Binary Search Learning Roadmap: From Beginner to Interview-Ready in 6 Weeks

You want to master binary search, but where do you start? Which variant should you learn first? How do you progress from basic search to optimization problems?

This roadmap answers all those questions. It's a structured 6-week learning path that takes you from zero to mastery, with curated problems, clear milestones, and a proven progression.

Follow this roadmap, and in 6 weeks, you'll confidently solve any binary search problem in interviews.

How to Use This Roadmap

Time Commitment

• Beginner: 1-2 hours per day, 5 days per week
• Intermediate: 2-3 hours per day, 5 days per week
• Total: 6 weeks to interview-ready

Progression Philosophy

1. Master classic binary search before variants
2. Understand the math behind each pattern
3. Debug systematically on every problem
4. Recognize patterns in 30 seconds
5. Build intuition for monotonicity

Milestones

• ✅ Week 2: Solve classic binary search problems confidently
• ✅ Week 3: Handle duplicates and bounds correctly
• ✅ Week 4: Master rotated arrays and 2D matrices
• ✅ Week 6: Interview-ready for any binary search problem

Phase 1: Foundations (Weeks 1-2)

Goal: Master classic binary search and understand why it works.

Week 1: Classic Binary Search

Concepts to Learn:

• What is binary search?
• Why sorted data is required
• Monotonicity principle
• Loop conditions and pointer updates
• Off-by-one errors

Required Reading:

1. Complete Binary Search Guide - Read sections 1-4
2. Why Sorted Data Required
3. Off-by-One Errors

Problems to Solve (5 problems):

Practice Template:

# Memorize this template
left, right = 0, len(arr) - 1

while left <= right:
    mid = left + (right - left) // 2
    
    if arr[mid] == target:
        return mid
    elif arr[mid] < target:
        left = mid + 1
    else:
        right = mid - 1

return -1

Checkpoint: Can you solve Binary Search (#704) from memory without any bugs?

Week 2: Debugging and Common Mistakes

Concepts to Learn:

• Integer overflow in mid calculation
• Infinite loop causes
• Wrong loop conditions
• Edge case handling

Required Reading:

1. Implementation Mistakes
2. Infinite Loop Debugging
3. Pattern Recognition

Problems to Solve (6 problems):

Debugging Checklist:

• Using mid = left + (right - left) // 2?
• Pointer updates always make progress?
• Loop condition matches pointer updates?
• Handling empty arrays?
• Testing edge cases?

Checkpoint: Can you debug a broken binary search in under 3 minutes?

Phase 2: Bounds and Duplicates (Week 3)

Goal: Master lower bound, upper bound, and handle duplicates correctly.

Week 3: Lower Bound and Upper Bound

Concepts to Learn:

• Lower bound (first >= target)
• Upper bound (first > target)
• Finding first and last occurrence
• The one-character difference (< vs <=)

Required Reading:

1. First and Last Position Template
2. Lower Bound vs Upper Bound Mistakes

Problems to Solve (7 problems):

Lower Bound Template:

left, right = 0, len(arr)

while left < right:
    mid = left + (right - left) // 2
    
    if arr[mid] < target:  # <
        left = mid + 1
    else:
        right = mid

return left

Upper Bound Template:

left, right = 0, len(arr)

while left < right:
    mid = left + (right - left) // 2
    
    if arr[mid] <= target:  # <=
        left = mid + 1
    else:
        right = mid

return left

Checkpoint: Can you explain the difference between < and <= and when to use each?

Phase 3: Advanced Variants (Week 4)

Goal: Master rotated arrays, 2D matrices, and understand the proofs.

Week 4: Rotated Arrays and 2D Matrices

Concepts to Learn:

• Why one half is always sorted in rotated arrays
• Handling duplicates in rotated arrays
• 2D matrix index mapping
• Staircase search for row-column sorted matrices

Required Reading:

1. Rotated Sorted Array
2. Rotated Array Proof
3. Duplicates in Rotated Arrays
4. 2D Matrix Search
5. 2D Matrix Index Mapping

Problems to Solve (8 problems):

Rotated Array Template:

while left <= right:
    mid = left + (right - left) // 2
    
    if arr[mid] == target:
        return mid
    
    # Identify which half is sorted
    if arr[left] <= arr[mid]:
        # Left half sorted
        if arr[left] <= target < arr[mid]:
            right = mid - 1
        else:
            left = mid + 1
    else:
        # Right half sorted
        if arr[mid] < target <= arr[right]:
            left = mid + 1
        else:
            right = mid - 1

Checkpoint: Can you explain why one half is always sorted in a rotated array?

Phase 4: Binary Search on Answer (Weeks 5-6)

Goal: Master optimization problems using binary search on answer.

Week 5: Minimize Maximum Pattern

Concepts to Learn:

• Binary search on answer space
• Monotonic feasibility
• Feasibility function design
• "Minimize the maximum" pattern

Required Reading:

1. Binary Search on Answer
2. Why Binary Search on Answer Works
3. Minimize Maximum vs Maximize Minimum
4. Feasibility Function Mistakes

Problems to Solve (8 problems):

Minimize Maximum Template:

def minimize_maximum(min_val, max_val, is_feasible):
    left, right = min_val, max_val
    
    while left < right:
        mid = left + (right - left) // 2
        
        if is_feasible(mid):
            # mid works, try smaller
            right = mid
        else:
            # mid doesn't work, need larger
            left = mid + 1
    
    return left

Checkpoint: Can you identify "minimize maximum" keywords in a problem statement?

Week 6: Maximize Minimum and Interview Mastery

Concepts to Learn:

• "Maximize the minimum" pattern
• Complexity analysis (when it's not O(log n))
• Pattern recognition in 30 seconds
• Interview communication

Required Reading:

1. When Binary Search Is NOT O(log n)
2. Binary Search vs Linear Search

Problems to Solve (10 problems):

Maximize Minimum Template:

def maximize_minimum(min_val, max_val, is_feasible):
    left, right = min_val, max_val
    result = min_val
    
    while left <= right:
        mid = left + (right - left) // 2
        
        if is_feasible(mid):
            # mid works, try larger
            result = mid
            left = mid + 1
        else:
            # mid doesn't work, need smaller
            right = mid - 1
    
    return result

Interview Simulation:

• Set 25-minute timer
• Solve problem from scratch
• Explain solution out loud
• Handle follow-up questions

Checkpoint: Can you solve any binary search problem in under 20 minutes?

Supplementary Resources

Templates to Memorize

1. Classic Binary Search

left, right = 0, len(arr) - 1
while left <= right:
    mid = left + (right - left) // 2
    if arr[mid] == target:
        return mid
    elif arr[mid] < target:
        left = mid + 1
    else:
        right = mid - 1
return -1

2. Lower Bound

left, right = 0, len(arr)
while left < right:
    mid = left + (right - left) // 2
    if arr[mid] < target:
        left = mid + 1
    else:
        right = mid
return left

3. Upper Bound

left, right = 0, len(arr)
while left < right:
    mid = left + (right - left) // 2
    if arr[mid] <= target:
        left = mid + 1
    else:
        right = mid
return left

4. Binary Search on Answer

def solve(min_val, max_val):
    def is_feasible(x):
        # Check if x works
        return check(x)
    
    left, right = min_val, max_val
    while left < right:
        mid = left + (right - left) // 2
        if is_feasible(mid):
            right = mid  # For minimize
        else:
            left = mid + 1
    return left

Common Mistakes Checklist

• Using (left + right) // 2 instead of left + (right - left) // 2
• Wrong loop condition (< vs <=)
• Using right = mid - 1 when should use right = mid
• Confusing lower bound and upper bound (< vs <=)
• Not handling duplicates in rotated arrays
• Wrong feasibility direction (minimize vs maximize)
• Using floor division when need ceiling
• Forgetting to update state in greedy feasibility

Pattern Recognition Checklist

1. Is data sorted?
   ├─ Yes → Classic binary search
   └─ Rotated? → Rotated binary search

2. Finding first/last occurrence?
   └─ Use lower/upper bound

3. "Minimize maximum" or "maximize minimum"?
   └─ Binary search on answer

4. 2D matrix?
   ├─ Fully sorted → Treat as 1D
   └─ Row-column sorted → Staircase search

5. Can verify if answer works?
   └─ Check monotonicity → BS on answer

Progress Tracking

Week-by-Week Checklist

Week 1:

• Read Complete Binary Search Guide
• Solve 5 classic problems
• Memorize classic template
• Can solve Binary Search (#704) from memory

Week 2:

• Read Implementation Mistakes guide
• Solve 6 problems
• Understand all 7 common mistakes
• Can debug in under 3 minutes

Week 3:

• Read Lower/Upper Bound guides
• Solve 7 problems
• Master both bound templates
• Can explain < vs <= difference

Week 4:

• Read Rotated Array and 2D Matrix guides
• Solve 8 problems
• Understand rotated array proof
• Can solve rotated array from memory

Week 5:

• Read Binary Search on Answer guides
• Solve 8 problems
• Master minimize maximum pattern
• Can write feasibility functions

Week 6:

• Solve 10 advanced problems
• Practice interview simulation
• Achieve 20-minute solve time
• Interview-ready confidence

Success Metrics

By the end of 6 weeks, you should be able to:

✅ Recognize patterns instantly (< 30 seconds)
✅ Solve easy problems in under 8 minutes
✅ Solve medium problems in under 20 minutes
✅ Write bug-free binary search on first attempt (90%+ of the time)
✅ Debug solutions in under 3 minutes
✅ Explain monotonicity clearly
✅ Design feasibility functions for optimization problems

Beyond the Roadmap

After completing this roadmap:

1. Maintain skills - Solve 2-3 binary search problems per week
2. Explore advanced topics - Ternary search, fractional cascading
3. Teach others - Explaining solidifies understanding
4. Apply to real problems - Use in competitive programming
5. Review proofs - Deepen mathematical understanding

Final Tips

Do's

✅ Understand the math behind each pattern
✅ Visualize pointer movement on paper
✅ Test edge cases systematically
✅ Practice explaining solutions out loud
✅ Build intuition for monotonicity
✅ Use correct templates consistently

Don'ts

❌ Memorize without understanding
❌ Skip the proof articles
❌ Ignore off-by-one errors
❌ Rush through feasibility functions
❌ Confuse minimize and maximize patterns
❌ Use binary search on unsorted data

Conclusion

This roadmap is your structured path to binary search mastery. Follow it consistently, and in 6 weeks, you'll be interview-ready.

Remember:

• Week 1-2: Master classic binary search
• Week 3: Handle duplicates with bounds
• Week 4: Rotated arrays and 2D matrices
• Week 5-6: Binary search on answer mastery

The journey is systematic, and the reward is confidence. Binary search is a fundamental skill that appears in countless interview problems.

Start with Week 1, Problem #1 (Binary Search #704), and begin your journey to mastery.

Good luck, and happy searching! 🚀

Ready to start? Begin with the Complete Binary Search Guide and solve your first problem today.