Why First and Last Occurrence of Element in DSA Typescript?

The Big Idea

Discover how to instantly pinpoint where something starts and ends in a list without endless searching!

The Scenario

Imagine you have a long list of names written on paper, and you want to find where a particular name first appears and where it appears last.

Doing this by scanning the list every time someone asks is tiring and slow.

The Problem

Manually searching through the list means checking each name one by one.

This takes a lot of time if the list is long, and you might lose track or make mistakes.

The Solution

Using the method to find the first and last occurrence of an element helps you quickly locate where the element starts and ends in the list.

This saves time and reduces errors by automating the search.

Before vs After

✗ Before

let index = -1;
for(let i = 0; i < arr.length; i++) {
  if(arr[i] === target) {
    index = i;
    break;
  }
}

✓ After

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

What It Enables

This lets you quickly find the exact range where an element appears, enabling faster data analysis and decision-making.

Real Life Example

In a list of daily temperatures, finding the first and last day a certain temperature occurred helps understand weather patterns.

Key Takeaways

Manual search is slow and error-prone for large lists.

Finding first and last occurrence automates and speeds up locating elements.

This method helps in many real-world data tracking tasks.

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