First and Last Occurrence of Element in DSA Go - 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 when reading from left to right.

beginner

What is the difference between 'First Occurrence' and 'Last Occurrence' of an element?

First Occurrence is the earliest index where the element appears; Last Occurrence is the latest index where the element appears in the array.

intermediate

Why is binary search useful for finding first and last occurrences in a sorted array?

Binary search helps find the target element quickly by dividing the search space in half repeatedly, making it efficient to find first and last positions without scanning the whole array.

beginner

In Go, what is a simple way to represent the result of first and last occurrence search?

Use two integers representing the first and last index positions. If the element is not found, return -1 for both.

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 step.

What should be returned if the element is not found in the array?

A Nil or null

B 0 for both first and last occurrence

C Length of the array

D -1 for both first and last occurrence

Returning -1 indicates the element does not exist in the array.

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

A Depth-first search

B Linear search

C Binary search

D Breadth-first search

Binary search efficiently finds elements in sorted arrays by halving the search space.

If an element appears multiple times, what does 'last occurrence' mean?

A The last index where element appears

B The first index where element appears

C The middle index of appearances

D The count of appearances

Last occurrence is the highest index where the element is found.

What is the initial search range for binary search in an array of length n?

A From 1 to n

B From 0 to n-1

C From -1 to n

D From 0 to n

Array indices start at 0, so the range is 0 to n-1.

Which of these is NOT a correct step in finding first occurrence using binary search?

A Stop immediately when element is found without checking neighbors

B Move right if element is greater than mid element

C Move left if element found to check earlier indices

D Update result when element is found

We continue searching left to find the earliest occurrence, not stop immediately.

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

Think about narrowing down the search to find earliest and latest positions.

Describe the difference between linear search and binary search for finding occurrences of an element.

Compare how each method moves through the array.

Practice

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

easy

A. The sum of all elements in the array

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

C. The maximum and minimum values in the array

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 positions of a specific element in an array.

2. Step 2: Identify what is required

   We need to return the indices of the first and last occurrence of the element, not sums or counts.

3. Final Answer:

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

4. Quick Check:

   First and last occurrence = positions [OK]

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

Common Mistakes:

• Confusing occurrence with sum or count
• Looking for max/min instead of positions
• Ignoring the last occurrence

2. Which of the following Go code snippets correctly declares a function to find the first occurrence of an element in a slice?

easy

A. func firstOccurrence(arr []int, x int) int { for _, v := range arr { if v == x { return i } } return -1 }

B. func firstOccurrence(arr []int, x int) int { for i := range arr { if arr[i] = x { return i } } return -1 }

C. func firstOccurrence(arr []int, x int) { for i := 0; i < len(arr); i++ { if arr[i] == x { return i } } return -1 }

D. func firstOccurrence(arr []int, x int) int { for i := 0; i < len(arr); i++ { if arr[i] == x { return i } } return -1 }

Solution

1. Step 1: Check function signature and return type

   The function must return an int index, so signature must be func firstOccurrence(arr []int, x int) int.

2. Step 2: Verify loop and condition syntax

   func firstOccurrence(arr []int, x int) int { for i := 0; i < len(arr); i++ { if arr[i] == x { return i } } return -1 } uses a for loop with index and correct equality check (arr[i] == x) and returns index or -1.

3. Final Answer:

   func firstOccurrence(arr []int, x int) int { for i := 0; i < len(arr); i++ { if arr[i] == x { return i } } return -1 } -> Option D

4. Quick Check:

   Correct syntax and return type = func firstOccurrence(arr []int, x int) int { for i := 0; i < len(arr); i++ { if arr[i] == x { return i } } return -1 } [OK]

Hint: Check function return type and equality operator carefully [OK]

Common Mistakes:

• Missing return type in function signature
• Using assignment '=' instead of equality '=='
• Returning inside a void function

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

arr := []int{2, 4, 4, 4, 6, 7}
first := -1
last := -1
x := 4
for i, v := range arr {
  if v == x {
    if first == -1 {
      first = i
    }
    last = i
  }
}
fmt.Println(first, last)

medium

A. 1 3

B. 2 4

C. 1 4

D. 0 3

Solution

1. Step 1: Trace the loop to find first and last occurrence of 4

   Indices with value 4 are 1, 2, 3. First occurrence is 1, last occurrence is 3.

2. Step 2: Confirm printed values

   Variables first and last hold 1 and 3 respectively, so output is "1 3".

3. Final Answer:

   1 3 -> Option A

4. Quick Check:

   First=1, Last=3 for element 4 [OK]

Hint: Track indices where element matches, update first once, last every time [OK]

Common Mistakes:

• Confusing index positions starting at 0
• Updating first occurrence multiple times
• Not updating last occurrence correctly

4. Identify the bug in this Go function that finds the last occurrence of an element in a slice:

func lastOccurrence(arr []int, x int) int {
  last := -1
  for i := 0; i <= len(arr); i++ {
    if arr[i] == x {
      last = i
    }
  }
  return last
}

medium

A. Loop condition should be i < len(arr), not i <= len(arr) to avoid out-of-range error

B. Variable 'last' should be initialized to 0 instead of -1

C. The function should return first occurrence, not last

D. The if condition should use '!=' instead of '=='

Solution

1. Step 1: Check loop boundary conditions

   The loop uses i <= len(arr), which causes index out-of-range error because valid indices are 0 to len(arr)-1.

2. Step 2: Correct loop condition

   Change to i < len(arr) to safely access elements without error.

3. Final Answer:

   Loop condition should be i < len(arr), not i <= len(arr) to avoid out-of-range error -> Option A

4. Quick Check:

   Loop index must be less than length [OK]

Hint: Use i < len(arr) for loops to avoid index errors [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Initializing last to 0 causing wrong default
• Confusing last occurrence with first

5. Given a sorted slice of integers, which approach is the most efficient to find the first and last occurrence of a target element x?

hard

A. Sort the slice again and then find occurrences linearly

B. Scan the slice from start to end once, record first and last occurrence

C. Use two binary searches: one to find first occurrence, one for last occurrence

D. Use a hash map to store all indices of elements and look up x

Solution

1. Step 1: Understand the input is sorted

   Since the slice is sorted, binary search can be used to find positions efficiently.

2. Step 2: Use two binary searches

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

3. Step 3: Compare with other options

   Linear scan is O(n), sorting again is unnecessary and costly, hash map adds extra space and complexity.

4. Final Answer:

   Use two binary searches: one to find first occurrence, one for last occurrence -> Option C

5. Quick Check:

   Sorted array + binary search = efficient [OK]

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

Common Mistakes:

• Using linear scan on sorted data ignoring binary search
• Sorting already sorted data again
• Using extra space unnecessarily