Why Binary Search and What Sorted Order Gives You in DSA Python - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to start binary search with the correct initial left index.

DSA Python

def binary_search(arr, target):
    left = [1]
    right = len(arr) - 1
    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

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

A0

B1

C-1

Dlen(arr)

Attempts:

3 left

💡 Hint

Common Mistakes

Starting left at 1 skips the first element.

Starting left at -1 or len(arr) causes index errors.

The binary search starts with the left index at 0, which is the first element of the sorted list.

2fill in blank

medium

Complete the code to calculate the middle index correctly in binary search.

DSA Python

def binary_search(arr, target):
    left = 0
    right = len(arr) - 1
    while left <= right:
        mid = ([1] + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

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

Alen(arr)

Bright

C0

Dleft

Attempts:

3 left

💡 Hint

Common Mistakes

Using right twice instead of left and right.

Using len(arr) instead of indices.

The middle index is the average of left and right indices, so we add left and right and divide by 2.

3fill in blank

hard

Fix the error in the binary search condition to correctly continue the search loop.

DSA Python

def binary_search(arr, target):
    left = 0
    right = len(arr) - 1
    while [1]:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

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

Aleft <= right

Bleft < right

Cleft == right

Dleft > right

Attempts:

3 left

💡 Hint

Common Mistakes

Using left < right misses checking when left equals right.

Using left == right only checks one position.

The loop should continue while left is less than or equal to right to check all possible positions.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

DSA Python

words = ['tree', 'cat', 'house', 'dog']
lengths = {word: [1] for word in words if [2]

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

Alen(word)

Blen(word) > 3

Cword

Dlen(words)

Attempts:

3 left

💡 Hint

Common Mistakes

Using word instead of len(word) for the value.

Using word instead of len(word) > 3 in the condition.

The dictionary maps each word to its length (len(word)) only if the length is greater than 3 (len(word) > 3).

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths only if length is less than or equal to 4.

DSA Python

words = ['tree', 'cat', 'house', 'dog']
result = { [1]: [2] for word in words if [3] }

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

Aword.upper()

Blen(word)

Clen(word) <= 4

Dword.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Using word.lower() instead of word.upper() for keys.

Using len(word) > 4 instead of len(word) <= 4 in the condition.

The dictionary maps each word in uppercase (word.upper()) to its length (len(word)) only if the length is 4 or less (len(word) <= 4).

Practice

1. Why is binary search only applicable on a sorted list?

easy

A. Because it divides the search space based on order to find elements quickly

B. Because it can search any list regardless of order

C. Because it uses random guessing to find elements

D. Because it checks every element one by one

Solution

1. Step 1: Understand binary search method

   Binary search works by repeatedly dividing the list into halves and deciding which half to search next based on order.

2. Step 2: Importance of sorted order

   If the list is not sorted, we cannot decide which half to discard, so binary search fails.

3. Final Answer:

   Because it divides the search space based on order to find elements quickly -> Option A

4. Quick Check:

   Binary search needs sorted list = Because it divides the search space based on order to find elements quickly [OK]

Hint: Binary search needs order to skip halves fast [OK]

Common Mistakes:

• Thinking binary search works on unsorted lists
• Confusing binary search with linear search
• Believing binary search guesses randomly

2. Which of the following is the correct syntax to perform binary search using Python's bisect module on a sorted list arr to find position of x?

easy

A. pos = bisect.find(arr, x)

B. pos = bisect.search(arr, x)

C. pos = bisect.bisect_left(arr, x)

D. pos = bisect.index(arr, x)

Solution

1. Step 1: Recall bisect module functions

   The bisect module provides bisect_left to find insertion position for x in sorted arr.

2. Step 2: Check options for correct function

   Only bisect_left is valid; others like search, find, index do not exist in bisect.

3. Final Answer:

   pos = bisect.bisect_left(arr, x) -> Option C

4. Quick Check:

   bisect_left finds position = pos = bisect.bisect_left(arr, x) [OK]

Hint: Use bisect_left for binary search position in Python [OK]

Common Mistakes:

• Using non-existent bisect functions
• Confusing bisect with list methods
• Trying to use bisect on unsorted lists

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

arr = [2, 4, 6, 8, 10]
left, right = 0, len(arr) - 1
x = 6
while left <= right:
    mid = (left + right) // 2
    if arr[mid] == x:
        print(mid)
        break
    elif arr[mid] < x:
        left = mid + 1
    else:
        right = mid - 1
else:
    print(-1)

medium

A. 2

B. 3

C. -1

D. 0

Solution

1. Step 1: Trace binary search steps

   Initial left=0, right=4, mid=2 (value 6). Since arr[mid] == x, print mid=2 and break.

2. Step 2: Confirm output

   The loop breaks after printing 2, so output is 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Index of 6 in arr is 2 [OK]

Hint: Check mid index value equals target to stop [OK]

Common Mistakes:

• Miscomputing mid index
• Confusing index with value
• Forgetting to break loop on find

4. The following code is intended to perform binary search on a sorted list nums to find target. What is the error?

def binary_search(nums, target):
    left, right = 0, len(nums)
    while left <= right:
        mid = (left + right) // 2
        if nums[mid] == target:
            return mid
        elif nums[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

medium

A. left should start from 1 instead of 0

B. right should be initialized as len(nums) - 1

C. mid calculation should be (left - right) // 2

D. The loop condition should be while left < right

Solution

1. Step 1: Check initialization of right pointer

   right is set to len(nums), which is out of index range since list indices go from 0 to len(nums)-1.

2. Step 2: Correct right initialization

   right should be len(nums) - 1 to avoid index error when accessing nums[mid].

3. Final Answer:

   right should be initialized as len(nums) - 1 -> Option B

4. Quick Check:

   Index max = len(nums)-1 [OK]

Hint: Right pointer max index is length minus one [OK]

Common Mistakes:

• Setting right to length causes index error
• Changing left start incorrectly
• Wrong mid calculation formula

5. You have a sorted list of unique integers representing book IDs: books = [101, 203, 305, 407, 509]. You want to find the position to insert a new book ID 400 so the list remains sorted. Which approach correctly finds the insertion index using binary search logic?

hard

A. Use linear search to find first element greater than 400 and insert before it

B. Insert 400 at the end always because list is sorted

C. Insert 400 at index 0 always to keep list sorted

D. Check middle element; if less than 400, move right pointer; else move left pointer until left > right, then insert at left

Solution

1. Step 1: Understand binary search insertion logic

   Binary search narrows down where to insert by comparing middle element with target and adjusting pointers.

2. Step 2: Apply logic to find insertion index

   When left pointer passes right, left is the correct insertion index to keep list sorted.

3. Final Answer:

   Check middle element; if less than 400, move right pointer; else move left pointer until left > right, then insert at left -> Option D

4. Quick Check:

   Binary search insertion index = Check middle element; if less than 400, move right pointer; else move left pointer until left > right, then insert at left [OK]

Hint: Insert at left pointer after binary search ends [OK]

Common Mistakes:

• Inserting at wrong fixed position
• Using linear search instead of binary
• Not updating pointers correctly