Sliding window technique in Data Structures Theory - Mini Project: Build & Apply

Sliding Window Technique

📖 Scenario: Imagine you are analyzing daily temperatures over a week to find the hottest 3-day period.

🎯 Goal: Build a step-by-step understanding of the sliding window technique by creating a list of temperatures, setting a window size, calculating sums of each window, and identifying the hottest 3-day period.

📋 What You'll Learn

Create a list called temperatures with exact values: 70, 72, 68, 75, 74, 73, 69

Create a variable called window_size and set it to 3

Use a for loop with variable i to iterate over the list and calculate the sum of each 3-day window

Create a variable called max_sum to track the highest sum and a variable called max_start_index to track the start of the hottest window

💡 Why This Matters

🌍 Real World

Sliding window technique is used in weather analysis, stock market trends, and network traffic monitoring to analyze data in fixed-size chunks.

💼 Career

Understanding sliding windows helps in roles like data analysis, software development, and system monitoring where efficient data processing is needed.

1

Create the temperature list

Create a list called temperatures with these exact values: 70, 72, 68, 75, 74, 73, 69.

Data Structures Theory

# Create the list of temperatures
# Your code here

Hint

Use square brackets to create a list and separate numbers with commas.

2

Set the window size

Create a variable called window_size and set it to 3.

Data Structures Theory

temperatures = [70, 72, 68, 75, 74, 73, 69]
# Set the window size to 3
# Your code here

Hint

Assign the number 3 to the variable window_size.

3

Calculate sums of each window

Use a for loop with variable i to iterate over temperatures and calculate the sum of each 3-day window using temperatures[i:i+window_size]. Store each sum in a list called window_sums.

Data Structures Theory

temperatures = [70, 72, 68, 75, 74, 73, 69]
window_size = 3
window_sums = []
# Use a for loop to calculate sums of each window
# Your code here

Hint

Use range(len(temperatures) - window_size + 1) to avoid going past the list end.

4

Find the hottest 3-day period

Create variables max_sum and max_start_index. Use a for loop with variable i to find the maximum sum in window_sums and store its index in max_start_index.

Data Structures Theory

temperatures = [70, 72, 68, 75, 74, 73, 69]
window_size = 3
window_sums = []
for i in range(len(temperatures) - window_size + 1):
    current_sum = sum(temperatures[i:i+window_size])
    window_sums.append(current_sum)

# Find the maximum sum and its start index
# Your code here

Hint

Initialize max_sum with the first window sum and update it when a larger sum is found.

Practice

1. What is the main purpose of the sliding window technique in data processing?

easy

A. To efficiently process continuous segments of data without repeated work

B. To sort data in ascending order

C. To store data permanently in memory

D. To randomly access elements in a list

Solution

1. Step 1: Understand the sliding window concept

   The sliding window technique moves a fixed-size window over data to process parts efficiently.

2. Step 2: Identify the main goal

   It avoids repeated calculations by updating results as the window moves, improving efficiency.

3. Final Answer:

   To efficiently process continuous segments of data without repeated work -> Option A

4. Quick Check:

   Sliding window = efficient continuous data processing [OK]

Hint: Think of a moving window checking parts step-by-step [OK]

Common Mistakes:

• Confusing sliding window with sorting algorithms
• Thinking it stores data permanently
• Assuming it accesses data randomly

2. Which of the following is the correct way to initialize a sliding window of size 3 over a list arr in Python?

easy

A. window = arr{0:3}

B. window = arr(0,3)

C. window = arr[0:3]

D. window = arr[3]

Solution

1. Step 1: Recall Python slicing syntax

   Python uses square brackets and colon to slice lists: arr[start:end] extracts elements from start up to but not including end.

2. Step 2: Apply slicing for window size 3

   To get first 3 elements, use arr[0:3]. Other options use incorrect syntax.

3. Final Answer:

   window = arr[0:3] -> Option C

4. Quick Check:

   Python slice for first 3 elements = arr[0:3] [OK]

Hint: Remember Python slices use square brackets and colon [OK]

Common Mistakes:

• Using parentheses instead of brackets for slicing
• Using curly braces which are invalid for lists
• Accessing a single element instead of a slice

3. Consider the Python code below using sliding window to find the maximum sum of any 3 consecutive numbers in arr:

arr = [2, 1, 5, 1, 3, 2]
window_sum = sum(arr[0:3])
max_sum = window_sum
for i in range(3, len(arr)):
    window_sum += arr[i] - arr[i-3]
    if window_sum > max_sum:
        max_sum = window_sum
print(max_sum)

What is the output?

medium

A. 7

B. 8

C. 6

D. 9

Solution

1. Step 1: Calculate initial window sum

   Sum of first 3 elements: 2 + 1 + 5 = 8. Set max_sum = 8.

2. Step 2: Slide window and update sums

   i=3: window_sum = 8 + arr[3] - arr[0] = 8 + 1 - 2 = 7 (max_sum=8)
   i=4: window_sum = 7 + arr[4] - arr[1] = 7 + 3 - 1 = 9 (max_sum=9)
   i=5: window_sum = 9 + arr[5] - arr[2] = 9 + 2 - 5 = 6 (max_sum=9)

3. Final Answer:

   9 -> Option D

4. Quick Check:

   Max sum of 3 consecutive = 9 [OK]

Hint: Add new element, subtract old element to update sum [OK]

Common Mistakes:

• Recalculating sum of window each time instead of updating
• Mixing up indices when subtracting old element
• Not updating max_sum correctly

4. The following code attempts to find the minimum sum of any 2 consecutive numbers in arr using sliding window:

arr = [4, 3, 7, 1, 2]
window_sum = arr[0] + arr[1]
min_sum = window_sum
for i in range(2, len(arr)):
    window_sum = window_sum + arr[i] - arr[i-1]
    if window_sum < min_sum:
        min_sum = window_sum
print(min_sum)

What is the error in this code?

medium

A. The window size is incorrectly handled in subtraction index

B. The loop range should start from 1, not 2

C. The initial window sum is calculated incorrectly

D. The comparison operator in if statement is wrong

Solution

1. Step 1: Analyze window size and indices

   The window size is 2. When sliding to include arr[i], subtract the leaving element arr[i-2].

2. Step 2: Identify the error

   Code subtracts arr[i-1], but should subtract arr[i-2]. arr[i-1] remains in the window.

3. Step 3: Verify with trace

   i=2: should be 7 + 7 - 4 = 10, but code 7 + 7 - 3 = 11 (wrong).

4. Final Answer:

   The window size is incorrectly handled in subtraction index -> Option A

5. Quick Check:

   For size k=2, subtract arr[i-k] [OK]

Hint: Check subtraction index matches window size [OK]

Common Mistakes:

• Using wrong index for element leaving the window
• Starting loop at wrong index
• Incorrect initial sum calculation

5. You want to find the longest substring of a string s that contains at most 2 distinct characters using the sliding window technique. Which approach correctly applies the sliding window here?

hard

A. Fix window size to 2 and slide over the string

B. Expand the window by moving right pointer, shrink from left when distinct chars exceed 2

C. Count total distinct characters in the string once and return that count

D. Use nested loops to check all substrings of length 2

Solution

1. Step 1: Understand problem requirements

   We want the longest substring with at most 2 distinct characters, so window size is variable.

2. Step 2: Apply sliding window logic

   Expand window by moving right pointer. If distinct chars exceed 2, shrink window from left until condition holds.

3. Step 3: Evaluate options

   Expand the window by moving right pointer, shrink from left when distinct chars exceed 2 matches this approach. Fix window size to 2 and slide over the string fixes window size incorrectly. Options C and D do not use sliding window properly.

4. Final Answer:

   Expand the window by moving right pointer, shrink from left when distinct chars exceed 2 -> Option B

5. Quick Check:

   Variable window size with condition check = Expand the window by moving right pointer, shrink from left when distinct chars exceed 2 [OK]

Hint: Adjust window size dynamically based on distinct chars count [OK]

Common Mistakes:

• Fixing window size instead of adjusting dynamically
• Not shrinking window when condition breaks
• Using brute force nested loops instead of sliding window