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Rest APIprogramming~10 mins

Sliding window algorithm in Rest API - Step-by-Step Execution

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Concept Flow - Sliding window algorithm
Start with window at beginning
↓
Check window size
↓
Process current window
↓
Slide window forward by 1
↓
More elements?
No→End
↩Back to Check window size
The sliding window algorithm moves a fixed-size window over data, processing each window step by step.
Execution Sample
Rest API
def max_sum_subarray(arr, k):
    max_sum = 0
    window_sum = 0
    for i in range(len(arr)):
        window_sum += arr[i]
        if i >= k - 1:
            max_sum = max(max_sum, window_sum)
            window_sum -= arr[i - k + 1]
This code finds the maximum sum of any subarray of size k by sliding a window over the array.
Execution Table
Stepi (index)window_sum before addAdd arr[i]window_sum after addCondition i >= k-1max_sum updateSubtract arr[i-k+1]window_sum after subtract
100arr[0]=22Falsemax_sum=0
212arr[1]=13Falsemax_sum=0
323arr[2]=58Truemax_sum=8Subtract arr[0]=26
436arr[3]=17Truemax_sum=8Subtract arr[1]=16
546arr[4]=39Truemax_sum=9Subtract arr[2]=54
654arr[5]=26Truemax_sum=9Subtract arr[3]=15
765arr[6]=16Truemax_sum=9Subtract arr[4]=33
873arr[7]=25Truemax_sum=9Subtract arr[5]=23
983arr[8]=14Truemax_sum=9Subtract arr[6]=13
1093arr[9]=47Truemax_sum=9Subtract arr[7]=25
11105arr[10]=38Truemax_sum=9Subtract arr[8]=17
12117arr[11]=29Truemax_sum=9Subtract arr[9]=45
13125arr[12]=16Truemax_sum=9Subtract arr[10]=33
14133arr[13]=25Truemax_sum=9Subtract arr[11]=23
15143arr[14]=14Truemax_sum=9Subtract arr[12]=13
16153arr[15]=25Truemax_sum=9Subtract arr[13]=23
17163arr[16]=14Truemax_sum=9Subtract arr[14]=13
18173arr[17]=25Truemax_sum=9Subtract arr[15]=23
19183arr[18]=14Truemax_sum=9Subtract arr[16]=13
20193arr[19]=25Truemax_sum=9Subtract arr[17]=23
21203arr[20]=14Truemax_sum=9Subtract arr[18]=13
22213arr[21]=25Truemax_sum=9Subtract arr[19]=23
23223arr[22]=14Truemax_sum=9Subtract arr[20]=13
24233arr[23]=25Truemax_sum=9Subtract arr[21]=23
25243arr[24]=14Truemax_sum=9Subtract arr[22]=13
26253arr[25]=25Truemax_sum=9Subtract arr[23]=23
27263arr[26]=14Truemax_sum=9Subtract arr[24]=13
28273arr[27]=25Truemax_sum=9Subtract arr[25]=23
29283arr[28]=14Truemax_sum=9Subtract arr[26]=13
30293arr[29]=25Truemax_sum=9Subtract arr[27]=23
31303arr[30]=14Truemax_sum=9Subtract arr[28]=13
32313arr[31]=25Truemax_sum=9Subtract arr[29]=23
33323arr[32]=14Truemax_sum=9Subtract arr[30]=13
34333arr[33]=25Truemax_sum=9Subtract arr[31]=23
35343arr[34]=14Truemax_sum=9Subtract arr[32]=13
36353arr[35]=25Truemax_sum=9Subtract arr[33]=23
37363arr[36]=14Truemax_sum=9Subtract arr[34]=13
38373arr[37]=25Truemax_sum=9Subtract arr[35]=23
39383arr[38]=14Truemax_sum=9Subtract arr[36]=13
40393arr[39]=25Truemax_sum=9Subtract arr[37]=23
41403arr[40]=14Truemax_sum=9Subtract arr[38]=13
42413arr[41]=25Truemax_sum=9Subtract arr[39]=23
43423arr[42]=14Truemax_sum=9Subtract arr[40]=13
44433arr[43]=25Truemax_sum=9Subtract arr[41]=23
45443arr[44]=14Truemax_sum=9Subtract arr[42]=13
46453arr[45]=25Truemax_sum=9Subtract arr[43]=23
47463arr[46]=14Truemax_sum=9Subtract arr[44]=13
48473arr[47]=25Truemax_sum=9Subtract arr[45]=23
49483arr[48]=14Truemax_sum=9Subtract arr[46]=13
50493arr[49]=25Truemax_sum=9Subtract arr[47]=23
51503arr[50]=14Truemax_sum=9Subtract arr[48]=13
52513arr[51]=25Truemax_sum=9Subtract arr[49]=23
53523arr[52]=14Truemax_sum=9Subtract arr[50]=13
54533arr[53]=25Truemax_sum=9Subtract arr[51]=23
55543arr[54]=14Truemax_sum=9Subtract arr[52]=13
56553arr[55]=25Truemax_sum=9Subtract arr[53]=23
57563arr[56]=14Truemax_sum=9Subtract arr[54]=13
58573arr[57]=25Truemax_sum=9Subtract arr[55]=23
59583arr[58]=14Truemax_sum=9Subtract arr[56]=13
60593arr[59]=25Truemax_sum=9Subtract arr[57]=23
61603arr[60]=14Truemax_sum=9Subtract arr[58]=13
62613arr[61]=25Truemax_sum=9Subtract arr[59]=23
63623arr[62]=14Truemax_sum=9Subtract arr[60]=13
64633arr[63]=25Truemax_sum=9Subtract arr[61]=23
65643arr[64]=14Truemax_sum=9Subtract arr[62]=13
66653arr[65]=25Truemax_sum=9Subtract arr[63]=23
67663arr[66]=14Truemax_sum=9Subtract arr[64]=13
68673arr[67]=25Truemax_sum=9Subtract arr[65]=23
69683arr[68]=14Truemax_sum=9Subtract arr[66]=13
70693arr[69]=25Truemax_sum=9Subtract arr[67]=23
71703arr[70]=14Truemax_sum=9Subtract arr[68]=13
72713arr[71]=25Truemax_sum=9Subtract arr[69]=23
73723arr[72]=14Truemax_sum=9Subtract arr[70]=13
74733arr[73]=25Truemax_sum=9Subtract arr[71]=23
75743arr[74]=14Truemax_sum=9Subtract arr[72]=13
76753arr[75]=25Truemax_sum=9Subtract arr[73]=23
77763arr[76]=14Truemax_sum=9Subtract arr[74]=13
78773arr[77]=25Truemax_sum=9Subtract arr[75]=23
79783arr[78]=14Truemax_sum=9Subtract arr[76]=13
80793arr[79]=25Truemax_sum=9Subtract arr[77]=23
81803arr[80]=14Truemax_sum=9Subtract arr[78]=13
82813arr[81]=25Truemax_sum=9Subtract arr[79]=23
83823arr[82]=14Truemax_sum=9Subtract arr[80]=13
84833arr[83]=25Truemax_sum=9Subtract arr[81]=23
85843arr[84]=14Truemax_sum=9Subtract arr[82]=13
86853arr[85]=25Truemax_sum=9Subtract arr[83]=23
87863arr[86]=14Truemax_sum=9Subtract arr[84]=13
88873arr[87]=25Truemax_sum=9Subtract arr[85]=23
89883arr[88]=14Truemax_sum=9Subtract arr[86]=13
90893arr[89]=25Truemax_sum=9Subtract arr[87]=23
91903arr[90]=14Truemax_sum=9Subtract arr[88]=13
92913arr[91]=25Truemax_sum=9Subtract arr[89]=23
93923arr[92]=14Truemax_sum=9Subtract arr[90]=13
94933arr[93]=25Truemax_sum=9Subtract arr[91]=23
95943arr[94]=14Truemax_sum=9Subtract arr[92]=13
96953arr[95]=25Truemax_sum=9Subtract arr[93]=23
97963arr[96]=14Truemax_sum=9Subtract arr[94]=13
98973arr[97]=25Truemax_sum=9Subtract arr[95]=23
99983arr[98]=14Truemax_sum=9Subtract arr[96]=13
100993arr[99]=25Truemax_sum=9Subtract arr[97]=23
Exit-------Reached end of array
💡 Reached end of array, no more elements to slide window
Variable Tracker
VariableStartAfter 1After 2After 3After 4After 5Final
iN/A0123499
window_sum0238795
max_sum0008899
Key Moments - 2 Insights
Why do we subtract arr[i-k+1] after updating max_sum?
Because the window slides forward by removing the leftmost element, as shown in execution_table rows 3 and onwards where window_sum subtracts arr[i-k+1].
Why do we only update max_sum when i >= k-1?
Because before i reaches k-1, the window size is smaller than k, so we wait until the window is full to compare sums, as seen in execution_table rows 1 and 2 where condition is False.
Visual Quiz - 3 Questions
Test your understanding
Look at the execution_table at step 3, what is the window_sum after subtracting arr[i-k+1]?
A2
B8
C6
D0
💡 Hint
Check the 'window_sum after subtract' column at step 3 in execution_table.
At which step does max_sum first update to 9?
AStep 5
BStep 4
CStep 3
DStep 6
💡 Hint
Look at the 'max_sum update' column in execution_table rows 3 to 6.
If k was 2 instead of 3, when would the first max_sum update occur?
AAt i=2
BAt i=1
CAt i=0
DAt i=3
💡 Hint
Recall the condition i >= k-1 controls max_sum update; with k=2, this is i >= 1.
Concept Snapshot
Sliding window algorithm:
- Move a fixed-size window over data
- Add new element to window_sum
- When window full (i >= k-1), update max_sum
- Subtract element leaving window
- Repeat until end
Efficient for continuous subarray problems.
Full Transcript
The sliding window algorithm moves a fixed-size window over an array. It adds the new element to the window sum. When the window reaches the desired size, it updates the maximum sum found so far. Then it subtracts the element that leaves the window as it slides forward. This repeats until the window reaches the end of the array. This method avoids recalculating sums from scratch each time, making it efficient for problems like finding maximum sum subarrays.

Practice

(1/5)
1. What is the main advantage of using the sliding window algorithm in processing data streams?
easy
A. It processes data in fixed-size chunks efficiently by reusing previous computations.
B. It sorts the entire data before processing.
C. It stores all data in memory for faster access.
D. It processes data randomly without any order.

Solution

  1. Step 1: Understand the sliding window concept

    The sliding window algorithm processes data in fixed-size chunks, moving forward by removing the oldest data and adding new data.

  2. Step 2: Identify the main advantage

    This approach avoids recalculating over the entire data repeatedly, saving time and memory.

  3. Final Answer:

    It processes data in fixed-size chunks efficiently by reusing previous computations. -> Option A

  4. Quick Check:

    Sliding window = efficient chunk processing [OK]
Hint: Remember: sliding window reuses old results to save time [OK]
Common Mistakes:
  • Thinking it sorts data first
  • Assuming it stores all data in memory
  • Believing it processes data randomly
2. Which of the following is the correct way to initialize a sliding window of size 3 over a list named data in Python?
easy
A. window = data[3]
B. window = data[0:3]
C. window = data(0,3)
D. window = data[:]

Solution

  1. Step 1: Recall Python list slicing syntax

    To get the first 3 elements, use data[0:3], which includes indices 0, 1, and 2.

  2. Step 2: Check other options

    data(0,3) is invalid syntax, data[3] gets only one element at index 3, data[:] gets the whole list.

  3. Final Answer:

    window = data[0:3] -> Option B

  4. Quick Check:

    Slice first 3 elements = data[0:3] [OK]
Hint: Use data[start:end] to slice lists in Python [OK]
Common Mistakes:
  • Using parentheses instead of brackets
  • Selecting a single element instead of a slice
  • Taking the whole list instead of a window
3. Given the Python code below, what will be the output? 
data = [1, 3, 5, 7, 9]
window_size = 3
result = []
for i in range(len(data) - window_size + 1):
    window_sum = sum(data[i:i+window_size])
    result.append(window_sum)
print(result)
medium
A. [1, 3, 5]
B. [15, 21, 27]
C. [3, 5, 7]
D. [9, 15, 21]

Solution

  1. Step 1: Understand the loop range and slicing

    The loop runs from i=0 to i=2 (5 - 3 + 1 = 3 iterations). Each slice is data[i:i+3].

  2. Step 2: Calculate sums for each window

    i=0: sum([1,3,5])=9; i=1: sum([3,5,7])=15; i=2: sum([5,7,9])=21.

  3. Final Answer:

    [9, 15, 21] -> Option D

  4. Quick Check:

    Sliding sums = [9, 15, 21] [OK]
Hint: Sum slices of size window_size in a loop [OK]
Common Mistakes:
  • Incorrect loop range causing index errors
  • Summing wrong slices
  • Confusing window size with list length
4. The following code tries to implement a sliding window sum but has a bug. What is the error? 
data = [2, 4, 6, 8]
window_size = 2
result = []
for i in range(len(data) - window_size):
    window_sum = sum(data[i:i+window_size])
    result.append(window_sum)
print(result)
medium
A. The result list is not initialized.
B. The sum function is used incorrectly.
C. The loop range misses the last window, causing incomplete results.
D. Window size is larger than data length.

Solution

  1. Step 1: Analyze the loop range

    The loop runs from 0 to len(data) - window_size - 1, which is 4 - 2 - 1 = 1, so only indices 0 and 1.

  2. Step 2: Identify missing last window

    The last valid window starts at index 2 (data[2:4]), but the loop excludes it because it should run to len(data) - window_size + 1.

  3. Final Answer:

    The loop range misses the last window, causing incomplete results. -> Option C

  4. Quick Check:

    Loop range must cover all windows [OK]
Hint: Use range(len(data) - window_size + 1) for full coverage [OK]
Common Mistakes:
  • Using wrong loop range causing missed windows
  • Misusing sum function
  • Not initializing result list
5. You want to find the maximum sum of any sliding window of size 4 in a large list data. Which approach is most efficient?
hard
A. Use a sliding window by adding the new element and subtracting the oldest element from the previous sum.
B. Calculate sum of each window from scratch using sum(data[i:i+4]) in a loop.
C. Sort the entire list and pick the top 4 elements to sum.
D. Use recursion to calculate sums of all windows.

Solution

  1. Step 1: Understand the problem of efficiency

    Calculating sum from scratch for each window is slow for large data because it repeats work.

  2. Step 2: Apply sliding window optimization

    By keeping the previous window sum, add the new element and subtract the oldest element to get the next sum quickly.

  3. Step 3: Evaluate other options

    Sorting does not help find consecutive window sums; recursion adds overhead and is inefficient here.

  4. Final Answer:

    Use a sliding window by adding the new element and subtracting the oldest element from the previous sum. -> Option A

  5. Quick Check:

    Sliding window sum update = add new - remove old [OK]
Hint: Update sums by adding new and removing old element [OK]
Common Mistakes:
  • Recalculating sums fully each time
  • Sorting unrelated to consecutive sums
  • Using recursion unnecessarily