3D bar charts in Matplotlib - Time & Space Complexity

Time Complexity: 3D bar charts

O(n)

Understanding Time Complexity

When creating 3D bar charts, we want to know how the time to draw the chart changes as we add more bars.

How does adding more bars affect the work matplotlib does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x, y = np.arange(5), np.arange(5)
xpos, ypos = np.meshgrid(x, y)
xpos = xpos.flatten()
ypos = ypos.flatten()
zpos = np.zeros_like(xpos)

dx = dy = dz = np.ones_like(zpos)

ax.bar3d(xpos, ypos, zpos, dx, dy, dz)
plt.show()

This code creates a 3D bar chart with 25 bars arranged in a grid.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Drawing each bar in the 3D space.
• How many times: Once for each bar, here 25 times (5x5 grid).

How Execution Grows With Input

Each new bar adds a fixed amount of work to draw it.

Input Size (n bars)	Approx. Operations
10	10 drawing steps
100	100 drawing steps
1000	1000 drawing steps

Pattern observation: The work grows directly with the number of bars.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw the chart grows in a straight line as you add more bars.

Common Mistake

[X] Wrong: "Adding more bars won't affect drawing time much because they are all drawn together."

[OK] Correct: Each bar requires separate drawing steps, so more bars mean more work and longer drawing time.

Interview Connect

Understanding how drawing time grows helps you explain performance when visualizing large datasets with 3D charts.

Self-Check

What if we changed the bars to be stacked instead of side-by-side? How would the time complexity change?

Practice

1. What does a 3D bar chart in matplotlib primarily represent?

easy

A. Data with two position dimensions and one height dimension

B. Only two-dimensional data with color coding

C. A line graph with three lines

D. A pie chart with depth effect

Solution

1. Step 1: Understand the axes in 3D bar charts

   3D bar charts use two axes for position (x and y) and one axis for height (z).

2. Step 2: Identify the data representation

   The height of each bar shows the value, while the base position shows categories or coordinates.

3. Final Answer:

   Data with two position dimensions and one height dimension -> Option A

4. Quick Check:

   3D bar chart = 2D position + height [OK]

Hint: Remember: 3D bars have x, y positions and z height [OK]

Common Mistakes:

• Confusing 3D bars with 2D bar charts
• Thinking 3D bars only show color differences
• Assuming 3D bars are line graphs

2. Which of the following is the correct way to create 3D axes in matplotlib before plotting a 3D bar chart?

easy

A. ax = plt.axes3d()

B. ax = plt.subplots(projection='3d')

C. ax = plt.subplot(projection='3d')

D. ax = plt.figure().add_subplot(111, projection='3d')

Solution

1. Step 1: Recall how to create 3D axes in matplotlib

   The common method is to create a figure and add a 3D subplot using add_subplot(111, projection='3d').

2. Step 2: Check each option

   ax = plt.subplot(projection='3d') uses subplot instead of add_subplot, which is incorrect. ax = plt.subplots(projection='3d') returns a tuple (figure, axes), so assigning directly to ax is incorrect. ax = plt.axes3d() is not a valid matplotlib function.

3. Final Answer:

   ax = plt.figure().add_subplot(111, projection='3d') -> Option D

4. Quick Check:

   Use figure().add_subplot with projection='3d' [OK]

Hint: Use figure().add_subplot(111, projection='3d') to get 3D axes [OK]

Common Mistakes:

• Using plt.subplot instead of plt.figure().add_subplot
• Trying to call non-existent plt.axes3d()
• Confusing subplots() with subplot()

3. What will be the output of the following code snippet?

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = [1, 2]
y = [3, 4]
z = [0, 0]
dx = dy = dz = [1, 1]
ax.bar3d(x, y, z, dx, dy, dz, color='red')
plt.show()

medium

A. Two red bars at positions (1,3) and (2,4) with height 1

B. Two red bars at positions (0,0) and (1,1) with height 1

C. Error because dx, dy, dz should be scalars, not lists

D. Empty plot with no bars

Solution

1. Step 1: Understand the parameters of ax.bar3d

   Parameters x, y, z are the positions of bars. dx, dy, dz are the sizes along each axis. Here, x=[1,2], y=[3,4], z=[0,0], and dx=dy=dz=[1,1].

2. Step 2: Analyze the plot output

   Two bars will appear at (1,3,0) and (2,4,0) with width=1, depth=1, height=1, colored red.

3. Final Answer:

   Two red bars at positions (1,3) and (2,4) with height 1 -> Option A

4. Quick Check:

   Positions and sizes match bars at (1,3) and (2,4) [OK]

Hint: Check x,y,z positions and dx,dy,dz sizes carefully [OK]

Common Mistakes:

• Assuming dx, dy, dz must be scalars only
• Confusing bar positions with sizes
• Expecting bars at (0,0) instead of given x,y

4. Identify the error in this code for plotting a 3D bar chart:

import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = [1, 2, 3]
y = [4, 5]
z = [0, 0, 0]
dx = dy = dz = 1
ax.bar3d(x, y, z, dx, dy, dz)
plt.show()

medium

A. Missing import for Axes3D

B. Length of y does not match length of x and z

C. dx, dy, dz must be lists, not scalars

D. ax.bar3d does not accept scalar sizes

Solution

1. Step 1: Check lengths of position arrays

   x has length 3, y has length 2, z has length 3. They must all be the same length for bar3d.

2. Step 2: Verify size parameters

   dx, dy, dz can be scalars or lists matching length of bars, so scalars are allowed.

3. Final Answer:

   Length of y does not match length of x and z -> Option B

4. Quick Check:

   All position arrays must have equal length [OK]

Hint: Check all position lists have same length [OK]

Common Mistakes:

• Assuming dx, dy, dz must be lists
• Ignoring mismatch in array lengths
• Forgetting to import mpl_toolkits.mplot3d (not needed here)

5. You want to plot a 3D bar chart showing sales data for 3 products over 4 months. Which approach correctly sets up the data for ax.bar3d()?

hard

A. Use x, y, z all as sales values, dz as zeros

B. Use x as months, y as products, z as sales values, and dz as ones

C. Use x as product indices repeated for each month, y as month indices tiled for each product, z as zeros, and dz as sales values

D. Use x and y as sales values, z as product indices, dz as month indices

Solution

1. Step 1: Understand the data layout for 3D bars

   x and y represent positions (product and month), z is the base height (usually zero), dz is the height of bars (sales values).

2. Step 2: Arrange data correctly

   Repeat product indices for each month (x), tile month indices for each product (y), set z to zero, and use sales data as dz.

3. Final Answer:

   Use x as product indices repeated for each month, y as month indices tiled for each product, z as zeros, and dz as sales values -> Option C

4. Quick Check:

   Positions = product/month, height = sales [OK]

Hint: Map x,y to categories, dz to values for bar height [OK]

Common Mistakes:

• Mixing sales values as positions instead of heights
• Using z as sales height instead of dz
• Not repeating/tiling indices properly for grid