Linear Search Algorithm in DSA Python - Execution Trace

Concept Flow - Linear Search Algorithm

Start at index 0

↓

Check if element at index == target?

Yes→Return index, Found

No↓

Move to next index

↓

Check if index < length of list?

No→Return -1, Not Found

↩Back to Check element

Start from the first element, check each one until you find the target or reach the end.

Execution Sample

DSA Python

def linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] == target:
            return i
    return -1

Searches each element in the list one by one to find the target value.

Execution Table

Step	Operation	Index (i)	Element Checked	Condition (arr[i] == target)	Action	Result/Return
1	Start loop	0	3	3 == 5? False	Move to next index
2	Check element	1	5	5 == 5? True	Return index 1	1
3	Exit	-	-	-	-	Search ends, target found at index 1

💡 Target found at index 1, loop ends early

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
i	-	0	1	1
arr[i]	-	3	5	5
Return value	-		1	1

Key Moments - 3 Insights

Why does the search stop immediately when the target is found?

Because in step 2 of the execution_table, the condition is True and the function returns the index immediately, stopping the loop.

What happens if the target is not in the list?

The loop runs through all elements without returning, then returns -1 after the loop ends, indicating target not found.

Why do we check 'arr[i] == target' inside the loop?

To compare each element one by one until we find the target or finish checking all elements, as shown in steps 1 and 2.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'i' when the target is found?

A 1

B 0

C 2

D -1

💡 Hint

Check the 'Index (i)' column in step 2 where the condition is True.

At which step does the search end because the target is found?

A Step 3

B Step 1

C Step 2

D It never ends

💡 Hint

Look at the 'Action' and 'Result/Return' columns in the execution_table.

If the target was 7 (not in list), what would the function return?

A Index of 7

B -1

C 0

D Error

💡 Hint

Recall the key moment about what happens if target is not found.

Concept Snapshot

Linear Search Algorithm:
- Start from first element (index 0)
- Check each element if it equals target
- If found, return index immediately
- If not found after full list, return -1
- Simple, checks elements one by one

Full Transcript

Linear search checks each element in a list one by one from the start. If the element matches the target, it returns the index immediately. If it reaches the end without finding the target, it returns -1. This method is simple and works on any list but can be slow for large lists.

Practice

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

easy

A. Sort the list first then search using binary steps

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

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

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, one by one.

2. Step 2: Compare with other search methods

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

3. Final Answer:

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

4. Quick Check:

   Linear search = sequential check [OK]

Hint: Linear search checks items one by one [OK]

Common Mistakes:

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

2. Which of the following is the correct syntax to start a linear search loop over a list arr in Python?

easy

A. for i to len(arr):

B. for i in range(arr):

C. for i in arr:

D. for i in range(len(arr)):

Solution

1. Step 1: Identify how to loop over indices

   To access elements by index, use range(len(arr)).

2. Step 2: Check each option's correctness

   for i in arr: loops over elements, not indices; B is invalid because range needs an integer; D is invalid syntax.

3. Final Answer:

   for i in range(len(arr)): -> Option D

4. Quick Check:

   Loop indices = range(len(arr)) [OK]

Hint: Use range(len(arr)) to loop indices [OK]

Common Mistakes:

• Using range(arr) instead of range(len(arr))
• Trying to loop with invalid syntax like 'for i to len(arr)'
• Confusing looping over elements vs indices

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

def linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] == target:
            return i
    return -1

print(linear_search([4, 2, 7, 1, 3], 7))

medium

A. 2

B. 3

C. -1

D. 7

Solution

1. Step 1: Trace the loop and compare elements

   Check elements: arr[0]=4 (no), arr[1]=2 (no), arr[2]=7 (yes, matches target 7).

2. Step 2: Return index when found

   Function returns index 2 immediately when target found.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Index of 7 in list = 2 [OK]

Hint: Return index when target matches during loop [OK]

Common Mistakes:

• Returning element value instead of index
• Returning -1 even when target is present
• Confusing index with element value

4. Find the error in this linear search function:

def linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] = target:
            return i
    return -1

medium

A. Using '=' instead of '==' in the if condition

B. Missing colon ':' after for loop

C. Returning -1 instead of None when not found

D. Looping over range(len(arr)) instead of arr

Solution

1. Step 1: Identify syntax error in condition

   The if condition uses '=' which is assignment, not comparison.

2. Step 2: Correct operator for comparison

   Use '==' to compare values in if condition.

3. Final Answer:

   Using '=' instead of '==' in the if condition -> Option A

4. Quick Check:

   Comparison needs '==' not '=' [OK]

Hint: Use '==' for comparison, '=' is assignment [OK]

Common Mistakes:

• Using single '=' in if condition
• Confusing assignment and comparison operators
• Ignoring syntax errors causing runtime failure

5. You want to find all positions of a target number in a list using linear search. Which modification to the code below will achieve this?

def linear_search_all(arr, target):
    positions = []
    for i in range(len(arr)):
        if arr[i] == target:
            # What to do here?
    return positions

print(linear_search_all([1, 3, 7, 3, 9, 3], 3))

hard

A. Return i immediately when target is found

B. Append index i to positions list inside the if block

C. Break the loop after first match

D. Use positions = target instead of list

Solution

1. Step 1: Understand requirement to find all matches

   We must collect all indices where target appears, not stop at first.

2. Step 2: Append matching indices to list

   Inside if, add positions.append(i) to store all found positions.

3. Final Answer:

   Append index i to positions list inside the if block -> Option B

4. Quick Check:

   Collect all indices by appending [OK]

Hint: Append all matching indices to list [OK]

Common Mistakes:

• Returning immediately on first match
• Breaking loop early
• Assigning target to positions instead of appending