function shuffle(a){for(let i=a.length-1;i>0;i--){const j=Math.floor(Math.random()*(i+1));[a[i],a[j]]=[a[j],a[i]]}return a} function topology(n,regions){ const peers=Array.from({length:n*n},(_,i)=>{const s=new Set();for(let j=0;jregions.filter(x=>x===r).length);return {peers,sizes}; } function solve(values,t,limit=2,budget=80000,random=false){let count=0,solution=null,nodes=0,aborted=false;const a=[...values]; function visit(){if(++nodes>budget){aborted=true;return}let best=-1,opts=[];for(let i=0;ia[j]===v))o.push(v);if(!o.length)return;if(best<0||o.length=limit||aborted)return}} for(let i=0;it.sizes[i]||t.peers[i].some(j=>a[j]===a[i])))return {count:0,solution:null,aborted:false};visit();return {count,solution,aborted};} function validPuzzle(p){ if(!p||![6,8,9].includes(p.n)||!Number.isInteger(p.level)||p.level<1||p.level>9||typeof p.id!=='string')return false; const {n,regions,solution,givens}=p,length=n*n; if(![regions,solution,givens].every(a=>Array.isArray(a)&&a.length===length))return false; if(!regions.every(r=>Number.isInteger(r)&&r>=0))return false; const t=topology(n,regions); for(const r of new Set(regions)){ const cells=regions.map((v,i)=>v===r?i:-1).filter(i=>i>=0),seen=new Set([cells[0]]),queue=[cells[0]]; if(cells.length<1||cells.length>5)return false; while(queue.length){const i=queue.pop();for(const j of [i-n,i+n,...(i%n?[i-1]:[]),...(i%n=0&&jt.sizes[i]||t.peers[i].some(j=>solution[j]===solution[i])||!Number.isInteger(givens[i])||givens[i]<0||(givens[i]&&givens[i]!==solution[i]))return false; const check=solve(givens,t,2,500000); return !check.aborted&&check.count===1&&check.solution.every((v,i)=>v===solution[i]); } function generate(n,level){ if(![6,8].includes(n)||!Number.isInteger(level)||level<1||level>9)throw Error('Unsupported puzzle settings.'); let regions,t,result; for(let attempt=0;attempt<500;attempt++){ // Randomize a Hamiltonian walk with endpoint reconnections, then partition it. // Every region stays connected, with no isolated single-cell leftovers. let path=Array.from({length:n*n},(_,i)=>Math.floor(i/n)*n+(Math.floor(i/n)%2?n-1-i%n:i%n)); for(let k=0;kj>=0&&j1)path=[...path.slice(0,at).reverse(),...path.slice(at)]} const fours=(4*n*n)%5,chunks=shuffle([...Array(fours).fill(4),...Array((n*n-4*fours)/5).fill(5)]);regions=Array(n*n).fill(-1);let offset=0;chunks.forEach((size,r)=>{for(const i of path.slice(offset,offset+size))regions[i]=r;offset+=size}); t=topology(n,regions);result=solve(Array(n*n).fill(0),t,1,18000,true);if(result.count&&!result.aborted)break; } if(!result?.solution)throw Error('Please try generating again.'); const solution=result.solution,givens=[...solution];const target=Math.floor(n*n*(.64-level*.046)); for(const i of shuffle([...givens.keys()])){if(givens.filter(Boolean).length<=target)break;givens[i]=0;const check=solve(givens,t,2,25000);if(check.count!==1||check.aborted)givens[i]=solution[i]} const puzzle={id:globalThis.crypto?.randomUUID?.()||Date.now().toString(36)+Math.random().toString(36).slice(2),n,level,regions,solution,givens}; if(!validPuzzle(puzzle))throw Error('Puzzle validation failed. Please try again.'); return puzzle; }

6 × 6 LEVEL 1