Sliding window technique in Data Structures Theory - Step-by-Step Execution

Concept Flow - Sliding window technique

Start with window at beginning

↓

Check window size or condition

↓

If condition met

→Process current window

↓

Slide window forward by moving start and/or end

↓

Repeat until end of data reached

↓

Stop

The sliding window technique moves a fixed or variable size window over data, processing each window efficiently by updating from the previous one.

Execution Sample

Data Structures Theory

arr = [1, 3, 2, 5, 1, 1, 2]
window_size = 3
for i in range(len(arr) - window_size + 1):
    window = arr[i:i+window_size]
    print(sum(window))

This code calculates the sum of every subarray of size 3 by sliding a window over the array.

Analysis Table

Step	Window Start Index	Window End Index	Window Elements	Sum of Window	Action
1	0	2	[1, 3, 2]	6	Calculate sum of first window
2	1	3	[3, 2, 5]	10	Slide window right by 1, calculate sum
3	2	4	[2, 5, 1]	8	Slide window right by 1, calculate sum
4	3	5	[5, 1, 1]	7	Slide window right by 1, calculate sum
5	4	6	[1, 1, 2]	4	Slide window right by 1, calculate sum
6	-	-	-	-	Reached end of array, stop

💡 Window end index reached the last element, no more windows possible.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
i	-	0	1	2	3	4	End
window	-	[1, 3, 2]	[3, 2, 5]	[2, 5, 1]	[5, 1, 1]	[1, 1, 2]	-
sum(window)	-	6	10	8	7	4	-

Key Insights - 3 Insights

Why do we stop when the window end index reaches the last element?

Because the window size is fixed, once the end index reaches the last element, we cannot form a full window beyond that point. See execution_table row 6.

Why do we slide the window by moving the start index forward?

Sliding the window forward means removing the first element and adding the next element after the current window. This keeps the window size constant and allows efficient processing. See execution_table rows 2-5.

Can the window size change during sliding?

Yes, in some problems the window size can vary based on conditions, but in this example it is fixed. Variable window sizes require adjusting start and end pointers carefully.

Visual Quiz - 3 Questions

Look at the execution_table, what is the sum of the window at step 3?

A 7

B 8

C 10

D 6

💡 Hint

Check the 'Sum of Window' column at step 3 in the execution_table.

At which step does the window first include the element '5'?

A Step 2

B Step 1

C Step 3

D Step 4

💡 Hint

Look at the 'Window Elements' column in execution_table rows to find when '5' appears.

If the window size was 2 instead of 3, how many steps would the loop run?

A 5

B 4

C 6

D 7

💡 Hint

Calculate len(arr) - window_size + 1 with window_size=2 and compare with execution_table step count.

Concept Snapshot

Sliding window technique:
- Move a window over data to process subarrays or substrings
- Window size can be fixed or variable
- Slide by moving start and/or end pointers
- Efficient for problems needing continuous segment analysis
- Avoids repeated full scans by reusing previous computations

Full Transcript

The sliding window technique involves moving a window of fixed or variable size over a data sequence. At each step, the window covers a subset of elements which can be processed efficiently. For example, summing elements inside the window can be done by updating the previous sum instead of recalculating fully. The window slides forward by moving its start and end positions, stopping when the window can no longer fit inside the data. This technique is useful for problems involving continuous segments like subarrays or substrings. The execution table shows how the window moves step-by-step, what elements it covers, and the sum calculated at each step. Key points include understanding when to stop sliding and how the window moves forward. This approach reduces repeated work and improves performance in many algorithms.