First and Last Occurrence of Element in DSA Python - Execution Trace

Concept Flow - First and Last Occurrence of Element

Start

↓

Initialize first = -1, last = -1

↓

Traverse array from i=0 to n-1

↓

Check if arr[i

↓

If first == -1, set first = i

↓

Set last = i

↓

Continue traversal

↓

End traversal

↓

Return first and last

We scan the array once, updating first and last positions when we find the target element.

Execution Sample

DSA Python

arr = [2, 3, 5, 3, 7]
target = 3
first = -1
last = -1
for i in range(len(arr)):
    if arr[i] == target:
        if first == -1:
            first = i
        last = i
print(first, last)

Finds the first and last index of 3 in the array.

Execution Table

Step	Operation	Index i	arr[i]	Condition arr[i] == target	first	last	Visual State
1	Initialize first and last	-	-	-	-1	-1	[2, 3, 5, 3, 7]
2	Check arr[0]	0	2	False	-1	-1	[2, 3, 5, 3, 7]
3	Check arr[1]	1	3	True	1	1	[2, 3, 5, 3, 7]
4	Check arr[2]	2	5	False	1	1	[2, 3, 5, 3, 7]
5	Check arr[3]	3	3	True	1	3	[2, 3, 5, 3, 7]
6	Check arr[4]	4	7	False	1	3	[2, 3, 5, 3, 7]
7	End traversal	-	-	-	1	3	[2, 3, 5, 3, 7]

💡 Traversal ends after last index; first=1 and last=3 are returned.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
first	-1	-1	1	1	1	1	1
last	-1	-1	1	1	3	3	3
i	-	0	1	2	3	4	-

Key Moments - 3 Insights

Why do we check if first == -1 before setting it?

Because first should store the very first index where target appears. We only set it once, at the first occurrence (see Step 3 and Step 5 in execution_table).

Why do we update last every time we find the target?

Because last should always point to the most recent occurrence of the target as we scan (see Step 3 and Step 5). This way, after traversal, last is the last occurrence.

What if the target is not in the array?

Then first and last remain -1 (see Step 2 and Step 4 where condition is False and variables don't change). This indicates target not found.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'first' after Step 3?

A 0

B -1

C 1

D 3

💡 Hint

Check the 'first' column in execution_table at Step 3.

At which Step does 'last' get updated to 3?

A Step 2

B Step 5

C Step 3

D Step 6

💡 Hint

Look at the 'last' column and see when it changes to 3 in execution_table.

If the target was 10 (not in array), what would be the final values of first and last?

A -1 and -1

B 0 and 4

C 1 and 3

D 0 and -1

💡 Hint

Refer to key_moments about target not found and initial values in variable_tracker.

Concept Snapshot

First and Last Occurrence:
- Initialize first and last as -1
- Traverse array once
- If element == target:
  - If first == -1, set first = index
  - Always update last = index
- After traversal, first and last hold positions or -1 if not found

Full Transcript

To find the first and last occurrence of an element in an array, we start with first and last set to -1, meaning not found. We scan the array from start to end. When we find the target element, if first is still -1, we set first to the current index. We always update last to the current index when the target is found. After scanning all elements, first and last hold the first and last positions of the target. If the target is not found, both remain -1. This method uses one pass and simple checks to track positions.

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