Linear Search Algorithm in DSA Rust - Execution Trace

Concept Flow - Linear Search Algorithm

Start at index 0

↓

Check if element == target?

No→Move to next index

↓

Index < length?

No→Not found

↓

Return index

Start from the first element, check each one if it matches the target. If yes, return index. If no, move to next until end.

Execution Sample

DSA Rust

fn linear_search(arr: &[i32], target: i32) -> Option<usize> {
    for (i, &item) in arr.iter().enumerate() {
        if item == target {
            return Some(i);
        }
    }
    None
}

Searches array elements one by one to find the target and returns its index or None if not found.

Execution Table

Step	Operation	Current Index	Current Element	Check (element == target?)	Action	Result
1	Start search	0	4	4 == 3? No	Move to next index	Continue
2	Check element	1	2	2 == 3? No	Move to next index	Continue
3	Check element	2	3	3 == 3? Yes	Return index 2	Found at index 2
4	End	-	-	-	-	Search stops

💡 Element found at index 2, search stops early.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
i (index)	-	0	1	2	2
item (element)	-	4	2	3	3
result	None	None	None	Some(2)	Some(2)

Key Moments - 3 Insights

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

Because the algorithm returns the index as soon as it finds the target (see Step 3 in execution_table), no need to check further.

What happens if the target is not in the array?

The loop completes without returning, so the function returns None after checking all elements (not shown in this trace but implied after Step 4).

Why do we check element == target inside the loop?

To compare each element one by one with the target; this is the core of linear search (see 'Check (element == target?)' column).

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'i' at Step 2?

A 1

B 2

C 0

D 3

💡 Hint

Check the 'Current Index' column at Step 2 in execution_table.

At which step does the algorithm find the target element?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look for 'Check (element == target?)' column where it says 'Yes'.

If the target was 5 instead of 3, what would happen in the execution_table?

A The search would stop at Step 3

B The search would check all elements and return None

C The search would return index 0

D The search would find the target at Step 2

💡 Hint

Think about what happens when no element matches the target in the loop.

Concept Snapshot

Linear Search Algorithm:
- Start from first element (index 0)
- Check each element if it equals target
- If yes, return index immediately
- If no, move to next element
- If end reached without match, return None

Full Transcript

Linear search checks each element in order to find a target value. It starts at index 0 and compares the element with the target. If they match, it returns the current index immediately. If not, it moves to the next element and repeats. If the target is not found after checking all elements, it returns None. This method is simple but can be slow for large arrays because it may check every element.

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. Use a hash table to find the target instantly

C. Sort the list first then search using binary steps

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

Solution

1. Step 1: Understand linear search process

   Linear search checks each element in order from start to end.

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 D

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 data
• Assuming linear search uses extra memory

2. Which of the following is the correct Rust syntax to start a linear search loop over a vector arr?

easy

A. while i < arr.len() { }

B. for i in arr { }

C. for i in 0..arr.len() { }

D. loop i in arr.len() { }

Solution

1. Step 1: Identify correct Rust for loop syntax

   Rust uses for i in 0..arr.len() to loop over indices.

2. Step 2: Check other options for syntax errors

   for i in arr iterates over values, not indices; while needs initialization; loop i in is invalid.

3. Final Answer:

   for i in 0..arr.len() { } -> Option C

4. Quick Check:

   Rust for loop over range = for i in 0..len() [OK]

Hint: Use for i in 0..arr.len() to loop indices [OK]

Common Mistakes:

• Using for i in arr to get indices instead of values
• Writing invalid loop syntax like loop i in ...
• Forgetting to initialize loop variable in while loops

3. What will be the output of this Rust code snippet?

let arr = vec![3, 5, 7, 9];
let target = 7;
let mut index = -1;
for i in 0..arr.len() {
    if arr[i] == target {
        index = i as i32;
        break;
    }
}
println!("{}", index);

medium

A. 0

B. 2

C. 3

D. -1

Solution

1. Step 1: Trace the loop to find target index

   Loop checks arr[0]=3, arr[1]=5, arr[2]=7 matches target, sets index=2 and breaks.

2. Step 2: Print the index value

   After break, index is 2, so printed output is 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Target 7 found at index 2 [OK]

Hint: Stop loop at first match, print that index [OK]

Common Mistakes:

• Not breaking loop after finding target
• Printing index before loop ends
• Confusing index type casting

4. Identify the error in this Rust linear search code and choose the fix:

let arr = vec![1, 2, 3];
let target = 4;
let mut found = false;
for i in 0..arr.len() {
    if arr[i] = target {
        found = true;
        break;
    }
}
println!("{}", found);

medium

A. Use '==' for comparison instead of '='

B. Change 'found' to integer type

C. Remove the break statement

D. Use while loop instead of for loop

Solution

1. Step 1: Check the if condition syntax

   The code uses '=' which is assignment, not comparison. It should be '==' to compare values.

2. Step 2: Verify other options

   Changing 'found' type or removing break won't fix syntax error. Using while loop is valid but not necessary.

3. Final Answer:

   Use '==' for comparison instead of '=' -> Option A

4. Quick Check:

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

Hint: Use '==' to compare values, '=' assigns [OK]

Common Mistakes:

• Using '=' instead of '==' in if conditions
• Removing break causing unnecessary iterations
• Changing variable types unnecessarily

5. You want to find all indices of a target value in a vector arr using linear search in Rust. Which approach correctly collects all matching indices?

hard

A. Use a loop over indices, push index to a vector when element equals target

B. Break the loop at first match and return that index

C. Sort the vector first, then use binary search for all matches

D. Use a hash map to store element counts and find indices

Solution

1. Step 1: Understand requirement to find all indices

   We must check every element and collect indices where element equals target.

2. Step 2: Evaluate options for correctness

   Breaking loop stops early, sorting changes order, hash map counts but doesn't store indices. Only pushing indices in loop works.

3. Final Answer:

   Use a loop over indices, push index to a vector when element equals target -> Option A

4. Quick Check:

   Collect all matches by looping and storing indices [OK]

Hint: Collect indices by checking all elements without breaking [OK]

Common Mistakes:

• Breaking loop too early to find all matches
• Sorting vector which changes original order
• Using hash map counts instead of indices