Binary Search on Answer Technique in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Binary Search on Answer for Minimum Maximum Subarray Sum

What is the output of the following TypeScript code that uses binary search on answer to find the minimum largest sum among subarrays?

DSA Typescript

function canSplit(nums: number[], maxSum: number, m: number): boolean {
  let currentSum = 0, count = 1;
  for (const num of nums) {
    if (num > maxSum) return false;
    if (currentSum + num > maxSum) {
      count++;
      currentSum = num;
      if (count > m) return false;
    } else {
      currentSum += num;
    }
  }
  return true;
}

function splitArray(nums: number[], m: number): number {
  let left = Math.max(...nums);
  let right = nums.reduce((a, b) => a + b, 0);
  while (left < right) {
    const mid = Math.floor((left + right) / 2);
    if (canSplit(nums, mid, m)) {
      right = mid;
    } else {
      left = mid + 1;
    }
  }
  return left;
}

const nums = [7,2,5,10,8];
const m = 2;
console.log(splitArray(nums, m));

A 18

B 15

C 20

D 23

💡 Hint

Think about how the array can be split into 2 subarrays with minimum largest sum.

The function tries to find the smallest maximum subarray sum possible when splitting the array into m parts. For [7,2,5,10,8] and m=2, the minimum largest sum is 18, achieved by splitting as [7,2,5] and [10,8].

🧠 Conceptual

intermediate

Understanding Binary Search on Answer Technique

Which of the following best describes the main idea behind the binary search on answer technique?

A Using binary search to find the correct value in a sorted array directly.

B Using binary search to find the index of a target value in a linked list.

C Using binary search to sort an unsorted array efficiently.

D Using binary search over a range of possible answers to find the minimum or maximum value that satisfies a condition.

💡 Hint

Think about searching over a range of values, not array indices.

Binary search on answer searches over a range of possible answers (not array indices) to find the smallest or largest value that meets a problem's condition.

🔧 Debug

advanced

Identify the Bug in Binary Search on Answer Implementation

What is the bug in the following TypeScript code that tries to find the minimum maximum time to complete tasks by workers using binary search on answer?

DSA Typescript

function canComplete(tasks: number[], maxTime: number, workers: number): boolean {
  let currentTime = 0;
  let count = 1;
  for (const task of tasks) {
    if (task > maxTime) return false;
    if (currentTime + task > maxTime) {
      count++;
      currentTime = task;
      if (count > workers) return false;
    } else {
      currentTime += task;
    }
  }
  return true;
}

function minTime(tasks: number[], workers: number): number {
  let left = Math.max(...tasks);
  let right = tasks.reduce((a, b) => a + b, 0);
  while (left < right) {
    const mid = Math.floor((left + right) / 2);
    if (canComplete(tasks, mid, workers)) {
      right = mid;
    } else {
      left = mid + 1;
    }
  }
  return left;
}

const tasks = [3, 6, 7, 11];
const workers = 2;
console.log(minTime(tasks, workers));

A The mid calculation should use (left + right + 1) / 2 to avoid infinite loop.

B The condition 'currentTime + task >= maxTime' should be 'currentTime + task > maxTime' to avoid extra worker count.

C The function should return false if tasks array is empty.

D The initial left boundary should be 0 instead of max task time.

💡 Hint

Check the condition that triggers a new worker assignment.

Using '>=' causes a new worker to be assigned even when currentTime + task equals maxTime, which is unnecessary and leads to incorrect results.

❓ Predict Output

advanced

Output of Binary Search on Answer for Aggressive Cows Problem

What is the output of the following TypeScript code that uses binary search on answer to place cows in stalls maximizing minimum distance?

DSA Typescript

function canPlaceCows(stalls: number[], distance: number, cows: number): boolean {
  let count = 1;
  let lastPosition = stalls[0];
  for (let i = 1; i < stalls.length; i++) {
    if (stalls[i] - lastPosition >= distance) {
      count++;
      lastPosition = stalls[i];
      if (count >= cows) return true;
    }
  }
  return false;
}

function aggressiveCows(stalls: number[], cows: number): number {
  stalls.sort((a, b) => a - b);
  let left = 1;
  let right = stalls[stalls.length - 1] - stalls[0];
  let result = 0;
  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    if (canPlaceCows(stalls, mid, cows)) {
      result = mid;
      left = mid + 1;
    } else {
      right = mid - 1;
    }
  }
  return result;
}

const stalls = [1, 2, 8, 4, 9];
const cows = 3;
console.log(aggressiveCows(stalls, cows));

A 4

B 5

C 3

D 6

💡 Hint

Think about placing cows with maximum minimum distance between them.

The maximum minimum distance to place 3 cows in stalls [1,2,4,8,9] is 3, placing cows at positions 1, 4, and 8.

🧠 Conceptual

expert

When to Use Binary Search on Answer Technique?

Which scenario is the best fit for applying binary search on answer technique?

A When the problem asks for an optimal numeric value that can be checked by a yes/no condition over a range.

B When you need to find an element in a sorted array by index.

C When you want to sort an array in O(n log n) time.

D When you need to traverse a tree in depth-first order.

💡 Hint

Think about searching over a range of possible answers with a feasibility check.

Binary search on answer is used when the answer is a number in a range and you can check if a candidate answer satisfies the problem's constraints.

Practice

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

easy

A. We guess an answer and check if it satisfies the problem constraints, then adjust the guess.

B. We sort the input array before applying binary search.

C. We use binary search only on sorted arrays to find elements.

D. We divide the input into two halves and solve each recursively.

Solution

1. Step 1: Understand the technique's purpose

   Binary Search on Answer guesses a possible answer value and checks if it meets the problem's conditions.

2. Step 2: Adjust guess based on check

   If the guess is valid, we try smaller or larger values accordingly to find the optimal answer.

3. Final Answer:

   We guess an answer and check if it satisfies the problem constraints, then adjust the guess. -> Option A

4. Quick Check:

   Guess and check approach = C [OK]

Hint: Think of guessing answers and verifying them stepwise [OK]

Common Mistakes:

• Confusing with normal binary search on arrays
• Assuming input must be sorted
• Thinking it divides input recursively

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

easy

A. while (low <= high) { let mid = (low + high) / 2; }

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

C. while (low <= high) { let mid = Math.floor((low + high) / 2); }

D. if (low < high) { let mid = (low + high) >> 1; }

Solution

1. Step 1: Identify correct mid calculation

   Midpoint must be an integer index, so use Math.floor to avoid decimals.

2. Step 2: Confirm loop condition and syntax

   Use while loop with condition low <= high for binary search iteration.

3. Final Answer:

   while (low <= high) { let mid = Math.floor((low + high) / 2); } -> Option C

4. Quick Check:

   Integer mid with while loop = B [OK]

Hint: Use Math.floor for mid to avoid decimals in binary search [OK]

Common Mistakes:

• Using division without floor causing float mid
• Using for loop instead of while
• Using bitwise shift without understanding

3. Consider this TypeScript code snippet using binary search on answer to find minimum capacity to ship packages within D days:

function canShip(weights: number[], capacity: number, D: number): boolean {
  let days = 1, total = 0;
  for (const w of weights) {
    if (total + w > capacity) {
      days++;
      total = 0;
    }
    total += w;
  }
  return days <= D;
}

function shipWithinDays(weights: number[], D: number): number {
  let low = Math.max(...weights);
  let high = weights.reduce((a, b) => a + b, 0);
  while (low < high) {
    const mid = Math.floor((low + high) / 2);
    if (canShip(weights, mid, D)) high = mid;
    else low = mid + 1;
  }
  return low;
}

console.log(shipWithinDays([1,2,3,4,5,6,7,8,9,10], 5));

What is the output?

medium

A. 15

B. 10

C. 20

D. 5

Solution

1. Step 1: Understand problem and code

   We find minimum ship capacity to ship weights in 5 days. Minimum capacity is max weight (10), max capacity is sum (55).

2. Step 2: Trace binary search and canShip checks

   Binary search narrows capacity to 15, which allows shipping in 5 days by grouping weights properly.

3. Final Answer:

   15 -> Option A

4. Quick Check:

   Minimum capacity = 15 [OK]

Hint: Check max weight as low and sum as high for binary search [OK]

Common Mistakes:

• Choosing max weight instead of sum as answer
• Confusing days count in canShip function
• Not using Math.floor for mid calculation

4. The following TypeScript code tries to find the maximum minimum distance between elements placed in positions array using binary search on answer. Identify the bug:

function canPlace(positions: number[], distance: number, m: number): boolean {
  let count = 1, lastPos = positions[0];
  for (let i = 1; i < positions.length; i++) {
    if (positions[i] - lastPos >= distance) {
      count++;
      lastPos = positions[i];
    }
  }
  return count >= m;
}

function maxMinDistance(positions: number[], m: number): number {
  positions.sort((a, b) => a - b);
  let low = 0, high = positions[positions.length - 1] - positions[0];
  while (low < high) {
    const mid = Math.floor((low + high + 1) / 2);
    if (canPlace(positions, mid, m)) low = mid;
    else high = mid - 1;
  }
  return low;
}

medium

A. Missing increment of count inside canPlace

B. Binary search mid calculation should not add 1

C. Binary search loop condition should be low <= high

D. No bug; code works correctly

Solution

1. Step 1: Analyze canPlace function

   It correctly counts placements with given minimum distance.

2. Step 2: Check binary search logic

   Mid uses upper mid to avoid infinite loop, loop condition low < high is valid, and updates low/high correctly.

3. Final Answer:

   No bug; code works correctly -> Option D

4. Quick Check:

   Code logic correct = A [OK]

Hint: Use upper mid to avoid infinite loop in binary search [OK]

Common Mistakes:

• Changing loop condition incorrectly
• Removing +1 in mid causing infinite loop
• Forgetting to sort positions array

5. You want to find the minimum maximum time to complete all tasks by k workers, where each worker does continuous tasks. Given tasks array of times, how would you apply binary search on answer to solve this?
Choose the best approach.

hard

A. Calculate average time and assign tasks evenly without binary search.

B. Binary search on time range; check if tasks can be split into ≤ k groups with max sum ≤ mid.

C. Use binary search on number of tasks per worker directly.

D. Sort tasks and assign largest tasks first to workers.

Solution

1. Step 1: Define search space for answer

   Minimum max time is max single task time; maximum is sum of all tasks.

2. Step 2: Check feasibility with mid value

   Check if tasks can be divided into ≤ k continuous groups with max sum ≤ mid.

3. Step 3: Adjust search space based on feasibility

   If feasible, try smaller max time; else increase it.

4. Final Answer:

   Binary search on time range; check if tasks can be split into ≤ k groups with max sum ≤ mid. -> Option B

5. Quick Check:

   Binary search on max time with group check = D [OK]

Hint: Binary search answer space, check feasibility with grouping [OK]

Common Mistakes:

• Sorting tasks instead of binary searching answer
• Trying to binary search on task count directly
• Ignoring continuous group constraint