Interview Tips: Validation and Drawing Advice

Binary search problems in interviews require careful validation and visualization. Here are practical tips to avoid common mistakes and communicate your solution effectively.

Validation Strategies

1. Verify Loop Invariants

At the start of each iteration, verify:

left <= right (or left < right depending on template)
If answer exists, it's in [left, right]
Array bounds are respected

2. Test Edge Cases

Always test these scenarios:

# Empty array
nums = []

# Single element
nums = [1]

# Two elements
nums = [1, 2]

# Target at boundaries
target = nums[0]
target = nums[-1]

# Target not in array
target = nums[0] - 1
target = nums[-1] + 1

# All elements same
nums = [5, 5, 5, 5]

3. Add Debugging Output

During interviews, it's okay to add print statements to verify your logic:

while left <= right:
    mid = left + (right - left) // 2
    print(f"left={left}, right={right}, mid={mid}, nums[mid]={nums[mid]}")

    if nums[mid] == target:
        return mid
    elif nums[mid] < target:
        left = mid + 1
    else:
        right = mid - 1

Drawing Advice

1. Visualize the Search Space

Draw the array and mark your pointers:

Array: [1, 3, 5, 7, 9, 11, 13, 15]
        ↑                    ↑
      left                 right
                    ↑
                   mid

2. Show the Transition Point

For boundary problems, clearly mark where the property changes:

[False, False, False, True, True, True]
                    ↑
            Transition Point

3. Track Pointer Movement

Show how pointers move with each iteration:

Round 1: [1, 3, 5, 7, 9, 11, 13, 15]
                    ↑ mid=9 > 7
         left       right

Round 2: [1, 3, 5, 7]
               ↑ mid=5 < 7
         left  right

Round 3:       [7]
               ↑ mid=7 == 7
         left=right
         Found!

Common Mistakes to Avoid

Mistake 1: Off-by-One Errors

# Wrong - might miss element
while left < right:  # Should be <= for Template 1
    ...

# Right
while left <= right:
    ...

Mistake 2: Infinite Loops

# Wrong - doesn't move left
if nums[mid] < target:
    left = mid  # Should be mid + 1

# Right
if nums[mid] < target:
    left = mid + 1

Mistake 3: Wrong Mid Calculation

# Could overflow in some languages
mid = (left + right) // 2

# Safe
mid = left + (right - left) // 2

Mistake 4: Wrong Template Choice

Using Template 1 when you need Template 2 (boundary finding)
Using Template 2 when you need Template 3 (neighbor checks)
Not recognizing when to use binary search on answer space

Communication Tips

1. State Your Approach First

"I'll use binary search because the array is sorted and we can eliminate half the search space with each comparison."

2. Explain Your Template Choice

"I'll use Template 2 because we're finding the first occurrence, which is a boundary-finding problem."

3. Walk Through an Example

"Let me trace through with [1, 3, 5, 7, 9] and target 5..."

4. Discuss Edge Cases

"What if the array is empty? What if the target isn't in the array?"

Practice Validation Checklist

Before submitting your solution, verify:

Key Takeaway

Validation and visualization are crucial for binary search problems. Always test edge cases, draw your search space, and communicate your approach clearly. These practices help you catch bugs early and demonstrate strong problem-solving skills.