per index.

Interview Connect

Understanding how functions like np.unravel_index() scale helps you reason about performance in data processing tasks.

Self-Check

What if we changed the input to a single large index instead of many small ones? How would the time complexity change?

Practice

1. What does np.unravel_index() do in NumPy?

easy

A. It returns the total number of elements in an array.

B. It converts a flat index into a tuple of coordinate indices for a given shape.

C. It reshapes an array into a new shape without changing data.

D. It flattens a multi-dimensional array into a one-dimensional array.

Solution

1. Step 1: Understand the function purpose

   np.unravel_index() takes a flat index and a shape to find the multi-dimensional coordinates.

2. Step 2: Compare options with function behavior

   Only It converts a flat index into a tuple of coordinate indices for a given shape. describes converting a flat index to multi-dimensional indices, which matches the function's purpose.

3. Final Answer:

   It converts a flat index into a tuple of coordinate indices for a given shape. -> Option B

4. Quick Check:

   Function purpose = convert flat index to coordinates [OK]

Hint: Remember: unravel means 'find coordinates' from flat index [OK]

Common Mistakes:

• Confusing unravel_index with flatten or reshape functions
• Thinking it returns the total number of elements
• Assuming it changes the array data

2. Which of the following is the correct syntax to use np.unravel_index() for a flat index 5 in a shape (3, 3)?

easy

A. np.unravel_index((3, 3), 5)

B. np.unravel_index(5, 3, 3)

C. np.unravel_index(5, (3, 3))

D. np.unravel_index([5], (3, 3))

Solution

1. Step 1: Recall the function signature

   The correct syntax is np.unravel_index(indices, shape), where indices is an integer or array and shape is a tuple.

2. Step 2: Match options to syntax

   np.unravel_index(5, (3, 3)) matches the correct syntax with index 5 and shape (3, 3). np.unravel_index([5], (3, 3)) uses a list for index which is allowed but less common for single index.

3. Final Answer:

   np.unravel_index(5, (3, 3)) -> Option C

4. Quick Check:

   Syntax = np.unravel_index(index, shape) [OK]

Hint: Use np.unravel_index(index, shape) with shape as a tuple [OK]

Common Mistakes:

• Swapping the order of arguments
• Passing shape as separate numbers instead of a tuple
• Using list instead of integer for single index without need

3. What is the output of the following code?

import numpy as np
index = 7
shape = (3, 3)
result = np.unravel_index(index, shape)
print(result)

medium

A. (1, 1)

B. (1, 2)

C. (2, 0)

D. (2, 1)

Solution

1. Step 1: Understand the shape and flat index

   The shape is (3, 3), so the array has 3 rows and 3 columns. Flat indices go row-wise: 0 to 8.

2. Step 2: Calculate multi-dimensional indices for flat index 7

   Index 7 corresponds to row = 7 // 3 = 2, column = 7 % 3 = 1, so position is (2, 1).

3. Final Answer:

   (2, 1) -> Option D

4. Quick Check:

   Row = 7//3=2, Col = 7%3=1 [OK]

Hint: Divide index by shape dims to find row, mod for column [OK]

Common Mistakes:

• Mixing row and column order
• Using zero-based index incorrectly
• Confusing division and modulo operations

4. The code below raises an error. What is the cause?

import numpy as np
index = 10
shape = (3, 3)
result = np.unravel_index(index, shape)
print(result)

medium

A. Index 10 is out of bounds for shape (3, 3).

B. Shape must be a list, not a tuple.

C. np.unravel_index requires a 1D array, not a scalar index.

D. Missing import statement for numpy.

Solution

1. Step 1: Check the shape size

   Shape (3, 3) means total elements = 3*3 = 9, so valid flat indices are 0 to 8.

2. Step 2: Analyze the index value

   Index 10 is greater than 8, so it is out of bounds and causes an error.

3. Final Answer:

   Index 10 is out of bounds for shape (3, 3). -> Option A

4. Quick Check:

   Max index = 8, given index = 10 [OK]

Hint: Check if index < product of shape dims to avoid errors [OK]

Common Mistakes:

• Assuming tuple shape is invalid
• Thinking np.unravel_index needs array input only
• Ignoring index bounds for given shape

5. You have a 3D array with shape (4, 3, 2). You want to find the multi-dimensional indices for flat indices [5, 10, 15]. Which code correctly returns these positions?

hard

A. np.unravel_index([5, 10, 15], (4, 3, 2))

B. np.unravel_index(5, 10, 15, (4, 3, 2))

C. np.unravel_index((5, 10, 15), (4, 3, 2))

D. np.unravel_index([5, 10, 15], 4, 3, 2)

Solution

1. Step 1: Understand input for multiple indices

   To convert multiple flat indices, pass a list or array of indices as first argument and shape tuple as second.

2. Step 2: Match options to correct syntax

   np.unravel_index([5, 10, 15], (4, 3, 2)) correctly passes a list of indices and the shape tuple. np.unravel_index((5, 10, 15), (4, 3, 2)) passes a tuple instead of list, which also works but less common. np.unravel_index(5, 10, 15, (4, 3, 2)) and D have wrong argument formats.

3. Final Answer:

   np.unravel_index([5, 10, 15], (4, 3, 2)) -> Option A

4. Quick Check:

   Multiple indices = list + shape tuple [OK]

Hint: Use list of indices and shape tuple for multiple positions [OK]

Common Mistakes:

• Passing multiple indices as separate arguments
• Using tuple instead of list for indices (less common but works)
• Passing shape as separate numbers instead of tuple