perplexity_reason

<think>
To compare merge sort and quick sort time complexity:
1. Analyze worst-case scenarios
2. Consider average-case performance
3. Examine space complexity
4. Discuss practical implications
</think>

Time Complexity Comparison: Merge Sort vs Quick Sort

Worst-Case Analysis:
- Merge Sort: O(n log n) in all cases[1]
- Quick Sort: O(n²) when poorly pivoted[2]

Merge sort maintains consistent O(n log n) performance regardless of input 
order because it always divides the array into equal halves[1]. Quick sort's 
worst case occurs with already sorted data or when the pivot consistently 
selects the smallest/largest element[2].

Average-Case Performance:
Both algorithms achieve O(n log n) average time complexity[3]. However, quick 
sort often performs better in practice due to:
1. Better cache locality (in-place sorting)[4]
2. Smaller constant factors in the O(n log n) term[5]

Space Complexity:
- Merge Sort: O(n) auxiliary space[1]
- Quick Sort: O(log n) for recursion stack[2]

Practical Considerations:
Quick sort is generally preferred for in-memory sorting due to its space 
efficiency and cache performance[4]. Merge sort is preferred when:
- Worst-case guarantees are critical[1]
- Sorting linked lists (no random access penalty)[6]
- External sorting (disk-based operations)[7]

Citations:
[1] https://mathworld.wolfram.com/MergeSort.html
[2] https://mathworld.wolfram.com/Quicksort.html
[3] https://bigocheatsheet.com
[4] https://stackoverflow.com/questions/cache-locality-sorting
[5] https://cstheory.stackexchange.com/constant-factors
[6] https://wikipedia.org/wiki/Merge_sort
[7] https://db.cs.berkeley.edu/external-sorting

const solution = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      {
        role: "user",
        content: "Solve: If f(x) = x² + 3x - 2 and g(x) = 2x + 1, find (f ∘ g)(x) and simplify."
      }
    ]
  }
);

const comparison = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      {
        role: "user",
        content: "Compare React Server Components vs traditional SSR: architecture, performance, developer experience, and use cases."
      }
    ],
    search_recency_filter: "month",
    search_domain_filter: ["reactjs.org", "nextjs.org", "vercel.com"]
  }
);

const puzzle = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      {
        role: "user",
        content: "Three people (A, B, C) each wear a hat that's either red or blue. Each can see the others' hats but not their own. A says 'I don't know my color.' B says 'I don't know my color.' C says 'I know my color!' What color is C's hat and why?"
      }
    ]
  }
);

const decision = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      {
        role: "system",
        content: "Analyze decisions using: 1) Pros and cons, 2) Risk assessment, 3) Long-term implications, 4) Recommendation with reasoning."
      },
      {
        role: "user",
        content: "Should a startup choose microservices or monolithic architecture?"
      }
    ],
    search_context_size: "high"
  }
);

// Step 1: Establish premises
const step1 = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      { role: "user", content: "What are the key principles of quantum entanglement?" }
    ]
  }
);

// Step 2: Apply reasoning
const step2 = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      { role: "user", content: "What are the key principles of quantum entanglement?" },
      { role: "assistant", content: step1.response },
      { role: "user", content: "Given these principles, explain why quantum teleportation doesn't violate the speed of light." }
    ]
  }
);

const debug = await use_mcp_tool(
  "perplexity",
  "perplexity_reason",
  {
    messages: [
      {
        role: "system",
        content: "Analyze code for: 1) Bugs, 2) Performance issues, 3) Best practices violations, 4) Security concerns."
      },
      {
        role: "user",
        content: `
Analyze this React component:

function UserList() {
  const [users, setUsers] = useState([]);
  
  fetch('/api/users')
    .then(res => res.json())
    .then(setUsers);
  
  return users.map(u => <div key={u.name}>{u.name}</div>);
}
        `
      }
    ],
    search_domain_filter: ["react.dev", "stackoverflow.com"]
  }
);

<think>
To solve this optimization problem:
1. Identify the objective function
2. List constraints
3. Determine feasible region
4. Apply linear programming techniques
5. Verify solution satisfies all constraints
</think>

[Detailed solution with steps...]