Binary Search on Answer Technique in DSA C# - Build from Scratch

Binary Search on Answer Technique

📖 Scenario: You are organizing a workshop and need to divide participants into groups. Each group should have at most a certain number of participants. You want to find the smallest possible maximum group size so that all participants fit into the given number of groups.

🎯 Goal: Build a program that uses the binary search on answer technique to find the minimum maximum group size needed to divide all participants into the specified number of groups.

📋 What You'll Learn

Create an array called participants with these exact values: 12, 34, 23, 45, 56, 78, 89, 90

Create an integer variable called maxGroups and set it to 5

Write a function called CanDivide that takes an integer maxSize and returns true if participants can be divided into groups with maximum size maxSize within maxGroups

Use binary search on the answer range to find the minimum maximum group size

Print the minimum maximum group size

💡 Why This Matters

🌍 Real World

This technique helps in resource allocation problems like dividing tasks, packing items, or scheduling where you want to find an optimal limit.

💼 Career

Binary search on answer is a common pattern in coding interviews and real-world optimization problems in software engineering.

1

Create the participants array

Create an integer array called participants with these exact values: 12, 34, 23, 45, 56, 78, 89, 90

DSA C#

# Your code here

Hint

Use int[] participants = { ... }; to create the array with the exact numbers.

2

Set the maximum number of groups

Create an integer variable called maxGroups and set it to 5

DSA C#

int[] participants = {12, 34, 23, 45, 56, 78, 89, 90};
# Your code here

Hint

Use int maxGroups = 5; to set the maximum number of groups.

3

Write the CanDivide function

Write a function called CanDivide that takes an integer maxSize and returns true if the participants can be divided into groups with maximum size maxSize within maxGroups. Use a loop to count how many groups are needed by summing participant sizes until exceeding maxSize.

DSA C#

int[] participants = {12, 34, 23, 45, 56, 78, 89, 90};
int maxGroups = 5;

// Your code here

Hint

Use a loop to add participant sizes until exceeding maxSize. Increase group count and reset sum when needed.

4

Find and print the minimum maximum group size

Use binary search on the range from the maximum participant size to the sum of all participants to find the minimum maximum group size. Print the result using Console.WriteLine.

DSA C#

int[] participants = {12, 34, 23, 45, 56, 78, 89, 90};
int maxGroups = 5;

bool CanDivide(int maxSize)
{
    int groups = 1;
    int currentSum = 0;
    foreach (int p in participants)
    {
        if (p > maxSize) return false;
        if (currentSum + p  maxGroups) return false;
        }
    }
    return true;
}

// Your code here

Hint

Use binary search between the largest participant size and the total sum. Use CanDivide to check feasibility. Print the final minimum maximum group size.

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