[1,[4,"h2",null,[5,"The Problem"]],[4,"p",null,[5,"The printing department has "],[4,"strong",null,[5,"rolls of paper"]],[5," ("],[4,"code",null,[5,"@"]],[5,") arranged on a grid. Forklifts can only access a roll if it has "],[4,"strong",null,[5,"fewer than 4 neighbors"]],[5," (out of 8 possible adjacent positions). Help optimize the forklifts to clear the way to the cafeteria!"]],[4,"h2",null,[5,"Summary"]],[4,"figure",{"className":"framer-table-wrapper"},[4,"table",null,[4,"tbody",null,[4,"tr",null,[4,"th",null,[4,"p",null,[5,"Part"]]],[4,"th",null,[4,"p",null,[5,"Question"]]],[4,"th",null,[4,"p",null,[5,"Strategy"]]]],[4,"tr",null,[4,"td",null,[4,"p",null,[4,"strong",null,[5,"1"]]]],[4,"td",null,[4,"p",null,[5,"How many rolls can forklifts "],[4,"strong",null,[5,"initially"]],[5," access?"]]],[4,"td",null,[4,"p",null,[5,"Count rolls with < 4 adjacent neighbors"]]]],[4,"tr",null,[4,"td",null,[4,"p",null,[4,"strong",null,[5,"2"]]]],[4,"td",null,[4,"p",null,[5,"How many "],[4,"strong",null,[5,"total"]],[5," rolls can be removed?"]]],[4,"td",null,[4,"p",null,[5,"Iteratively remove accessible rolls until stable"]]]]]]],[4,"h3",null,[5,"Part 1: Count Accessible Rolls"]],[4,"p",null,[4,"strong",null,[5,"Goal:"]],[5," Count rolls of paper ("],[4,"code",null,[5,"@"]],[5,") that have fewer than 4 filled neighbors."]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"local-module:canvasComponent/nVZKW5bHA:default",{"variant":"BLxBoiPct"},[]]],[4,"h4",null,[5,"The 8 Neighbors"]],[4,"p",null,[5,"Each cell has up to 8 adjacent positions (including diagonals):"]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"module:pVk4QsoHxASnVtUBp6jr/ttReBBOK4JjO79S16uu9/CodeBlock.js:default",{"code":"const adjacentPositions = [\n [-1, -1], [0, -1], [1, -1], // top row\n [-1, 0], [1, 0], // middle row\n [-1, 1], [0, 1], [1, 1], // bottom row\n];","language":"TypeScript"},[]]],[4,"h4",null,[5,"Counting Neighbors"]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"module:pVk4QsoHxASnVtUBp6jr/ttReBBOK4JjO79S16uu9/CodeBlock.js:default",{"code":"const getAdjacentCount = ({ grid, width, height, x, y }) => {\n return adjacentPositions.reduce((count, [dx, dy]) => {\n const newX = x + dx;\n const newY = y + dy;\n\n // Bounds check\n if (newX < 0 || newX >= width || newY < 0 || newY >= height) \n return count;\n\n return grid[newY]?.[newX] === FILLED ? count + 1 : count;\n }, 0);\n};","language":"TypeScript"},[]]],[4,"p",null,[5,"A roll is accessible if "],[4,"code",null,[5,"adjacentCount < 4"]],[5,". Simple scan of the grid:"]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"module:pVk4QsoHxASnVtUBp6jr/ttReBBOK4JjO79S16uu9/CodeBlock.js:default",{"code":"for (let y = 0; y < height; y++) {\n for (let x = 0; x < width; x++) {\n if (grid[y]?.[x] !== FILLED) continue;\n \n if (getAdjacentCount({ grid, width, height, x, y }) < 4) {\n count++;\n }\n }\n}","language":"TypeScript"},[]]],[4,"h3",null,[5,"Part 2: Cascade Removal 🎯"]],[4,"p",null,[4,"strong",null,[5,"Goal:"]],[5," Remove accessible rolls, then check again. Repeat until no more can be removed."]],[4,"p",null,[5,"This is a "],[4,"strong",null,[5,"cellular automaton"]],[5,"-style simulation! Removing rolls exposes new rolls that become accessible."]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"local-module:canvasComponent/nVZKW5bHA:default",{"variant":"vADF3OnAr"},[]]],[4,"h4",null,[5,"The Cascade Effect"]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"module:pVk4QsoHxASnVtUBp6jr/ttReBBOK4JjO79S16uu9/CodeBlock.js:default",{"code":"Initial: After removal:\n..@@.@@@@. .......@..\n@@@.@.@.@@ .@@.....@.\n@@@@@.@.@@ → .@@@@...@@\n... ","language":"Markdown"},[]]],[4,"p",null,[5,"Rolls on the edges or with few neighbors get removed first. This exposes interior rolls, which then become removable."]],[4,"h4",null,[5,"The Algorithm"]],[4,"div",{"className":"framer-text-module","style":{"width":"100%","height":"auto"},"data-width":"fill"},[3,"module:pVk4QsoHxASnVtUBp6jr/ttReBBOK4JjO79S16uu9/CodeBlock.js:default",{"code":"while (true) {\n const toRemove: [number, number][] = [];\n\n // Find all currently accessible rolls\n for (let y = 0; y < height; y++) {\n for (let x = 0; x < width; x++) {\n if (grid[y]?.[x] !== FILLED) continue;\n \n if (getAdjacentCount({ grid, width, height, x, y }) < 4) {\n toRemove.push([x, y]);\n }\n }\n }\n\n // No more accessible rolls? We're done!\n if (toRemove.length === 0) break;\n\n // Remove all accessible rolls simultaneously\n for (const [x, y] of toRemove) {\n grid[y][x] = EMPTY;\n }\n\n count += toRemove.length;\n}","language":"TypeScript"},[]]],[4,"h4",null,[5,"Why Batch Removal?"]],[4,"p",null,[5,"We collect "],[4,"strong",null,[5,"all"]],[5," accessible rolls before removing any. This ensures we don't accidentally affect the neighbor count of rolls we haven't checked yet in this iteration."]],[4,"p",null,[5,"If we removed one-by-one, the order would matter and we'd get inconsistent results!"]],[4,"h3",null,[5,"Performance"]],[4,"figure",{"className":"framer-table-wrapper"},[4,"table",null,[4,"tbody",null,[4,"tr",null,[4,"th",null,[4,"p",null,[5,"Part"]]],[4,"th",null,[4,"p",null,[5,"Time"]]]],[4,"tr",null,[4,"td",null,[4,"p",null,[5,"Part 1"]]],[4,"td",null,[4,"p",null,[5,"6.11ms"]]]],[4,"tr",null,[4,"td",null,[4,"p",null,[5,"Part 2"]]],[4,"td",null,[4,"p",null,[5,"40.77ms"]]]]]]],[4,"p",null,[5,"Part 2 is slower because it runs multiple iterations until the grid stabilizes. Each iteration requires a full grid scan. There is probably some optimization to do there."]]]