First and Last Occurrence of Element in DSA Go - Time & Space Complexity

Time Complexity: First and Last Occurrence of Element

O(n)

Understanding Time Complexity

We want to know how long it takes to find the first and last positions of a number in a list.

How does the time needed change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code finds the first and last places where the target number appears in the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: One loop that goes through each item in the list once.
• How many times: Exactly once for each item in the list, from start to end.

How Execution Grows With Input

As the list gets bigger, the time to check each item grows directly with the size.

Input Size (n)	Approx. Operations
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The number of checks grows evenly as the list grows.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows in a straight line with the size of the list.

Common Mistake

[X] Wrong: "Since we only want first and last, we can stop early and the time is always small."

[OK] Correct: The code checks every item to find the last occurrence, so it must look at the whole list in the worst case.

Interview Connect

Understanding this helps you explain how searching through data works and shows you can analyze simple loops clearly.

Self-Check

"What if we used binary search on a sorted list to find the first and last occurrence? How would the time complexity change?"

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