Binary Search Iterative Approach in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the binary search algorithm?

Binary search repeatedly divides a sorted list in half to find a target value quickly by comparing the middle element and deciding which half to search next.

beginner

In the iterative binary search, what variables are commonly used to keep track of the search range?

Two variables, usually called low and high, mark the start and end indexes of the current search range in the array.

intermediate

Why do we calculate the middle index as low + Math.floor((high - low) / 2) instead of (low + high) / 2?

Calculating middle this way prevents integer overflow when low and high are large numbers, ensuring safe and correct middle index calculation.

beginner

What condition ends the iterative binary search loop?

The loop ends when low becomes greater than high, meaning the target is not found in the array.

beginner

What is the time complexity of the binary search iterative approach and why?

The time complexity is O(log n) because the search range halves each step, quickly narrowing down the target position.

What must be true about the array for binary search to work correctly?

A The array must be sorted

B The array must contain only positive numbers

C The array must have unique elements

D The array must be unsorted

Binary search requires a sorted array to decide which half to search next.

In iterative binary search, if the middle element is less than the target, what happens next?

A Return the middle index immediately

B Search the left half by moving high

C Search the right half by moving low

D Stop the search

If middle element is less than target, the target must be in the right half, so low is moved to middle + 1.

What does the iterative binary search return if the target is not found?

A -1

B The index of the closest element

C 0

D The middle index

Returning -1 is a common way to indicate the target is not found.

Which of these is the correct way to calculate the middle index safely?

A (low + high) / 2

B low + Math.floor((high - low) / 2)

C high - low / 2

D low * high / 2

Using low + Math.floor((high - low) / 2) avoids overflow issues.

What is the main advantage of binary search over linear search?

A Works on unsorted arrays

B Simpler to implement

C Uses less memory

D Faster search time on sorted arrays

Binary search is faster because it halves the search space each step.

Explain how the iterative binary search algorithm works step-by-step.

Think about dividing the search range repeatedly.

Describe why binary search requires a sorted array and what happens if the array is not sorted.

Consider how you decide to go left or right.

Practice

1. What is the main purpose of the Binary Search Iterative Approach in a sorted array?

easy

A. To find the maximum value in the array

B. To sort the array elements in ascending order

C. To reverse the array elements

D. To find the position of a target value efficiently by repeatedly dividing the search interval in half

Solution

1. Step 1: Understand the goal of binary search

   Binary search is used to find a target value in a sorted array by dividing the search space repeatedly.

2. Step 2: Identify the iterative approach

   The iterative approach uses a loop to narrow down the search range until the target is found or the range is empty.

3. Final Answer:

   To find the position of a target value efficiently by repeatedly dividing the search interval in half -> Option D

4. Quick Check:

   Binary search = efficient target search [OK]

Hint: Binary search halves the search space each step [OK]

Common Mistakes:

• Confusing binary search with sorting algorithms
• Thinking binary search works on unsorted arrays
• Assuming it finds max/min values

2. Which of the following is the correct way to initialize the middle index in an iterative binary search in TypeScript?

easy

A. const mid = (low + high) / 2;

B. const mid = Math.floor((low + high) / 2);

C. const mid = Math.ceil((low + high) / 2);

D. const mid = low + high;

Solution

1. Step 1: Understand index calculation in binary search

   The middle index must be an integer index, so we use Math.floor to round down the division result.

2. Step 2: Check each option

   const mid = (low + high) / 2; returns a float, const mid = Math.floor((low + high) / 2); correctly floors the value, const mid = Math.ceil((low + high) / 2); rounds up which can cause errors, const mid = low + high; sums indices without division.

3. Final Answer:

   const mid = Math.floor((low + high) / 2); -> Option B

4. Quick Check:

   Use Math.floor for middle index [OK]

Hint: Always floor the average of low and high [OK]

Common Mistakes:

• Using division without flooring causing float index
• Using ceil which may skip elements
• Adding indices without dividing

3. What will be the output of the following TypeScript code snippet?

function binarySearch(arr: number[], target: number): number {
  let low = 0;
  let high = arr.length - 1;
  while (low <= high) {
    const mid = Math.floor((low + high) / 2);
    if (arr[mid] === target) return mid;
    else if (arr[mid] < target) low = mid + 1;
    else high = mid - 1;
  }
  return -1;
}

const result = binarySearch([2, 4, 6, 8, 10], 6);
console.log(result);

medium

A. 2

B. 3

C. -1

D. 4

Solution

1. Step 1: Trace the binary search for target 6

   Initial low=0, high=4, mid=2 (element 6). arr[mid] equals target, so return 2.

2. Step 2: Confirm output

   Function returns index 2, which is printed.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Target 6 found at index 2 [OK]

Hint: Check mid index value matches target first [OK]

Common Mistakes:

• Off-by-one errors in index calculation
• Returning wrong index when target found
• Confusing return value with element value

4. Identify the bug in this iterative binary search code snippet and select the correct fix:

function binarySearch(arr: number[], target: number): number {
  let low = 0;
  let high = arr.length;
  while (low <= high) {
    const mid = Math.floor((low + high) / 2);
    if (arr[mid] === target) return mid;
    else if (arr[mid] < target) low = mid + 1;
    else high = mid - 1;
  }
  return -1;
}

medium

A. Change let high = arr.length; to let high = arr.length - 1;

B. Change low <= high to low < high

C. Change mid = Math.floor((low + high) / 2); to mid = Math.ceil((low + high) / 2);

D. Remove the else before if (arr[mid] < target)

Solution

1. Step 1: Identify the initialization error

   High should be the last valid index, which is arr.length - 1, not arr.length.

2. Step 2: Understand impact of wrong high value

   Setting high to arr.length causes out-of-bound access at arr[mid] when mid equals arr.length.

3. Final Answer:

   Change let high = arr.length; to let high = arr.length - 1; -> Option A

4. Quick Check:

   High index must be last valid array index [OK]

Hint: High index = array length minus one [OK]

Common Mistakes:

• Setting high to array length causing out-of-bounds
• Changing loop condition incorrectly
• Using ceil instead of floor for mid

5. Given a sorted array with possible duplicate values, how can you modify the iterative binary search to find the first occurrence of a target value?

hard

A. When arr[mid] equals target, update low to mid + 1 and continue searching right

B. Return mid immediately when arr[mid] equals target

C. When arr[mid] equals target, update high to mid - 1 and continue searching left

D. Use recursion instead of iteration

Solution

1. Step 1: Understand the problem with duplicates

   Standard binary search returns any occurrence, not necessarily the first.

2. Step 2: Modify search to find first occurrence

   When target found at mid, move high to mid - 1 to continue searching left side for earlier occurrence.

3. Step 3: Keep track of potential answer

   Store mid as potential answer and continue until low > high.

4. Final Answer:

   When arr[mid] equals target, update high to mid - 1 and continue searching left -> Option C

5. Quick Check:

   Move left on match to find first occurrence [OK]

Hint: On match, search left side to find first occurrence [OK]

Common Mistakes:

• Returning immediately on first match
• Searching right side on match
• Ignoring duplicates in binary search