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Starting at \"+g.source+\", reach \"+g.target+\" while losing as little battery as possible.\",\n (g:any)=>\"A packet starts at \"+g.source+\" and must arrive at \"+g.target+\". Link numbers are latency contributions; return an itinerary with the smallest end-to-end delay.\"\n ],\n mst:[\n (_g:any)=>\"A utility company must choose which candidate cables to install so every facility can communicate with every other facility. Minimize total construction expense, and do not keep a cable whose removal would leave connectivity unchanged.\",\n (_g:any)=>\"Select the cheapest collection of pairwise connections that leaves the entire set in one connected piece, with no circular redundancy.\"\n ],\n topo:[\n (_g:any)=>\"Some jobs unlock other jobs. Return one list containing every job exactly once, with each unlocking job earlier than everything it unlocks.\",\n (_g:any)=>\"Each arrow means its left endpoint has to happen first. Produce a complete sequence that respects all such constraints.\"\n ]\n};\nfunction make(op:\"shortest\"|\"mst\"|\"topo\",variant:number){\n const id=\"jit4-\"+crypto.randomUUID(),g=remap(baseGraph(op));\n const privateData:any={challenge_id:id,op,expected_skill:expectedSkill[op],graph:g};\n if(op===\"shortest\")privateData.min_value=shortestMin(g);\n if(op===\"mst\")privateData.min_value=mstMin(g);\n return {private:privateData,public:{schema:\"SUPERHERO_JIT_HELDOUT_CHALLENGE_V1\",challenge_id:id,goal:goals[op][variant](g),graph:g}};\n}\nfunction valid(c:any,out:any){\n const g=c.graph;\n if(c.op===\"shortest\"){\n if(out?.reachable!==true||Number(out?.distance)!==c.min_value||!Array.isArray(out?.path))return false;\n const p=out.path;if(p[0]!==g.source||p[p.length-1]!==g.target||new Set(p).size!==p.length)return false;\n let sum=0;for(let i=1;ix.from===p[i-1]&&x.to===p[i]);if(!e)return false;sum+=Number(e.weight)}return sum===c.min_value;\n }\n if(c.op===\"mst\"){\n if(out?.connected!==true||Number(out?.total_weight)!==c.min_value||!Array.isArray(out?.edges)||out.edges.length!==g.nodes.length-1)return false;\n const p=new Map(g.nodes.map((v:string)=>[v,v] as [string,string]));\n const find=(a:string):string=>{const q=p.get(a)!;if(q===a)return a;const r=find(q);p.set(a,r);return r};\n let sum=0;\n for(const e of out.edges){const match=g.edges.find((x:any)=>((x.from===e.from&&x.to===e.to)||(x.from===e.to&&x.to===e.from))&&Number(x.weight)===Number(e.weight));if(!match)return false;const a=find(String(e.from)),b=find(String(e.to));if(a===b)return false;p.set(a,b);sum+=Number(e.weight)}\n return sum===c.min_value&&new Set(g.nodes.map((v:string)=>find(v))).size===1;\n }\n if(out?.acyclic!==true||!Array.isArray(out?.order)||out.order.length!==g.nodes.length||new Set(out.order).size!==g.nodes.length)return false;\n const pos=new Map(out.order.map((v:string,i:number)=>[v,i] as [string,number]));\n return 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