Sliding Window on Arrays in DSA Python - Build from Scratch

Sliding Window on Arrays

📖 Scenario: You are analyzing daily temperatures for a week to find the hottest 3-day period.

🎯 Goal: Build a program that uses the sliding window technique to find the maximum sum of temperatures over any 3 consecutive days.

📋 What You'll Learn

Create a list of daily temperatures for 7 days

Create a variable for the window size set to 3

Use a sliding window approach to find the maximum sum of any 3 consecutive days

Print the maximum sum found

💡 Why This Matters

🌍 Real World

Analyzing temperature trends helps in weather forecasting and planning outdoor activities.

💼 Career

Sliding window technique is widely used in data analysis, signal processing, and performance optimization tasks.

1

Create the list of daily temperatures

Create a list called temperatures with these exact values: [30, 32, 31, 29, 35, 36, 33]

DSA Python

# Create the list of temperatures
# Your code here

Hint

Use square brackets and separate numbers with commas.

2

Set the window size

Create a variable called window_size and set it to 3

DSA Python

temperatures = [30, 32, 31, 29, 35, 36, 33]
# Set the window size to 3
# Your code here

Hint

Just assign the number 3 to the variable window_size.

3

Find the maximum sum of any 3 consecutive days using sliding window

Create a variable called max_sum and set it to the sum of the first 3 elements in temperatures. Then use a for loop with variable i from 1 to len(temperatures) - window_size to slide the window. Inside the loop, update current_sum by subtracting the element leaving the window and adding the new element entering the window. Update max_sum if current_sum is greater.

DSA Python

temperatures = [30, 32, 31, 29, 35, 36, 33]
window_size = 3
# Calculate max_sum using sliding window
# Your code here

Hint

Start with the sum of the first 3 days. Then slide the window by removing the first day and adding the next day in each step.

4

Print the maximum sum

Print the value of max_sum

DSA Python

temperatures = [30, 32, 31, 29, 35, 36, 33]
window_size = 3
max_sum = sum(temperatures[0:window_size])
current_sum = max_sum
for i in range(1, len(temperatures) - window_size + 1):
    current_sum = current_sum - temperatures[i - 1] + temperatures[i + window_size - 1]
    if current_sum > max_sum:
        max_sum = current_sum
# Print the maximum sum
# Your code here

Hint

Use print(max_sum) to show the result.

Practice

1. What does the sliding window technique help to optimize when working with arrays?

easy

A. It reduces the time complexity by avoiding repeated calculations over overlapping subarrays.

B. It sorts the array in ascending order.

C. It finds the maximum element in the entire array.

D. It reverses the array elements.

Solution

1. Step 1: Understand the sliding window purpose

   The sliding window technique moves a fixed-size window over the array to process elements efficiently without recalculating everything each time.

2. Step 2: Identify what it optimizes

   It avoids repeated work on overlapping parts of the array, thus reducing time complexity compared to naive methods.

3. Final Answer:

   It reduces the time complexity by avoiding repeated calculations over overlapping subarrays. -> Option A

4. Quick Check:

   Sliding window = avoids repeated calculations [OK]

Hint: Sliding window avoids redoing work on overlapping parts [OK]

Common Mistakes:

• Thinking it sorts the array
• Assuming it finds max element always
• Confusing it with reversing arrays

2. Which of the following is the correct syntax to initialize a sliding window sum for the first 3 elements of an array arr in Python?

easy

A. window_sum = sum(arr[0:3])

B. window_sum = sum(arr[1:4])

C. window_sum = sum(arr[0:2])

D. window_sum = sum(arr[3:6])

Solution

1. Step 1: Identify the first 3 elements slice

   The first 3 elements are at indices 0, 1, and 2, so the slice is arr[0:3] because the end index is exclusive.

2. Step 2: Use sum function on correct slice

   sum(arr[0:3]) correctly sums elements at indices 0, 1, and 2.

3. Final Answer:

   window_sum = sum(arr[0:3]) -> Option A

4. Quick Check:

   sum(arr[0:3]) sums first 3 elements [OK]

Hint: Remember Python slices exclude the end index [OK]

Common Mistakes:

• Using wrong slice indices like arr[1:4]
• Using arr[0:2] which misses the third element
• Using arr[3:6] which skips first elements

3. What is the output of the following code?

arr = [2, 1, 5, 1, 3, 2]
window_size = 3
window_sum = sum(arr[0:3])
result = [window_sum]
for i in range(3, len(arr)):
    window_sum += arr[i] - arr[i - window_size]
    result.append(window_sum)
print(result)

medium

A. [2, 1, 5, 1]

B. [8, 9, 7, 6]

C. [8, 7, 9, 6]

D. [6, 7, 8, 9]

Solution

1. Step 1: Calculate initial window sum

   sum(arr[0:3]) = 2 + 1 + 5 = 8, so result starts as [8].

2. Step 2: Slide window and update sums

   i=3: window_sum = 8 + arr[3] - arr[0] = 8 + 1 - 2 = 7; result = [8,7] i=4: window_sum = 7 + arr[4] - arr[1] = 7 + 3 - 1 = 9; result = [8,7,9] i=5: window_sum = 9 + arr[5] - arr[2] = 9 + 2 - 5 = 6; result = [8,7,9,6]

3. Final Answer:

   [8, 7, 9, 6] -> Option C

4. Quick Check:

   Sliding sums = [8,7,9,6] [OK]

Hint: Add new element, subtract old element in window sum [OK]

Common Mistakes:

• Not subtracting the element leaving the window
• Incorrect initial sum calculation
• Appending wrong values to result

4. Find the error in the following sliding window code that calculates sums of windows of size 2:

arr = [4, 3, 2, 1]
window_size = 2
window_sum = sum(arr[0:window_size])
result = [window_sum]
for i in range(window_size, len(arr)):
    window_sum = window_sum + arr[i] + arr[i - window_size]
    result.append(window_sum)
print(result)

medium

A. The loop range should start from 0, not window_size.

B. The window_sum update should subtract arr[i - window_size], not add it.

C. The initial window_sum calculation is incorrect.

D. The result list should be initialized as empty.

Solution

1. Step 1: Analyze window_sum update

   The code adds both arr[i] and arr[i - window_size], but it should add the new element and subtract the element leaving the window.

2. Step 2: Correct the update formula

   Change window_sum = window_sum + arr[i] + arr[i - window_size] to window_sum = window_sum + arr[i] - arr[i - window_size].

3. Final Answer:

   The window_sum update should subtract arr[i - window_size], not add it. -> Option B

4. Quick Check:

   Subtract leaving element, not add [OK]

Hint: Subtract old element leaving window, add new element [OK]

Common Mistakes:

• Adding both new and old elements instead of subtracting old
• Wrong loop start index
• Incorrect initial sum

5. Given an array arr = [1, 3, 2, 6, -1, 4, 1, 8, 2] and window size 5, which sliding window sum is the maximum?
Use the sliding window technique to find the maximum sum of any 5 consecutive elements.

hard

A. 16

B. 19

C. 17

D. 18

Solution

1. Step 1: Calculate initial window sum for first 5 elements

   sum(arr[0:5]) = 1 + 3 + 2 + 6 + (-1) = 11

2. Step 2: Slide window and update sums, track max

   i=5: sum = 11 + 4 - 1 = 14 (max=14) i=6: sum = 14 + 1 - 3 = 12 (max=14) i=7: sum = 12 + 8 - 2 = 18 (max=18) i=8: sum = 18 + 2 - 6 = 14 (max=18)

3. Final Answer:

   18 -> Option D

4. Quick Check:

   Max sliding sum = 18 [OK]

Hint: Track max while sliding window sums update [OK]

Common Mistakes:

• Not updating max after each slide
• Wrong initial sum calculation
• Forgetting to subtract element leaving window