Linear Search Algorithm in DSA Typescript - Time & Space Complexity

Time Complexity: Linear Search Algorithm

O(n)

Understanding Time Complexity

We want to understand how long it takes to find a value in a list using linear search.

How does the time needed grow as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code looks through each item in the list one by one to find the target value.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each element in the array one by one.
• How many times: Up to n times, where n is the number of elements in the array.

How Execution Grows With Input

As the list gets bigger, the number of checks grows roughly the same amount.

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

Pattern observation: The number of operations grows directly with the size of the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the target grows in a straight line as the list gets bigger.

Common Mistake

[X] Wrong: "Linear search is always fast because it just checks items one by one."

[OK] Correct: If the target is near the end or not in the list, it has to check almost every item, which can take a long time for big lists.

Interview Connect

Understanding linear search time helps you explain why some searches are slow and when to use better methods, a key skill in coding interviews.

Self-Check

"What if the array was sorted and we used binary search instead? How would the time complexity change?"

Practice

1. What is the main idea behind the Linear Search Algorithm?

easy

A. Divide the list into halves repeatedly to find the target

B. Check each element one by one until the target is found or list ends

C. Sort the list first then search using binary steps

D. Use a hash table to find the target instantly

Solution

1. Step 1: Understand linear search process

   Linear search checks each element in order, from start to end, to find the target.

2. Step 2: Compare with other search methods

   Binary search divides list, hash uses extra memory, but linear search is simple sequential check.

3. Final Answer:

   Check each element one by one until the target is found or list ends -> Option B

4. Quick Check:

   Linear search = sequential check [OK]

Hint: Linear search means checking items one by one [OK]

Common Mistakes:

• Confusing linear search with binary search
• Thinking linear search requires sorted list
• Assuming linear search is always fastest

2. Which of the following is the correct TypeScript syntax to start a linear search loop over an array arr?

easy

A. for (let i = 0; i < arr.length; i++)

B. for (let i = 1; i <= arr.length; i++)

C. for (let i = 0; i <= arr.length; i++)

D. for (let i = 1; i < arr.length; i++)

Solution

1. Step 1: Identify correct loop start and end

   Array indices start at 0 and go up to length-1, so loop must start at 0 and run while i < length.

2. Step 2: Check each option's loop condition

   for (let i = 0; i < arr.length; i++) uses i=0 and i < arr.length, which is correct. Others either start at 1 or use <= which causes out-of-bounds.

3. Final Answer:

   for (let i = 0; i < arr.length; i++) -> Option A

4. Quick Check:

   Loop from 0 to length-1 [OK]

Hint: Array loops start at 0 and run while less than length [OK]

Common Mistakes:

• Starting loop at 1 instead of 0
• Using <= instead of < causing index errors
• Confusing array length with last index

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

const arr = [4, 7, 1, 9];
const target = 1;
let index = -1;
for (let i = 0; i < arr.length; i++) {
  if (arr[i] === target) {
    index = i;
    break;
  }
}
console.log(index);

medium

A. 1

B. -1

C. 2

D. 3

Solution

1. Step 1: Trace the loop and compare elements

   Check arr[0]=4 (not 1), arr[1]=7 (not 1), arr[2]=1 (match found), set index=2 and break loop.

2. Step 2: Output the index variable

   After loop, index is 2, so console.log prints 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Target found at index 2 [OK]

Hint: Stop at first match and print its index [OK]

Common Mistakes:

• Not breaking loop and returning last index
• Confusing index with value
• Assuming index starts at 1

4. Find the error in this linear search code snippet and choose the fix:

const arr = [5, 3, 8];
const target = 3;
let index = -1;
for (let i = 0; i <= arr.length; i++) {
  if (arr[i] === target) {
    index = i;
    break;
  }
}
console.log(index);

medium

A. Change loop condition to i < arr.length

B. Initialize index to 0 instead of -1

C. Remove the break statement

D. Change target to 5

Solution

1. Step 1: Identify loop boundary error

   The loop uses i <= arr.length, which causes i to reach arr.length, an invalid index (out of bounds).

2. Step 2: Fix loop condition to prevent out-of-bounds

   Changing condition to i < arr.length ensures i stays within valid indices 0 to length-1.

3. Final Answer:

   Change loop condition to i < arr.length -> Option A

4. Quick Check:

   Loop must run while i < length [OK]

Hint: Use < not <= for array index loops [OK]

Common Mistakes:

• Using <= causing runtime error
• Changing unrelated variables
• Removing break causing unnecessary iterations

5. You want to find the last occurrence of a target number in an array using linear search. Which modification to this code will achieve that?

const arr = [2, 5, 3, 5, 7];
const target = 5;
let index = -1;
for (let i = 0; i < arr.length; i++) {
  if (arr[i] === target) {
    index = i;
    break;
  }
}
console.log(index);

hard

A. Sort the array before searching

B. Add break after setting index to stop at first occurrence

C. Start loop from the end and break at first match

D. Remove the break statement to continue searching all elements

Solution

1. Step 1: Understand current code behavior

   The loop checks all elements; each time target matches, index updates to current i, so last match index remains after loop.

2. Step 2: Identify why removing break helps

   If break was present, loop would stop at first match. Removing break ensures full array is checked for last occurrence.

3. Final Answer:

   Remove the break statement to continue searching all elements -> Option D

4. Quick Check:

   Keep searching to find last occurrence [OK]

Hint: To find last occurrence, check all elements without break [OK]

Common Mistakes:

• Adding break stops search too early
• Sorting changes original order and index meaning
• Starting loop from end requires different logic