Pattern1 Practice3 Interview

Fixed-size Window

GuideCode Labs

Slide a window of constant length while adding the entering value and removing the leaving value. Learn its decision rule, maintained state, Python cost model, and transfer from a focused drill to a full Interview Problem.

Recognize it when

Consider Fixed-size Window when the prompt's constraints and required operations match this shape: Slide a window of constant length while adding the entering value and removing the leaving value.

On this page · Fix the Window Width Up Front

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Fix the Window Width Up Front

When every candidate has the same width, boundary movement is predetermined. The algorithm needs only the aggregate for the current complete window.

Build the First Window Once

Compute the first width elements before sliding. If width exceeds input length, no complete candidate exists; define the sentinel rather than returning a misleading partial aggregate.

Trace Fixed Window Updates

Reference

def fixed_window_trace(values,width):
    if width>len(values): return []
    total=sum(values[:width]); trace=[[0,width-1,total]]
    for right in range(width,len(values)):
        total+=values[right]-values[right-width]
        trace.append([right-width+1,right,total])
    return trace

Practice

Implement fixed_window_trace(values,width). Return [left,right,sum] for every complete window.

def fixed_window_trace(values,width):
    pass

Public tests

Replace one leaving value

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Subtract Leaving Add Entering

Moving right by one removes exactly the value at right minus width and adds the new right value. This constant-time transition avoids recomputing each O(width) slice.

Find Maximum Fixed Window Sum

Reference

def max_window_sum(values,width):
    if width>len(values): return None
    total=sum(values[:width]); best=total
    for right in range(width,len(values)):
        total+=values[right]-values[right-width]
        best=max(best,total)
    return best

Practice

Implement max_window_sum(values,width). Return the maximum sum of exactly width values, or None when no complete window exists.

def max_window_sum(values,width):
    pass

Public tests

Compare every complete window

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Choose a Fixed Window or Prefix Sums

Use a fixed window for one left-to-right pass and incremental state. Use prefix sums when many arbitrary immutable ranges must be queried. Both build in O(n), but prefix queries support varying boundaries with O(n) storage.

Explain It in an Interview

Say: “Every candidate contains exactly width items. Each slide replaces one leaving value with one entering value, so the aggregate remains exact.” Count the initial sum and clarify width, empty input, and negative values.

Python Version Note

Python 3.11+

The examples use the standard Python syntax and containers supported by the browser Judge; the Fixed-size Window invariant is independent of a minor Python release.

Verify in Python docs

Complexity & Invariants

Interview bounds depend on the stated representation, input model, and real Python operations.

Operation	Average	Worst	Interview note
Fixed-size Window decision loop	`O(n)`	`O(n)`	When every candidate segment has the same width, reuse the previous aggregate instead of recomputing each segment. Before appending a result, the rolling total contains exactly values[right - width + 1:right + 1].

Space

O(n) for the returned sums for the focused Slide a Fixed Window implementation.

Assumptions

The first total covers exactly the first width values. Each slide removes the value leaving the window and adds the value entering it, so every appended total belongs to the requested contiguous window.
The bound includes real Python operations; no repeated slicing, linear list membership, or hidden sorting is treated as free.

Invariants Worth Saying Aloud

State the precise Fixed-size Window invariant before coding and preserve it after every update, traversal step, or recursive return.
The summary always contains exactly k consecutive items.
Every result is recorded only after the window reaches size k.
When every candidate segment has the same width, reuse the previous aggregate instead of recomputing each segment. Preserve this property after every transition.
Before appending a result, the rolling total contains exactly values[right - width + 1:right + 1]. Preserve this property after every transition.

When To Use Or Avoid Fixed-size Window

Use It When

Use Fixed-size Window when the prompt exposes the ordering, monotonicity, recurrence, or constraint that makes this decision safe.
Use it when the summary always contains exactly k consecutive items.

Choose Another Tool When

Avoid Fixed-size Window when its decision rule cannot eliminate work or preserve the required state.
Avoid forcing the label onto a prompt whose simpler direct scan already meets the constraints.

Common Pitfalls

These are the mistakes most likely to survive a happy-path example and fail a boundary case.

Moving state without a proof

Applying the pattern without proving its ordering, monotonicity, or window invariant can silently miss valid candidates.

Prevent it: Write the decision rule beside the loop and verify it against Slide a Fixed Window before optimizing.

Avoid

def fixed_window_sums(values, width):
    pass

Use instead

def fixed_window_sums(values, width):
    if width > len(values):
        return []
    total = sum(values[:width])
    result = [total]
    for right in range(width, len(values)):
        total += values[right] - values[right - width]
        result.append(total)
    return result

Where you will hit this: Slide a Fixed Window(opens in a new tab)

Breaking the maintained state

Emits trailing partial windows after the last complete fixed-width segment.

Prevent it: Use the public tests and preserve this state: The summary always contains exactly k consecutive items.

Avoid

def fixed_window_sums(values, width):
    return [sum(values[start:start + width]) for start in range(len(values))]

Use instead

def fixed_window_sums(values, width):
    if width > len(values):
        return []
    total = sum(values[:width])
    result = [total]
    for right in range(width, len(values)):
        total += values[right] - values[right - width]
        result.append(total)
    return result

Where you will hit this: Slide a Fixed Window(opens in a new tab)

Hiding Python work in the hot path

Python slicing, copying, membership in lists, or repeated sorting inside the loop can invalidate the intended complexity.

Prevent it: Count every slice, copy, sort, membership check, and container update before claiming O(n).

Avoid

def fixed_window_sums(values, width):
    return [sum(values[start:start + width]) for start in range(len(values))]

Use instead

def fixed_window_sums(values, width):
    if width > len(values):
        return []
    total = sum(values[:width])
    result = [total]
    for right in range(width, len(values)):
        total += values[right] - values[right - width]
        result.append(total)
    return result

Where you will hit this: K-Radius Subarray Averages(opens in a new tab)

Reviewed References

Official Python documentation supports language behavior. Canonical problem pages provide additional practice context.

Python deque Recipes(opens in a new tab)
python-docs · checked 2026-07-27

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