Binary Search on Answer Technique in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the binary search boundaries correctly.

DSA C#

int low = [1];
int high = 1000;

Drag options to blanks, or click blank then click option'

Aint.MinValue

B-1

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Starting low from -1 causes off-by-one errors.

Using int.MinValue is unnecessary and can cause overflow.

We start binary search from 0 as the lowest possible answer.

2fill in blank

medium

Complete the code to calculate the middle point safely.

DSA C#

int mid = low [1] (high - low) / 2;

Drag options to blanks, or click blank then click option'

A-

B/

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using (low + high) / 2 can cause integer overflow.

Using subtraction or multiplication here is incorrect.

We add half the distance between low and high to low to avoid overflow.

3fill in blank

hard

Fix the error in the condition to update the binary search range.

DSA C#

if (CanAchieve(mid)) {
    low = mid [1] 1;
} else {
    high = mid [2] 1;
}

Drag options to blanks, or click blank then click option'

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction to increase low causes infinite loops.

Using addition to decrease high causes wrong range updates.

When mid is achievable, move low up by 1. Otherwise, move high down by 1.

4fill in blank

hard

Fill both blanks to complete the binary search loop condition and update.

DSA C#

while (low [1] high) {
    int mid = low + (high - low) / 2;
    if (CanAchieve(mid)) {
        low = mid [2] 1;
    } else {
        high = mid - 1;
    }
}

Drag options to blanks, or click blank then click option'

A<=

B<

C>

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in loop condition can cause infinite loops if not careful.

Decreasing low instead of increasing it.

The loop runs while low is less than high. When achievable, low moves up by 1.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension filtering keys by value.

DSA C#

var result = new Dictionary<string, int> {
    { [1], [2] } for (var kvp in data) if (kvp.Value [3] 10)
};

Drag options to blanks, or click blank then click option'

Akvp.Key

Bkvp.Value

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using kvp.Value as key causes errors.

Using <= instead of > changes the filter logic.

We select keys and values where value is greater than 10.

Practice

1. What is the main idea behind the Binary Search on Answer technique?

easy

A. We sort the input array and then perform a binary search on the sorted array.

B. We guess an answer and check if it satisfies the problem, then adjust the guess using binary search.

C. We use binary search to find the maximum element in an unsorted array.

D. We apply binary search to find the first occurrence of a target value in a list.

Solution

1. Step 1: Understand the technique

   Binary Search on Answer guesses a possible solution and verifies if it meets the problem's conditions. If valid, adjust the guess (smaller/larger) using binary search to find the optimal answer.

2. Final Answer:

   We guess an answer and check if it satisfies the problem, then adjust the guess using binary search. -> Option B

3. Quick Check:

   Guess and verify with binary search = B [OK]

Hint: Guess answer, check condition, adjust guess with binary search [OK]

Common Mistakes:

• Confusing binary search on answer with normal binary search on array
• Thinking it only works on sorted arrays
• Not verifying the guessed answer properly

2. Which of the following is the correct C# syntax to start a binary search on answer between low and high?

easy

A. do { int mid = (low - high) / 2; } while (low < high);

B. for (int mid = low; mid <= high; mid++) { }

C. if (low < high) { int mid = low + high; }

D. while (low <= high) { int mid = (low + high) / 2; }

Solution

1. Step 1: Identify correct loop and mid calculation

   The binary search loop uses while (low <= high) and mid = (low + high) / 2 with integer division.

2. Final Answer:

   while (low <= high) { int mid = (low + high) / 2; } -> Option D

3. Quick Check:

   Correct binary search loop syntax = A [OK]

Hint: Use while(low <= high) and mid = (low + high) / 2 [OK]

Common Mistakes:

• Using for loop instead of while
• Incorrect mid calculation like (low - high)/2
• Using if instead of loop

3. Consider the following C# code snippet using binary search on answer to find minimum maximum load:

int low = 10, high = 50;
while (low <= high) {
  int mid = (low + high) / 2;
  if (IsPossible(mid))
    high = mid - 1;
  else
    low = mid + 1;
}
Console.WriteLine(low);

If IsPossible(30) returns true and IsPossible(20) returns false, what will be printed?

medium

A. 10

B. 30

C. 21

D. 20

Solution

1. Step 1: Trace binary search behavior

   IsPossible(mid) true means valid (try smaller, high=mid-1); false means invalid (low=mid+1). Given IsPossible(30)=true, IsPossible(20)=false, assuming monotonicity the search converges to smallest valid at 21.

2. Final Answer:

   21 -> Option C

3. Quick Check:

   Minimum valid answer after binary search = 21 [OK]

Hint: Answer is lowest valid mid after binary search ends [OK]

Common Mistakes:

• Printing high instead of low after loop
• Confusing true/false meaning of IsPossible
• Not updating low and high correctly

4. The following code tries to find the minimum maximum load using binary search on answer. What is the bug?

int low = 0, high = maxLoad;
while (low < high) {
  int mid = (low + high) / 2;
  if (IsPossible(mid))
    low = mid;
  else
    high = mid - 1;
}
Console.WriteLine(low);

medium

A. When IsPossible(mid) is true, 'low' should be set to 'mid + 1' instead of 'mid'.

B. When IsPossible(mid) is true, 'high' should be set to 'mid - 1' instead of 'low'.

C. The condition should be 'while (low <= high)' instead of 'while (low < high)'.

D. The mid calculation should be 'mid = low + (high - low) / 2' to avoid overflow.

Solution

1. Step 1: Identify incorrect update causing infinite loop

   When IsPossible(mid) true, low = mid risks no progress (infinite loop if low == mid); should set low = mid + 1 to advance.

2. Final Answer:

   When IsPossible(mid) is true, 'low' should be set to 'mid + 1' instead of 'mid'. -> Option A

3. Quick Check:

   Increment low by 1 to avoid infinite loop [OK]

Hint: Increment low by 1 when condition true to avoid infinite loop [OK]

Common Mistakes:

• Not incrementing low causing infinite loop
• Confusing when to move low or high
• Ignoring loop condition correctness

5. You want to split an array of weights into k contiguous subarrays so that the maximum sum among these subarrays is minimized. Which approach correctly uses binary search on answer to solve this?

hard

A. Binary search between max weight and sum of all weights; check if array can be split into ≤ k parts with max sum ≤ mid.

B. Sort the array and binary search for the kth largest weight.

C. Use binary search on the array indices to find the split points directly.

D. Apply binary search on the number of subarrays from 1 to k.

Solution

1. Step 1: Define search space and feasibility check

   Binary search from max weight (min possible max sum) to total sum; for mid, check if can split into ≤ k contiguous subarrays each with sum ≤ mid. If yes, try smaller mid; else larger.

2. Final Answer:

   Binary search between max weight and sum of all weights; check if array can be split into ≤ k parts with max sum ≤ mid. -> Option A

3. Quick Check:

   Search answer range and verify splits ≤ k [OK]

Hint: Search between max element and total sum, check splits ≤ k [OK]

Common Mistakes:

• Binary searching on indices instead of answer range
• Not checking contiguous subarray sums properly
• Sorting array unnecessarily