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

Recall & Review

beginner

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

It means the position (index) where the element appears for the very first time when reading the array from left to right.

beginner

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

It means the position (index) where the element appears for the very last time when reading the array from left to right.

intermediate

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

Finding these helps us know the range where the element appears, which is useful for counting how many times it occurs or for searching efficiently.

intermediate

How can binary search help find the first and last occurrence of an element in a sorted array?

Binary search can be modified to continue searching even after finding the element, moving left to find the first occurrence or right to find the last occurrence, making it faster than checking every element.

intermediate

What is the time complexity of finding first and last occurrence using binary search?

The time complexity is O(log n) because binary search divides the search space in half each time.

What is the first occurrence of element 5 in the array [1, 3, 5, 5, 7]?

A 1

B 2

C 3

D 4

The element 5 first appears at index 2 (0-based indexing).

If an element does not exist in the array, what should the first and last occurrence functions return?

A -1

B 0

C Array length

D Null

Returning -1 indicates the element is not found in the array.

Which search method is faster for finding first and last occurrence in a sorted array?

A Linear Search

B Bubble Sort

C Binary Search

D Insertion Sort

Binary Search is faster (O(log n)) compared to Linear Search (O(n)) for sorted arrays.

What is the last occurrence of element 5 in the array [1, 3, 5, 5, 7]?

A 3

B 4

C 1

D 2

The element 5 last appears at index 3.

Which of these is NOT a valid approach to find first and last occurrence?

A Using two pointers

B Linear Scan

C Modified Binary Search

D Sorting the array again

Sorting again is unnecessary if the array is already sorted and does not help find occurrences.

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

Think about narrowing down the search to the left side after finding the element.

Describe why finding both first and last occurrence is useful in counting element frequency.

Counting how many times an element appears is easier with these two positions.

Practice

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

easy

A. The maximum element in the array

B. The sum of all elements in the array

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

D. The number of unique elements in the array

Solution

1. Step 1: Understand the problem statement

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

2. Step 2: Identify what is required

   We need to locate where the element appears first and last, not sums or counts.

3. Final Answer:

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

4. Quick Check:

   First and last occurrence = positions of element [OK]

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

Common Mistakes:

• Confusing occurrence with sum or max
• Thinking about unique elements instead
• Ignoring the order of elements

2. Which of the following TypeScript function signatures correctly represents a function to find first and last occurrence of a number in an array?

easy

A. function findOccurrences(arr: number[], target: number): number

B. function findOccurrences(arr: string[], target: string): number

C. function findOccurrences(arr: number, target: number): number[]

D. function findOccurrences(arr: number[], target: number): [number, number]

Solution

1. Step 1: Analyze the function parameters

   The function should take an array of numbers and a target number to find.

2. Step 2: Analyze the return type

   We want to return two numbers (first and last index), so a tuple [number, number] is appropriate.

3. Final Answer:

   function findOccurrences(arr: number[], target: number): [number, number] -> Option D

4. Quick Check:

   Input array and target, output tuple of two indexes [OK]

Hint: Return a tuple of two numbers for first and last indexes [OK]

Common Mistakes:

• Using wrong input types like single number instead of array
• Returning only one number instead of two
• Returning array of wrong type

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

function findOccurrences(arr: number[], target: number): [number, number] {
  let first = -1;
  let last = -1;
  for (let i = 0; i < arr.length; i++) {
    if (arr[i] === target) {
      if (first === -1) first = i;
      last = i;
    }
  }
  return [first, last];
}

console.log(findOccurrences([5, 3, 7, 3, 9], 3));

medium

A. [1, 3]

B. [3, 3]

C. [0, 4]

D. [-1, -1]

Solution

1. Step 1: Trace the loop to find first occurrence

   At index 1, element is 3 which matches target, so first = 1.

2. Step 2: Update last occurrence while looping

   At index 3, element is 3 again, so last = 3.

3. Final Answer:

   [1, 3] -> Option A

4. Quick Check:

   First = 1, Last = 3 [OK]

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

Common Mistakes:

• Returning first occurrence twice
• Returning indexes of wrong elements
• Not updating last occurrence properly

4. Identify the bug in this TypeScript function to find first and last occurrence:

function findOccurrences(arr: number[], target: number): [number, number] {
  let first = 0;
  let last = 0;
  for (let i = 0; i < arr.length; i++) {
    if (arr[i] === target) {
      if (first === 0) first = i;
      last = i;
    }
  }
  return [first, last];
}

medium

A. last should be initialized to -1 instead of 0

B. first initialized to 0 causes wrong first occurrence when target is at index 0

C. Loop should start from 1 instead of 0

D. Missing return type annotation

Solution

1. Step 1: Check initialization of first

   first is set to 0, so if target is at index 0, condition first === 0 is true initially, causing incorrect logic.

2. Step 2: Understand impact on first occurrence

   If target is at index 0, first will never update correctly because first === 0 is true initially, so first stays 0 even if target not found.

3. Final Answer:

   first initialized to 0 causes wrong first occurrence when target is at index 0 -> Option B

4. Quick Check:

   Initialize first to -1 to fix [OK]

Hint: Initialize first to -1 to detect if target found [OK]

Common Mistakes:

• Initializing first to 0 instead of -1
• Not handling target at index 0 correctly
• Assuming first occurrence is always > 0

5. Given a sorted array with possible duplicates, which approach is the most efficient to find the first and last occurrence of a target element?

hard

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

B. Traverse the array from start to end to find first and last occurrence

C. Sort the array again and then find the element

D. Use a hash map to store all occurrences and then find first and last

Solution

1. Step 1: Understand the array is sorted

   Since the array is sorted, binary search can be used to find elements efficiently.

2. Step 2: Use binary search twice

   One binary search finds the first occurrence, another finds the last occurrence, both in O(log n) time.

3. Step 3: Compare with other options

   Traversing is O(n), sorting again is unnecessary, hash map uses extra space and is less efficient.

4. Final Answer:

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

5. Quick Check:

   Binary search twice = efficient for sorted arrays [OK]

Hint: Use binary search twice for first and last positions [OK]

Common Mistakes:

• Using linear search on sorted array
• Sorting array again unnecessarily
• Using extra space with hash map