Longest Substring Without Repeating Characters

Find the length of the longest substring without duplicate characters.

Minimum Window Substring

Find the minimum window substring in string S that contains all characters of string T.

Dynamic Programming & AdvancedIntermediate LevelStudy Time: 20 mins

Sliding Window Algorithm

The Sliding Window pattern reduces nested loop algorithms from O(N²) down to O(N) by maintaining a contiguous subarray window defined by start/end pointers.

Sliding Window Pattern Visualizer

Array loaded. Set window size K and click Slide Window to visualize window traversal.

Current Window Sum:-

Max Window Sum:-

4[0]

2[1]

1[2]

7[3]

8[4]

1[5]

2[6]

8[7]

1[8]

0[9]

Speed:

Sliding Window Maximum Sum Worked Trace

Sample Input:Array: [2, 1, 5, 1, 3, 2], Window Size K = 3

Step 1

Compute First Window Sum

Sum first K elements [2, 1, 5] -> Window Sum = 8, Max Sum = 8.

Window [2, 1, 5] -> Sum = 8 -> Max = 8

Initial window established in O(K) time.

Step 2

Slide Window Right (Subtract 2, Add 1)

Slide window to [1, 5, 1]. New Sum = 8 - 2 + 1 = 7. Max Sum remains 8.

Window [1, 5, 1] -> Sum = 7 -> Max = 8

Constant O(1) update avoids re-summing window elements!

Step 3

Slide Window Right (Subtract 1, Add 3)

Slide window to [5, 1, 3]. New Sum = 7 - 1 + 3 = 9. Max Sum updated to 9!

Window [5, 1, 3] -> Sum = 9 -> Max = 9

Final Maximum Subarray Sum of size 3 is 9.

Real-world analogy: Bus Camera Frame

Window Boundary

Hover over items for details

A camera window slides along a moving train track. As a new car enters the right side of the window, the oldest car exits on the left.

Window Boundary= Expand right pointer, contract left pointer.

Complexity analysis

Scenario Simulator: Dataset Size (N = 500)

Presets:

N = 10N = 10,000

Complexity Curve MapSliding Window: O(N) Linear Time

Hover curves to inspect classes

Time Steps (N=500)

500 steps (Linear)

O(N) Linear Time

Space Footprint

O(1) / O(N) Space

Memory growth rate as N expands.

Performance Rank

Efficient Tier

Relative efficiency rating for large N.

Operation	Time Complexity	Space Complexity
Sliding Window Execution	O(N)	O(1)

Code implementations

function maxSubarraySum(arr, k) {
  let maxSum = 0, windowSum = 0;
  for (let i = 0; i < k; i++) windowSum += arr[i];
  maxSum = windowSum;
  for (let i = k; i < arr.length; i++) {
    windowSum += arr[i] - arr[i - k];
    maxSum = Math.max(maxSum, windowSum);
  }
  return maxSum;
}