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docs(docs): add longest‑substring problem page and sliding‑window reference with SVG illustrations

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Prad Nukala committed 2026-08-25 13:18:32 -04:00
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apps/docs/public/sliding-window-fixed-size.svg
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
<!-- Background (REQUIRED) -->
<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
<!-- Title and Subtitle -->
<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Fixed Size</text>
<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Window of size K=3 moving through the array.</text>
<!-- Step 1: Initial window -->
<g transform="translate(150, 130)">
<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">1. Current window (Sum = 10)</text>
<!-- Array -->
<g transform="translate(0, 20)">
<rect x="0" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">2</text>
<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">3</text>
<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">5</text>
<rect x="210" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">1</text>
<rect x="280" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
<text x="310" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">8</text>
<!-- Bracket -->
<path d="M 0,60 L 0,70 L 200,70 L 200,60" fill="none" stroke="#10b981" stroke-width="2"/>
</g>
</g>
<!-- Transition -->
<g transform="translate(400, 260)">
<path d="M 0,0 L 0,30" stroke="#dee2e6" stroke-width="2" fill="none"/>
<text x="10" y="20" font-family="Arial, sans-serif" font-size="14" font-style="italic" fill="#7f8c8d">Slide window: -2, +1</text>
</g>
<!-- Step 2: Slid window -->
<g transform="translate(150, 340)">
<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">2. Next window (Sum = 9)</text>
<!-- Array -->
<g transform="translate(0, 20)">
<rect x="0" y="0" width="60" height="50" fill="#e5e7eb" stroke="#94a3b8" stroke-width="2" rx="3"/>
<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#94a3b8">2</text>
<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">3</text>
<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">5</text>
<rect x="210" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#1b5e20">1</text>
<rect x="280" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
<text x="310" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">8</text>
<!-- Bracket -->
<path d="M 70,60 L 70,70 L 270,70 L 270,60" fill="none" stroke="#10b981" stroke-width="2"/>
</g>
</g>
</svg>
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apps/docs/public/sliding-window-flexible.svg
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
<!-- Background (REQUIRED) -->
<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
<!-- Title and Subtitle -->
<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Flexible Size</text>
<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Window expands until invalid, then shrinks until valid again.</text>
<!-- Step 1: Invalid state -->
<g transform="translate(150, 130)">
<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">1. Expansion breaks invariant</text>
<!-- Array -->
<g transform="translate(0, 20)">
<rect x="0" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
<polygon points="30,60 25,70 35,70" fill="#27ae60"/>
<text x="30" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
<rect x="70" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
<rect x="140" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="3" rx="3"/>
<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
<rect x="210" y="0" width="60" height="50" fill="#fee2e2" stroke="#ef4444" stroke-width="4" rx="3"/>
<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
<polygon points="240,60 235,70 245,70" fill="#3498db"/>
<text x="240" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
<text x="300" y="32" font-family="Arial, sans-serif" font-size="14" fill="#ef4444" font-weight="bold">Duplicate 'a'!</text>
</g>
</g>
<!-- Transition -->
<g transform="translate(400, 260)">
<path d="M 0,0 L 0,30" stroke="#dee2e6" stroke-width="2" fill="none"/>
<text x="10" y="20" font-family="Arial, sans-serif" font-size="14" font-style="italic" fill="#7f8c8d">Shrink from left</text>
</g>
<!-- Step 2: Valid again -->
<g transform="translate(150, 340)">
<text x="0" y="-20" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">2. Invariant restored</text>
<!-- Array -->
<g transform="translate(0, 20)">
<rect x="0" y="0" width="60" height="50" fill="#e5e7eb" stroke="#94a3b8" stroke-width="2" rx="3"/>
<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#94a3b8">a</text>
<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
<polygon points="100,60 95,70 105,70" fill="#27ae60"/>
<text x="100" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
<rect x="210" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
<polygon points="240,60 235,70 245,70" fill="#3498db"/>
<text x="240" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
<text x="300" y="32" font-family="Arial, sans-serif" font-size="14" fill="#10b981" font-weight="bold">Valid again!</text>
</g>
</g>
</svg>
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apps/docs/public/sliding-window-frequency.svg
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<svg viewBox="0 0 800 450" xmlns="http://www.w3.org/2000/svg">
<!-- Background (REQUIRED) -->
<rect width="800" height="450" fill="#f8f9fa" rx="10"/>
<!-- Title and Subtitle -->
<text x="400" y="45" font-family="Arial, sans-serif" font-size="26" font-weight="bold" fill="#2c3e50" text-anchor="middle">Sliding Window: Frequency Tracking</text>
<text x="400" y="75" font-family="Arial, sans-serif" font-size="16" fill="#7f8c8d" text-anchor="middle">Maintaining a character frequency map for the current window.</text>
<!-- Left: Window -->
<g transform="translate(100, 150)">
<text x="0" y="-30" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">Current Window</text>
<!-- Array -->
<g transform="translate(0, 20)">
<rect x="0" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="30" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
<polygon points="30,60 25,70 35,70" fill="#27ae60"/>
<text x="30" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#27ae60" text-anchor="middle">L</text>
<rect x="70" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="100" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">b</text>
<rect x="140" y="0" width="60" height="50" fill="#d1fae5" stroke="#10b981" stroke-width="3" rx="3"/>
<text x="170" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">a</text>
<polygon points="170,60 165,70 175,70" fill="#3498db"/>
<text x="170" y="85" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#3498db" text-anchor="middle">R</text>
<rect x="210" y="0" width="60" height="50" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="3"/>
<text x="240" y="32" font-family="monospace" font-size="22" text-anchor="middle" fill="#2c3e50">c</text>
</g>
</g>
<!-- Right: Frequency Map -->
<g transform="translate(500, 150)">
<text x="0" y="-30" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#2c3e50">Frequency Map</text>
<!-- Map Container -->
<rect x="0" y="0" width="150" height="120" fill="#ffffff" stroke="#dee2e6" stroke-width="2" rx="8"/>
<!-- Entries -->
<g transform="translate(25, 35)">
<text x="0" y="0" font-family="monospace" font-size="18" fill="#2c3e50">'a' : 2</text>
<text x="0" y="30" font-family="monospace" font-size="18" fill="#2c3e50">'b' : 1</text>
<text x="0" y="60" font-family="monospace" font-size="18" fill="#7f8c8d">'c' : 0</text>
</g>
<!-- Invariant label -->
<rect x="-20" y="140" width="190" height="40" fill="#e3f2fd" stroke="#3498db" stroke-width="1" rx="5"/>
<text x="75" y="165" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#1565c0" text-anchor="middle">INVARIANT: SYNCED STATE</text>
</g>
<!-- Connector -->
<path d="M 380,195 L 480,195" stroke="#dee2e6" stroke-width="2" stroke-dasharray="5,5" fill="none"/>
</svg>
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