First and Last Occurrence of Element in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Find first and last occurrence indexes

What is the output of the following code that finds the first and last occurrence of the number 3 in the list?

DSA Python

def first_last_occurrence(arr, x):
    first = -1
    last = -1
    for i in range(len(arr)):
        if arr[i] == x:
            if first == -1:
                first = i
            last = i
    return (first, last)

arr = [1, 3, 5, 3, 7, 3, 9]
x = 3
print(first_last_occurrence(arr, x))

A (0, 6)

B (1, 3)

C (1, 5)

D (-1, -1)

💡 Hint

Check the positions where 3 appears in the list.

The number 3 appears first at index 1 and last at index 5 in the list.

❓ Predict Output

intermediate

Output of binary search for first occurrence

What will be the output of this code that uses binary search to find the first occurrence of 4 in a sorted list?

DSA Python

def first_occurrence(arr, x):
    low, high = 0, len(arr) - 1
    result = -1
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == x:
            result = mid
            high = mid - 1
        elif arr[mid] < x:
            low = mid + 1
        else:
            high = mid - 1
    return result

arr = [1, 2, 4, 4, 4, 5, 6]
x = 4
print(first_occurrence(arr, x))

A 4

B 2

C -1

D 3

💡 Hint

Binary search narrows down to the leftmost index of the target.

The first occurrence of 4 in the list is at index 2.

🔧 Debug

advanced

Identify the error in last occurrence function

What error will this code produce when trying to find the last occurrence of 7 in the list?

DSA Python

def last_occurrence(arr, x):
    low, high = 0, len(arr) - 1
    result = -1
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == x:
            result = mid
            low = mid + 1
        elif arr[mid] > x:
            high = mid - 1
        else:
            low = mid + 1
    return result

arr = [1, 3, 5, 7, 7, 7, 9]
x = 7
print(last_occurrence(arr, x))

A No error, output is 5

B IndexError

C Infinite loop

D TypeError

💡 Hint

Check the loop conditions and updates of low and high.

The code correctly finds the last occurrence at index 5 without errors.

❓ Predict Output

advanced

Output of first and last occurrence with no element found

What is the output of this code when searching for 10 in the list?

DSA Python

def first_last_occurrence(arr, x):
    first = -1
    last = -1
    for i in range(len(arr)):
        if arr[i] == x:
            if first == -1:
                first = i
            last = i
    return (first, last)

arr = [2, 4, 6, 8]
x = 10
print(first_last_occurrence(arr, x))

A (-1, -1)

B (0, 3)

C (3, 3)

D (None, None)

💡 Hint

Check what happens if the element is not found in the list.

Since 10 is not in the list, both first and last remain -1.

🧠 Conceptual

expert

Time complexity of first and last occurrence using binary search

What is the time complexity of finding the first and last occurrence of an element in a sorted list using binary search?

A O(1)

B O(n)

C O(n log n)

D O(log n)

💡 Hint

Binary search divides the search space in half each step.

Binary search runs in logarithmic time, so finding first and last occurrence is O(log n).

Practice

1. What does the term first occurrence of an element in a list mean?

easy

A. The total count of the element in the list

B. The last index where the element appears in the list

C. The index where the element appears first in the list

D. The element with the smallest value in the list

Solution

1. Step 1: Understand the meaning of first occurrence

   The first occurrence means the earliest position (index) where the element appears in the list when reading from left to right.

2. Step 2: Compare with other options

   Other options describe last occurrence, count, or smallest value, which are different concepts.

3. Final Answer:

   The index where the element appears first in the list -> Option C

4. Quick Check:

   First occurrence = first index [OK]

Hint: First occurrence means earliest index found [OK]

Common Mistakes:

• Confusing first occurrence with last occurrence
• Thinking it means the count of the element
• Mixing occurrence with element value

2. Which of the following Python code snippets correctly finds the first occurrence index of element 5 in list arr?

easy

A. arr.find(5)

B. arr.index(5)

C. arr.search(5)

D. arr.locate(5)

Solution

1. Step 1: Recall Python list methods

   Python lists have the method index() to find the first occurrence index of an element.

2. Step 2: Check other options

   Methods find(), search(), and locate() do not exist for Python lists.

3. Final Answer:

   arr.index(5) -> Option B

4. Quick Check:

   Use list.index(element) to find first occurrence [OK]

Hint: Use list.index() to get first occurrence index [OK]

Common Mistakes:

• Using non-existent methods like find or search on lists
• Confusing string methods with list methods
• Trying to use index without handling exceptions

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

arr = [2, 4, 5, 4, 5, 6]
first = arr.index(4)
last = len(arr) - 1 - arr[::-1].index(4)
print([first, last])

medium

A. [1, 3]

B. [3, 1]

C. [1, 4]

D. [4, 1]

Solution

1. Step 1: Find first occurrence of 4

   Using arr.index(4) returns 1 because 4 first appears at index 1.

2. Step 2: Find last occurrence of 4

   arr[::-1] reverses the list to [6, 5, 4, 5, 4, 2]. The first index of 4 in reversed list is 2. So last occurrence index = len(arr) - 1 - 2 = 6 - 1 - 2 = 3.

3. Final Answer:

   [1, 3] -> Option A

4. Quick Check:

   First = 1, Last = 3 [OK]

Hint: Reverse list and use index for last occurrence [OK]

Common Mistakes:

• Mixing up reversed index with original index
• Using last = arr.index(4) instead of reversed search
• Confusing first and last occurrence indexes

4. The following code is intended to find the first and last occurrence of element 7 in list nums. What is the error?

nums = [1, 7, 3, 7, 5]
first = nums.index(7)
last = nums.index(7, -1)
print(first, last)

medium

A. Using negative start index in index() causes ValueError

B. index() cannot find element 7 in the list

C. No error; code works correctly

D. The second index() call should use a positive start index

Solution

1. Step 1: Understand index() with start parameter

   The index() method can take a start index. Using -1 as start means start searching from the last element only.

2. Step 2: Identify the error in last occurrence search

   Using nums.index(7, -1) starts searching from index -1 (last element), so it only checks last element which is 5, not 7, causing ValueError.

3. Final Answer:

   The second index() call should use a positive start index -> Option D

4. Quick Check:

   index(start=-1) limits search to last element [OK]

Hint: Use positive start index in index() for last occurrence [OK]

Common Mistakes:

• Using negative start index in list.index()
• Expecting index() to find last occurrence without correct start
• Not handling ValueError when element not found

5. Given a sorted list data = [1, 2, 2, 2, 3, 4, 5], which approach is best to find the first and last occurrence of 2 efficiently?

hard

A. Use binary search to find first and last occurrence

B. Use linear search from start and end to find occurrences

C. Use list.index() and reversed list index() methods

D. Use count() method to find number of occurrences

Solution

1. Step 1: Understand the list is sorted

   Since the list is sorted, binary search can be used to find positions efficiently in O(log n) time.

2. Step 2: Compare approaches

   Linear search (Use linear search from start and end to find occurrences) is slower (O(n)). Using list.index() and reversed index() (Use list.index() and reversed list index() methods) is also linear. count() (Use count() method to find number of occurrences) gives count but not positions.

3. Step 3: Best approach

   Binary search can be adapted to find first and last occurrence indexes quickly.

4. Final Answer:

   Use binary search to find first and last occurrence -> Option A

5. Quick Check:

   Sorted list + binary search = efficient occurrence search [OK]

Hint: Use binary search on sorted list for fast occurrence indexes [OK]

Common Mistakes:

• Using linear search on sorted lists
• Using count() instead of finding indexes
• Not leveraging sorted property for efficiency