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105 lines
3.1 KiB
Plaintext
105 lines
3.1 KiB
Plaintext
---
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title: Sliding Window
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description: 'Sliding window is a specialized two-pointer family where the pointers define a contiguous interval and you maintain information about that entire interval as it moves.'
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hidden: true
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---
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:::warning
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This is the family where invariants matter the most
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:::
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## What Makes Sliding Window Different?
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Many problems have two moving boundaries. That alone does not make them sliding window problems.
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A problem belongs to this family when:
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- the answer depends on the subarray or substring between left and right
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- you can update the window state incrementally as elements enter or leave
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- you maintain a condition that tells you whether the window is valid
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## What is an Invariant?
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An invariant is a statement that stays true before and after every iteration.
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For sliding window, the invariant often looks like one of these:
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- "the current window is valid"
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- "the current window contains no duplicates"
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- "the current window sum is at most the target"
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- "the frequency map matches the characters currently inside the window"
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The invariant gives the loop its structure:
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- expand the window by moving right
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- update the window state
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- if the invariant breaks, shrink from the left until it holds again
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- update the answer only when you know the invariant is satisfied
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## Why Invariants Matter
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Without an invariant, shrinking the window becomes arbitrary. You no longer know:
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- when the window is valid
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- when to update the answer
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- why the left pointer should stop moving
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- The invariant is the reason the algorithm is correct.
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## The Main Subtypes
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### 1. Fixed-size windows
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:::tip
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The window size never changes. The main task is updating the window state efficiently when one element enters and one leaves.
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:::
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### 2. Flexible-size windows with a validity rule
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:::tip
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Here the window expands until invalid, then shrinks until valid again.
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:::
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### 3. Frequency-tracking windows
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:::tip
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The difficulty comes from keeping the bookkeeping correct as characters enter and leave.
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:::
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## How Sliding Window Differs From Other Two-Pointer Families
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Compare it with Container With Most Water:
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- In sliding window, the interval itself has meaning.
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- In container, the interval is just the remaining search space.
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Compare it with Remove Duplicates:
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- In sliding window, both pointers describe a live window.
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- In compaction, the left part of the array is already the answer prefix.
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## A Practical Template
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A common variable-size sliding window has this shape:
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1. Add the new rightmost element.
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2. Update the window state.
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3. While the invariant is broken, remove elements from the left.
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4. Once the invariant is restored, update the answer.
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The exact data structure changes from problem to problem, but the logic stays the same.
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As you work through this section, keep asking:
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:::warning
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What invariant does my window maintain, and at what moment is it safe to update the answer?
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:::
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