Why Sliding Window on Arrays in DSA Typescript?

The Big Idea

Discover how to save time and avoid mistakes when checking groups of numbers in a list!

The Scenario

Imagine you want to find the highest sum of 3 consecutive days' sales in a month. You try adding every group of 3 days manually, one by one, writing down each total.

The Problem

This manual way is slow and tiring because you add many numbers repeatedly. You waste time recalculating sums for overlapping days, and mistakes happen easily.

The Solution

The sliding window method moves a small window over the array, adding the new number and removing the old one from the sum. This way, you avoid repeating work and get results quickly and correctly.

Before vs After

✗ Before

let maxSum = 0;
for (let i = 0; i <= arr.length - 3; i++) {
  let sum = arr[i] + arr[i+1] + arr[i+2];
  if (sum > maxSum) maxSum = sum;
}

✓ After

let windowSum = 0;
for (let i = 0; i < 3; i++) windowSum += arr[i];
let maxSum = windowSum;
for (let i = 3; i < arr.length; i++) {
  windowSum += arr[i] - arr[i - 3];
  if (windowSum > maxSum) maxSum = windowSum;
}

What It Enables

This method lets you quickly find sums or averages of any fixed-size group in a list without repeating calculations.

Real Life Example

Checking the best 7-day weather temperature average to plan a vacation, without adding all 7 days again for each new week.

Key Takeaways

Manual sum calculation repeats work and wastes time.

Sliding window updates sums by adding new and removing old values.

This makes finding max/min sums or averages fast and easy.

Practice

1. What is the main purpose of the sliding window technique on arrays?

easy

A. To find the maximum element in the entire array

B. To sort the array in ascending order

C. To reverse the elements of the array

D. To efficiently process subarrays of fixed size without repeated work

Solution

1. Step 1: Understand the sliding window concept

   The sliding window technique moves a fixed-size window over the array to process subarrays efficiently.

2. Step 2: Identify the purpose

   It avoids recalculating values for overlapping parts of subarrays, improving performance.

3. Final Answer:

   To efficiently process subarrays of fixed size without repeated work -> Option D

4. Quick Check:

   Sliding window = efficient fixed-size subarray processing [OK]

Hint: Think of a moving window over array parts for efficiency [OK]

Common Mistakes:

• Confusing sliding window with sorting
• Thinking it reverses the array
• Assuming it finds max of whole array

2. Which of the following is the correct TypeScript syntax to start a sliding window loop for an array arr with window size k?

easy

A. for (let i = 0; i < arr.length; i += k)

B. for (let i = 0; i < arr.length + k; i++)

C. for (let i = 0; i <= arr.length - k; i++)

D. for (let i = 1; i <= arr.length - k; i++)

Solution

1. Step 1: Determine loop range for sliding window

   The window of size k must fit inside the array, so the last start index is arr.length - k.

2. Step 2: Check loop syntax correctness

   Loop from i = 0 up to and including arr.length - k ensures all windows are covered.

3. Final Answer:

   for (let i = 0; i <= arr.length - k; i++) -> Option C

4. Quick Check:

   Loop runs from 0 to arr.length - k inclusive [OK]

Hint: Loop until index allows full window inside array [OK]

Common Mistakes:

• Using < instead of <= causing last window to miss
• Starting loop at 1 instead of 0
• Incrementing by k skipping windows

3. What is the output of this TypeScript code?

const arr = [1, 3, 2, 6, -1, 4, 1, 8, 2];
const k = 5;
const result: number[] = [];
let windowSum = 0;

for (let i = 0; i < k; i++) {
  windowSum += arr[i];
}
result.push(windowSum);

for (let i = k; i < arr.length; i++) {
  windowSum += arr[i] - arr[i - k];
  result.push(windowSum);
}

console.log(result);

medium

A. [11, 14, 12, 18, 14]

B. [11, 10, 12, 15, 13]

C. [11, 14, 17, 20, 23]

D. [11, 13, 15, 17, 19]

Solution

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

   1 + 3 + 2 + 6 + (-1) = 11. result = [11]

2. Step 2: Slide window and update sums

   i=5: 11 - 1 + 4 = 14
   i=6: 14 - 3 + 1 = 12
   i=7: 12 - 2 + 8 = 18
   i=8: 18 - 6 + 2 = 14
   result = [11, 14, 12, 18, 14]

3. Final Answer:

   [11, 14, 12, 18, 14] -> Option A

4. Quick Check:

   windowSum += arr[i] - arr[i - k] each slide [OK]

Hint: Add new element, subtract old element for each slide [OK]

Common Mistakes:

• Not subtracting the element leaving the window
• Incorrect initial sum calculation
• Off-by-one errors in loop indices

4. Identify the error in this sliding window code snippet and choose the fix:

const arr = [2, 1, 5, 1, 3, 2];
const k = 3;
let maxSum = 0;
let windowSum = 0;

for (let i = 0; i < k; i++) {
  windowSum += arr[i];
}
maxSum = windowSum;

for (let i = k; i < arr.length; i++) {
  windowSum = windowSum + arr[i] - arr[i + k];
  if (windowSum > maxSum) {
    maxSum = windowSum;
  }
}
console.log(maxSum);

medium

A. Initialize maxSum to Number.MIN_VALUE

B. Change arr[i + k] to arr[i - k] in the second loop

C. Change first loop to run from i = 1 to k

D. Add a check if i + k < arr.length before subtraction

Solution

1. Step 1: Analyze the sliding window update

   The window slides by removing the element leaving the window and adding the new element entering it. The element leaving is at index i - k, not i + k.

2. Step 2: Correct the subtraction index

   Change arr[i + k] to arr[i - k] to correctly remove the leftmost element of the previous window.

3. Final Answer:

   Change arr[i + k] to arr[i - k] in the second loop -> Option B

4. Quick Check:

   Subtract element leaving window at i-k [OK]

Hint: Subtract element at i-k, not i+k, when sliding window [OK]

Common Mistakes:

• Using wrong index for element leaving window
• Not initializing maxSum correctly
• Loop range errors

5. Given an array of integers, write a sliding window algorithm to find the maximum sum of any subarray of size k. Which approach below correctly implements this in TypeScript?

hard

A. Initialize sum of first k elements, then slide window adding new element and subtracting old, updating max sum each time

B. Sort the array and sum the first k elements

C. Use nested loops to sum every subarray of size k and track max sum

D. Add all elements and divide by k to get average, then multiply by k for max sum

Solution

1. Step 1: Understand the sliding window max sum approach

   Calculate sum of first k elements as initial window sum.

2. Step 2: Slide window across array

   For each new element, add it and subtract the element leaving the window, update max sum if current sum is higher.

3. Step 3: Avoid inefficient methods

   Sorting or nested loops are less efficient; averaging does not find max sum.

4. Final Answer:

   Initialize sum of first k elements, then slide window adding new element and subtracting old, updating max sum each time -> Option A

5. Quick Check:

   Sliding window updates sum and tracks max [OK]

Hint: Slide window, update sum and max in one pass [OK]

Common Mistakes:

• Using nested loops causing slow performance
• Sorting array which changes element order
• Calculating average instead of max sum