Waterfall chart pattern in Matplotlib - Time & Space Complexity

Time Complexity: Waterfall chart pattern

O(n)

Understanding Time Complexity

We want to understand how the time to draw a waterfall chart changes as the data size grows.

How does the number of steps affect the work matplotlib does to build the chart?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt

values = [100, -30, 20, -10, 40]

cumulative = [0]
for v in values:
    cumulative.append(cumulative[-1] + v)

plt.bar(range(len(values)), values, bottom=cumulative[:-1])
plt.show()
    

This code builds a simple waterfall chart by stacking bars based on cumulative sums.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over the list of values to compute cumulative sums and draw bars.
• How many times: Once for each value in the input list.

How Execution Grows With Input

Each new data point adds one more bar and one more cumulative sum calculation.

Input Size (n)	Approx. Operations
10	About 10 cumulative sums and 10 bars drawn
100	About 100 cumulative sums and 100 bars drawn
1000	About 1000 cumulative sums and 1000 bars drawn

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

Final Time Complexity

Time Complexity: O(n)

This means the time to create the waterfall chart grows in a straight line as the data size increases.

Common Mistake

[X] Wrong: "Drawing a waterfall chart takes the same time no matter how many bars there are."

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

Interview Connect

Understanding how chart drawing time grows helps you explain performance in data visualization tasks clearly and confidently.

Self-Check

What if we added nested loops to compare each bar with every other bar? How would the time complexity change?

Practice

1. What is the main purpose of a waterfall chart in data visualization?

easy

A. To plot continuous data over time

B. To display the distribution of data points in categories

C. To show step-by-step changes from a starting value to an ending value

D. To compare multiple variables side by side

Solution

1. Step 1: Understand waterfall chart concept

   A waterfall chart visually breaks down how an initial value changes through a series of positive and negative steps to reach a final value.

2. Step 2: Compare with other chart types

   Other charts like histograms or line charts serve different purposes, such as distribution or trends over time, not stepwise changes.

3. Final Answer:

   To show step-by-step changes from a starting value to an ending value -> Option C

4. Quick Check:

   Waterfall charts = stepwise changes [OK]

Hint: Waterfall charts show how values add or subtract stepwise [OK]

Common Mistakes:

• Confusing waterfall charts with line charts
• Thinking waterfall charts show data distribution
• Assuming waterfall charts compare unrelated categories

2. Which of the following is the correct way to set the bottom parameter in plt.bar() to create a waterfall effect?

easy

A. Use cumulative sums of previous bars as the bottom values

B. Set bottom to zero for all bars

C. Use random values for bottom to create spacing

D. Set bottom to the maximum value of the dataset

Solution

1. Step 1: Understand the bottom parameter in bar charts

   The bottom parameter sets where each bar starts vertically. For waterfall charts, bars start where the previous bar ended.

2. Step 2: Use cumulative sums for correct stacking

   By using cumulative sums of previous values, each bar stacks correctly to show stepwise changes.

3. Final Answer:

   Use cumulative sums of previous bars as the bottom values -> Option A

4. Quick Check:

   Bottom = cumulative sums for waterfall [OK]

Hint: Bottom bars stack by adding previous bar heights [OK]

Common Mistakes:

• Setting bottom always to zero causes overlapping bars
• Using random bottoms breaks the waterfall flow
• Setting bottom to max value misplaces bars

3. What will be the output of this code snippet creating a waterfall chart?

import matplotlib.pyplot as plt
values = [100, -30, 20, -10]
cumulative = [100, 70, 90, 80]
plt.bar(range(4), values, bottom=[0, 100, 70, 90], color=['green', 'red', 'green', 'red'])
plt.show()

medium

A. A waterfall chart showing increases and decreases starting at 100

B. A bar chart with all bars starting at zero

C. A stacked bar chart with bars overlapping incorrectly

D. An error because bottom list length does not match values

Solution

1. Step 1: Analyze the bottom parameter values

   The bottom list [0, 100, 70, 90] correctly positions each bar to start where the previous ended, matching cumulative sums.

2. Step 2: Check colors and values

   Positive values are green, negative are red, showing increases and decreases clearly in a waterfall style.

3. Final Answer:

   A waterfall chart showing increases and decreases starting at 100 -> Option A

4. Quick Check:

   Bottom aligns bars for waterfall effect [OK]

Hint: Check bottom aligns with cumulative sums for correct waterfall [OK]

Common Mistakes:

• Confusing bottom values causing bars to overlap
• Ignoring color coding for increases/decreases
• Assuming bars start all at zero

4. Identify the error in this waterfall chart code:

import matplotlib.pyplot as plt
values = [50, -20, 30]
cumulative = [50, 30, 60]
plt.bar(range(3), values, bottom=[0, 50, 60], color=['green', 'red', 'green'])
plt.show()

medium

A. The bottom list should be [0, 50, 80] because 30 + 50 = 80

B. The bottom list should be [0, 50, 30] to match cumulative sums

C. The color list length does not match values length

D. The values list contains negative numbers which is not allowed

Solution

1. Step 1: Analyze cumulative sums and bottoms

   The cumulative sums are [50, 30, 60]. The bottoms are [0, 50, 60]. The third bottom should be 30 (cumulative[1]), not 60.

2. Step 2: Identify the mismatch

   The bottom list does not correctly match the cumulative sums; it should be [0, 50, 30].

3. Final Answer:

   The bottom list should be [0, 50, 30] to match cumulative sums -> Option B

4. Quick Check:

   Bottoms = [0] + cumulative[:-1] [OK]

Hint: Bottom bars must start where previous bar ends [OK]

Common Mistakes:

• Using incorrect cumulative sums for bottom
• Mismatching color list length
• Assuming negative values are invalid

5. You want to create a waterfall chart for monthly profit changes: start at 200, then +50, -30, +20, -10. Which code snippet correctly calculates the bottoms for the bars?

hard

A. bottoms = [0, 50, 20, -10, 0]

B. bottoms = [200, 250, 220, 240, 230]

C. bottoms = [200, 0, 0, 0, 0]

D. bottoms = [0, 200, 250, 220, 240]

Solution

1. Step 1: Calculate cumulative sums stepwise

   Start at 200, then add +50 = 250, then -30 = 220, then +20 = 240, then -10 = 230.

2. Step 2: Determine bottoms for each bar

   The first bar starts at 0, second at 200, third at 250, fourth at 220, fifth at 240 to show stepwise changes.

3. Final Answer:

   bottoms = [0, 200, 250, 220, 240] -> Option D

4. Quick Check:

   Bottoms = previous cumulative sums [OK]

Hint: Bottoms = cumulative sums before each step [OK]

Common Mistakes:

• Starting bottoms at data values instead of zero
• Using incorrect cumulative sums
• Setting all bottoms to zero