chore: clean up content phase organization

apps/docs/content/(01-linear-structures)/sliding-window/index.mdx

@@ -0,0 +1,104 @@
+---
+title: Sliding Window
+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.'
+hidden: true
+---
+
+:::warning
+This is the family where invariants matter the most
+:::
+
+## What Makes Sliding Window Different?
+
+Many problems have two moving boundaries. That alone does not make them sliding window problems.
+
+A problem belongs to this family when:
+
+- the answer depends on the subarray or substring between left and right
+- you can update the window state incrementally as elements enter or leave
+- you maintain a condition that tells you whether the window is valid
+
+## What is an Invariant?
+
+
+An invariant is a statement that stays true before and after every iteration.
+
+For sliding window, the invariant often looks like one of these:
+
+- "the current window is valid"
+- "the current window contains no duplicates"
+- "the current window sum is at most the target"
+- "the frequency map matches the characters currently inside the window"
+
+The invariant gives the loop its structure:
+
+- expand the window by moving right
+- update the window state
+- if the invariant breaks, shrink from the left until it holds again
+- update the answer only when you know the invariant is satisfied
+
+
+## Why Invariants Matter
+
+Without an invariant, shrinking the window becomes arbitrary. You no longer know:
+
+- when the window is valid
+- when to update the answer
+- why the left pointer should stop moving
+- The invariant is the reason the algorithm is correct.
+
+## The Main Subtypes
+
+### 1. Fixed-size windows
+
+:::tip
+The window size never changes. The main task is updating the window state efficiently when one element enters and one leaves.
+:::
+
+![Sliding Window Fixed Size](../../../public/sliding-window-fixed-size.svg)
+
+### 2. Flexible-size windows with a validity rule
+
+:::tip
+Here the window expands until invalid, then shrinks until valid again.
+:::
+
+![Flexible-size windows](../../../public/sliding-window-flexible.svg)
+
+
+### 3. Frequency-tracking windows
+
+:::tip
+The difficulty comes from keeping the bookkeeping correct as characters enter and leave.
+:::
+
+![Frequency-tracking windows](../../../public/sliding-window-frequency.svg)
+
+## How Sliding Window Differs From Other Two-Pointer Families
+
+Compare it with Container With Most Water:
+
+- In sliding window, the interval itself has meaning.
+- In container, the interval is just the remaining search space.
+
+Compare it with Remove Duplicates:
+
+- In sliding window, both pointers describe a live window.
+- In compaction, the left part of the array is already the answer prefix.
+
+## A Practical Template
+
+A common variable-size sliding window has this shape:
+
+1. Add the new rightmost element.
+2. Update the window state.
+3. While the invariant is broken, remove elements from the left.
+4. Once the invariant is restored, update the answer.
+
+The exact data structure changes from problem to problem, but the logic stays the same.
+
+As you work through this section, keep asking:
+
+:::warning
+What invariant does my window maintain, and at what moment is it safe to update the answer?
+:::