Pattern: Use two pointers to scan array
Use when: Need to find pairs, triplets, or subarrays
Example: "Find Instagram users who like each other"
Complexity: O(n) time, O(1) space

Pattern: Maintain a window that slides through array
Use when: Need to find subarray with certain property
Example: "Find trending topics in last N tweets"
Complexity: O(n) time, O(k) space

Pattern: Two pointers moving at different speeds
Use when: Detect cycles, find middle element
Example: "Detect circular dependency in package manager"
Complexity: O(n) time, O(1) space

Pattern: Level-order traversal using queue
Use when: Need level-by-level processing
Example: "Show friends by degree of connection"
Complexity: O(n) time, O(w) space (w = max width)

Pattern: Preorder, inorder, or postorder traversal
Use when: Need to explore all paths
Example: "Find all paths in file system"
Complexity: O(n) time, O(h) space (h = height)

Pattern: Explore neighbors level by level
Use when: Shortest path, level-based exploration
Example: "Find shortest connection path on LinkedIn"
Complexity: O(V + E) time, O(V) space

Pattern: Explore as far as possible before backtracking
Use when: Path finding, cycle detection
Example: "Detect circular references in social graph"
Complexity: O(V + E) time, O(V) space

Pattern: Order nodes by dependencies
Use when: Task scheduling, build systems
Example: "Order courses based on prerequisites"
Complexity: O(V + E) time, O(V) space

Pattern: Include or exclude each item
Use when: Optimization with constraints
Example: "Select best ads within budget"
Complexity: O(n * capacity) time and space

Pattern: Can use item unlimited times
Use when: Coin change, combinations
Example: "Minimum transactions to reach balance"
Complexity: O(n * target) time and space

Pattern: Current state depends on previous states
Use when: Climbing stairs, tiling problems
Example: "Ways to navigate through app screens"
Complexity: O(n) time, O(1) space optimized

Pattern: Compare two sequences
Use when: Diff tools, edit distance
Example: "Find similar code snippets"
Complexity: O(m * n) time and space

Pattern: Binary search on sorted or rotated array
Use when: Search in O(log n)
Example: "Find version when bug was introduced"
Complexity: O(log n) time, O(1) space

Pattern: Use heap to track K largest/smallest
Use when: Finding top items
Example: "Get top K trending hashtags"
Complexity: O(n log k) time, O(k) space

Pattern: Merge K sorted arrays/lists
Use when: Combining sorted data
Example: "Merge activity feeds from K users"
Complexity: O(n log k) time, O(k) space

Pattern: Try all possibilities with pruning
Use when: Generate permutations, combinations
Example: "Generate all valid parentheses combinations"
Complexity: Varies, often exponential

Pattern: Track connected components
Use when: Network connectivity, grouping
Example: "Find connected friend groups"
Complexity: O(α(n)) amortized per operation

Pattern: Merge, insert, or find overlapping intervals
Use when: Calendar scheduling, time ranges
Example: "Find free meeting slots"
Complexity: O(n log n) time, O(n) space

Pattern: Maintain increasing/decreasing stack
Use when: Next greater/smaller element
Example: "Stock price span calculation"
Complexity: O(n) time, O(n) space

Pattern: Prefix tree for string operations
Use when: Autocomplete, prefix matching
Example: "Implement search autocomplete"
Complexity: O(m) time per operation (m = word length)

Real Scenario: Count how many times user's posts were liked today
Pattern: Hash Map
Data Structure: Dictionary/HashMap
Languages: Python, TypeScript, Kotlin, Swift

Real Scenario: Find first unread message in channel
Pattern: Linear Search with Flag
Data Structure: Array
Teaches: Early termination

Real Scenario: Compute trip cost based on distance and time
Pattern: Simple Calculation
Data Structure: Numbers
Teaches: Math operations, rounding

Real Scenario: Find top N movies by rating
Pattern: Top K Elements (Heap)
Data Structure: Priority Queue
Teaches: Heap operations, partial sorting

Real Scenario: Find products running low in stock
Pattern: Filtering with Threshold
Data Structure: Array + HashMap
Teaches: Multi-criteria filtering

Real Scenario: Find most used hashtags in time window
Pattern: Sliding Window + Frequency Count
Data Structure: Queue + HashMap
Teaches: Time-based window management

Real Scenario: Find connection path between two users
Pattern: BFS
Data Structure: Graph (Adjacency List)
Teaches: Shortest path, level tracking

Real Scenario: Find free time slots for all attendees
Pattern: Interval Merging
Data Structure: Array of Intervals
Teaches: Sorting, merging overlapping intervals

Real Scenario: True random shuffle avoiding artist repetition
Pattern: Modified Fisher-Yates
Data Structure: Array
Teaches: Randomization with constraints

Real Scenario: Find longest common subsequence in files
Pattern: Dynamic Programming (LCS)
Data Structure: 2D Array
Teaches: DP state definition, optimization

Real Scenario: Rank listings by multiple weighted criteria
Pattern: Custom Sorting + Heap
Data Structure: Priority Queue with Comparator
Teaches: Complex comparisons, tie-breaking

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>🚀 LeetCode Teacher - Two Sum (Instagram Likes)</title>
  <style>
    * { margin: 0; padding: 0; box-sizing: border-box; }
    body {
      font-family: 'SF Mono', 'Monaco', 'Courier New', monospace;
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      font-size: 2.5em;
      margin-bottom: 10px;
      text-shadow: 2px 2px 4px rgba(0, 0, 0, 0.3);
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    .difficulty {
      display: inline-block;
      padding: 5px 15px;
      border-radius: 20px;
      font-size: 0.9em;
      font-weight: bold;
      margin-bottom: 20px;
    }
    .easy { background: #4CAF50; }
    .medium { background: #FF9800; }
    .hard { background: #F44336; }
    .problem {
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      border: none;
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      font-size: 1em;
      font-weight: bold;
      cursor: pointer;
      transition: transform 0.2s;
    }
    .btn-run {
      background: linear-gradient(135deg, #4CAF50, #45a049);
      color: white;
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    .btn-hint {
      background: linear-gradient(135deg, #FF9800, #F57C00);
      color: white;
    }
    .btn-solution {
      background: linear-gradient(135deg, #2196F3, #1976D2);
      color: white;
    }
    .btn:hover { transform: translateY(-2px); }
    .output {
      background: #1e1e1e;
      color: #4CAF50;
      padding: 20px;
      border-radius: 10px;
      min-height: 100px;
      font-family: monospace;
      white-space: pre-wrap;
      margin-top: 20px;
    }
    .test-case {
      background: rgba(255, 255, 255, 0.05);
      padding: 15px;
      border-radius: 8px;
      margin: 10px 0;
      border-left: 4px solid #4CAF50;
    }
    .test-failed {
      border-left-color: #F44336;
    }
    .stats {
      display: flex;
      justify-content: space-around;
      margin: 20px 0;
      padding: 20px;
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    .stat-value {
      font-size: 2em;
      font-weight: bold;
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      border-radius: 15px;
      margin: 5px;
      font-size: 0.9em;
    }
  </style>
</head>
<body>
  <div class="container">
    <!-- Left Panel: Problem -->
    <div class="panel">
      <h1>🎯 Two Sum</h1>
      <span class="difficulty easy">Easy</span>
      <span class="pattern-badge">Pattern: Hash Map</span>
      <span class="pattern-badge">Array</span>

      <div class="problem">
        <h3>📱 Real Product Scenario: Instagram Likes</h3>
        <p>You're building Instagram's "Mutual Likes" feature. Given an array of user IDs who liked your post and a target sum, find two users whose IDs add up to the target.</p>

        <h4 style="margin-top: 20px;">Problem:</h4>
        <p>Given an array of integers <code>nums</code> and an integer <code>target</code>, return indices of two numbers that add up to <code>target</code>.</p>

        <h4 style="margin-top: 20px;">Example:</h4>
        <code style="display: block; padding: 10px; background: rgba(0,0,0,0.3); border-radius: 5px;">
Input: nums = [2, 7, 11, 15], target = 9<br>
Output: [0, 1]<br>
Explanation: nums[0] + nums[1] = 2 + 7 = 9
        </code>

        <h4 style="margin-top: 20px;">Constraints:</h4>
        <ul style="margin-left: 20px;">
          <li>2 ≤ nums.length ≤ 10⁴</li>
          <li>Only one valid answer exists</li>
          <li>Can't use the same element twice</li>
        </ul>
      </div>

      <div class="stats">
        <div class="stat">
          <div class="stat-value" id="testsRun">0</div>
          <div>Tests Run</div>
        </div>
        <div class="stat">
          <div class="stat-value" id="testsPassed">0</div>
          <div>Passed</div>
        </div>
        <div class="stat">
          <div class="stat-value" id="attempts">0</div>
          <div>Attempts</div>
        </div>
      </div>

      <div id="hints" style="margin-top: 20px;"></div>
    </div>

    <!-- Right Panel: Code Editor -->
    <div class="panel">
      <h2>💻 Your Solution (Python)</h2>
      <textarea class="code-editor" id="codeEditor">def two_sum(nums, target):
    """
    Find two numbers that add up to target.

    Args:
        nums: List of integers
        target: Target sum

    Returns:
        List of two indices

    Time: O(n²) - Brute force
    Space: O(1)

    TODO: Optimize to O(n) using hash map!
    """
    # Your code here
    pass

  <div class="controls">
    <button class="btn btn-run" onclick="runCode()">▶️ Run Tests</button>
    <button class="btn btn-hint" onclick="getHint()">💡 Get Hint</button>
    <button class="btn btn-solution" onclick="showSolution()">✨ Show Solution</button>
  </div>

  <div class="output" id="output">Click "Run Tests" to test your solution...</div>
</div>

  document.getElementById('codeEditor').value = solution;
  alert('✨ Solution revealed! Study the pattern and try to implement it yourself next time.');
}

undefined

undefined

// Hash Map pattern
function twoSum(nums: number[], target: number): number[] {
    const seen = new Map<number, number>();

    for (let i = 0; i < nums.length; i++) {
        const complement = target - nums[i];

        if (seen.has(complement)) {
            return [seen.get(complement)!, i];
        }

        seen.set(nums[i], i);
    }

    return [];
}

// Hash Map pattern
fun twoSum(nums: IntArray, target: Int): IntArray {
    val seen = mutableMapOf<Int, Int>()

    nums.forEachIndexed { i, num ->
        val complement = target - num

        if (seen.containsKey(complement)) {
            return intArrayOf(seen[complement]!!, i)
        }

        seen[num] = i
    }

    return intArrayOf()
}

// Hash Map pattern
func twoSum(_ nums: [Int], _ target: Int) -> [Int] {
    var seen = [Int: Int]()

    for (i, num) in nums.enumerated() {
        let complement = target - num

        if let j = seen[complement] {
            return [j, i]
        }

        seen[num] = i
    }

    return []
}

See problem → Identify pattern → Apply template → Optimize

Always analyze:
- Time complexity: O(?)
- Space complexity: O(?)
- Can we do better?

1. Read problem
2. Write test cases
3. Think of edge cases
4. Code solution
5. Run tests
6. Optimize

Brute Force → Identify bottleneck → Apply pattern → Optimize space

- State assumptions
- Ask clarifying questions
- Think out loud
- Explain trade-offs
- Discuss alternatives