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Two Pointers & Sliding Window

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Two Sum Pattern

2 + 6 = 8

2

7

11

15

1

8

3

9

4

6

L=0target: 10R=9

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Two Pointers & Sliding Window

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Back to Two Pointers and Sliding Window

Maximum Sum Subarray

Slide a fixed-size window of length k across the array. Update the sum in O(1) per step by removing the outgoing element and adding the incoming one.

Visualization

Window k:

Speed

0

Current Sum

0

Max Sum

0–2

Window

0

2

1

1

2

5

3

1

4

3

5

2

Window [0..2] = [2, 1, 5]

Current windowMaximum window (final)Outside window

Ready — press Play or step through.

Complexity

O(n)

Time

O(1)

Space

O(k)

Initial Sum

O(1)

Per Slide

How It Works

1Compute the sum of the first k elements — this is the initial window sum and initial max
2Slide one step right: subtract the element leaving the left and add the element entering the right
3Update the maximum sum if the new window sum is larger
4Repeat until the window reaches the right end of the array

Applications

•Finding the busiest k-hour window in server logs
•Stock price analysis: best k-day gain window
•Image processing: sliding average filters (box blur)
•Network throughput: maximum bandwidth in any k-second window

Active Recall Quiz

Question 1 of 3

Why is the sliding window approach O(n) instead of O(n*k)?