First and Last Occurrence of Element in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does 'First Occurrence of Element' mean in an array?

It means finding the index of the first time a given element appears in the array, starting from the left (index 0).

beginner

What does 'Last Occurrence of Element' mean in an array?

It means finding the index of the last time a given element appears in the array, starting from the left (index 0).

intermediate

Why is it useful to find the first and last occurrence of an element?

It helps to know the range where the element appears, useful for counting how many times it occurs or for searching efficiently.

beginner

What is a simple way to find the first occurrence of an element in an array?

Start from the beginning of the array and check each element until you find the target element. Return that index.

intermediate

How can binary search help in finding first and last occurrences in a sorted array?

Binary search can be modified to find the first or last position of an element by adjusting the search boundaries when the element is found.

What index does the first occurrence of an element represent?

A The middle index of the array

B The largest index where the element appears

C The smallest index where the element appears

D The last index of the array

The first occurrence is the smallest index where the element is found.

If an element does not exist in the array, what should the function return?

A 0

B The length of the array

C The first index

D -1

Returning -1 indicates the element was not found.

Which search method is best for finding first and last occurrences in a sorted array?

A Binary search

B Linear search

C Depth-first search

D Breadth-first search

Binary search is efficient for sorted arrays.

What is the time complexity of linear search for first occurrence?

A O(1)

B O(n)

C O(n log n)

D O(log n)

Linear search checks each element, so it takes O(n) time.

In binary search for first occurrence, what do you do when you find the element?

A Search left half to find earlier occurrence

B Return immediately

C Search right half to find later occurrence

D Stop searching

To find the first occurrence, continue searching the left half.

Explain how to find the first and last occurrence of an element in a sorted array using binary search.

Think about how to move left or right when you find the element.

Describe a simple approach to find the first and last occurrence of an element in an unsorted array.

Check elements one by one from start and end.

Practice

1. What does the "First and Last Occurrence of Element" problem ask you to find in an array?

easy

A. The number of unique elements in the array

B. The sum of all elements in the array

C. The maximum and minimum elements in the array

D. The first and last positions where a given element appears

Solution

1. Step 1: Understand the problem statement

   The problem asks to find the first and last positions of a specific element in an array.

2. Step 2: Differentiate from other array queries

   It is not about sums, max/min, or counting unique elements, but about positions of a target element.

3. Final Answer:

   The first and last positions where a given element appears -> Option D

4. Quick Check:

   Positions of element = first and last occurrence [OK]

Hint: Look for positions of target element, not values or counts [OK]

Common Mistakes:

• Confusing with finding max or min element
• Trying to sum elements instead of finding positions
• Counting unique elements instead of occurrences

2. Which of the following C# code snippets correctly initializes an array to find the first and last occurrence of an element?

easy

A. int arr = {1, 2, 3, 4, 5};

B. int arr = new int[5] {1, 2, 3, 4, 5};

C. int[] arr = new int[] {1, 2, 3, 4, 5};

D. int arr[] = new int[] {1, 2, 3, 4, 5};

Solution

1. Step 1: Check array initialization syntax in C#

   Correct syntax is: int[] arr = new int[] {1, 2, 3, 4, 5};

2. Step 2: Identify incorrect options

   int arr = new int[5] {1, 2, 3, 4, 5}; has wrong syntax (cannot assign array with size and initializer like that), A is missing 'new int[]', D uses C-style syntax invalid in C#.

3. Final Answer:

   int[] arr = new int[] {1, 2, 3, 4, 5}; -> Option C

4. Quick Check:

   Correct C# array syntax = int[] arr = new int[] {1, 2, 3, 4, 5}; [OK]

Hint: Use 'int[] arr = new int[] { ... }' for array initialization [OK]

Common Mistakes:

• Using C/C++ style array declarations
• Omitting 'new int[]' keyword
• Assigning array size with initializer incorrectly

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

int[] arr = {5, 3, 7, 3, 9};
int target = 3;
int first = -1, last = -1;
for (int i = 0; i < arr.Length; i++) {
  if (arr[i] == target) {
    if (first == -1) first = i;
    last = i;
  }
}
Console.WriteLine($"{first} {last}");

medium

A. 3 1

B. 1 3

C. 0 4

D. -1 -1

Solution

1. Step 1: Trace the loop to find first and last occurrence of 3

   Array: [5, 3, 7, 3, 9]. Target = 3. Indices: 0 to 4.
   i=0: arr[0]=5 !=3 skip
   i=1: arr[1]=3 == target, first=-1 so first=1, last=1
   i=2: arr[2]=7 !=3 skip
   i=3: arr[3]=3 == target, first=1 (unchanged), last=3
   i=4: arr[4]=9 !=3 skip

2. Step 2: Print first and last

   first=1, last=3

3. Final Answer:

   1 3 -> Option B

4. Quick Check:

   First and last index of 3 = 1 and 3 [OK]

Hint: Track first when found, update last every time [OK]

Common Mistakes:

• Swapping first and last indices
• Not updating last occurrence correctly
• Initializing first and last with wrong values

4. Identify the error in the following code that tries to find the first and last occurrence of an element:

int[] arr = {2, 4, 2, 5, 2};
int target = 2;
int first = 0, last = 0;
for (int i = 0; i < arr.Length; i++) {
  if (arr[i] == target) {
    first = i;
    last = i;
  }
}
Console.WriteLine($"{first} {last}");

medium

A. first and last are initialized incorrectly, causing wrong output

B. Loop condition should be i <= arr.Length

C. Target value is not assigned properly

D. Console.WriteLine syntax is incorrect

Solution

1. Step 1: Analyze initialization of first and last

   Both first and last start at 0. Inside loop, first and last are set to i every time target is found, so first will be overwritten and end up as last occurrence index.

2. Step 2: Identify correct approach

   First should be set only once when first occurrence is found (e.g., if first == -1). Last should update every time target is found.

3. Final Answer:

   first and last are initialized incorrectly, causing wrong output -> Option A

4. Quick Check:

   Initialize first to -1 and update only once [OK]

Hint: Initialize first to -1 and update only once [OK]

Common Mistakes:

• Overwriting first occurrence index
• Using wrong loop boundary
• Incorrect Console.WriteLine format

5. Given a sorted array with possible duplicates, how can you efficiently find the first and last occurrence of a target element using C#?

hard

A. Use two binary searches: one for first occurrence, one for last occurrence

B. Traverse the array twice: once from start, once from end

C. Use a dictionary to store element counts

D. Sort the array again and find the target

Solution

1. Step 1: Understand the array is sorted with duplicates

   Sorted array allows binary search to find positions efficiently.

2. Step 2: Use binary search twice

   One binary search finds the first occurrence by moving left when target found, another finds last occurrence by moving right.

3. Step 3: Avoid full traversal or extra sorting

   Traversing twice or sorting again is inefficient. Dictionary counts do not give positions.

4. Final Answer:

   Use two binary searches: one for first occurrence, one for last occurrence -> Option A

5. Quick Check:

   Binary search twice = efficient first and last occurrence [OK]

Hint: Binary search twice for first and last occurrence in sorted array [OK]

Common Mistakes:

• Using linear search on large sorted arrays
• Sorting array again unnecessarily
• Using dictionary counts instead of positions