Backtracking Concept and Decision Tree Visualization in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to start backtracking by calling the helper function.

DSA Python

def backtrack(path, choices):
    if not choices:
        print(path)
        return

# Start backtracking with empty path and full choices
backtrack([1], [1, 2, 3])

Drag options to blanks, or click blank then click option'

ANone

B[0]

C[]

D[1]

Attempts:

3 left

💡 Hint

Common Mistakes

Starting with None instead of an empty list.

Starting with a list containing elements instead of empty.

We start backtracking with an empty path represented by an empty list [].

2fill in blank

medium

Complete the code to choose the next option in backtracking.

DSA Python

def backtrack(path, choices):
    if not choices:
        print(path)
        return

    for i in range(len(choices)):
        backtrack(path + [choices[[1]]], choices[:i] + choices[i+1:])

Drag options to blanks, or click blank then click option'

Ai

B0

C-1

Dlen(choices)

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 always, which picks only the first choice repeatedly.

Using len(choices), which is out of range.

We use index i to pick the current choice from the list.

3fill in blank

hard

Fix the error in the backtracking base case to print the complete path.

DSA Python

def backtrack(path, choices):
    if len(choices) == 0:
        print([1])
        return

Drag options to blanks, or click blank then click option'

Apath

Bchoices

Clen(path)

DNone

Attempts:

3 left

💡 Hint

Common Mistakes

Printing choices instead of path.

Printing None or length instead of the actual path.

We print the current path when no choices remain to show the complete solution.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each choice to its square if the choice is even.

DSA Python

result = { [1] : [2] for x in [1, 2, 3, 4] if x % 2 == 0 }

Drag options to blanks, or click blank then click option'

Ax

Bx**2

Cx*2

Dx+1

Attempts:

3 left

💡 Hint

Common Mistakes

Using x*2 instead of x**2 for the value.

Using x+1 which does not square the number.

We map each even number x to its square x**2 in the dictionary.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase keys to values greater than 10.

DSA Python

filtered = { [1] : [2] for k, v in data.items() if v [3] 10 }

Drag options to blanks, or click blank then click option'

Ak.upper()

Bv

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using k instead of k.upper() for keys.

Using <= instead of > for filtering values.

Keys are converted to uppercase with k.upper(), values are v, and we filter values greater than 10 with >.

Practice

1. What is the main idea behind backtracking in problem solving?

easy

A. Store all results in a list without removing any

B. Use a loop to repeat the same action multiple times

C. Sort data before processing it

D. Try all possible options and undo choices when they lead to failure

Solution

1. Step 1: Understand backtracking approach

   Backtracking tries choices one by one and goes back if a choice fails.

2. Step 2: Compare options

   Only Try all possible options and undo choices when they lead to failure describes trying and undoing choices, which is backtracking.

3. Final Answer:

   Try all possible options and undo choices when they lead to failure -> Option D

4. Quick Check:

   Backtracking = Try and undo choices [OK]

Hint: Backtracking means try, fail, undo, and try again [OK]

Common Mistakes:

• Confusing backtracking with simple loops
• Thinking backtracking only stores results
• Believing backtracking sorts data

2. Which of the following is the correct syntax to start a backtracking function in Python?

easy

A. backtrack(path, choices) =>

B. def backtrack(path, choices):

C. def backtrack[]:

D. function backtrack(path, choices):

Solution

1. Step 1: Recall Python function syntax

   Python functions start with def, followed by name and parameters in parentheses.

2. Step 2: Check options

   def backtrack(path, choices): uses correct Python syntax: def backtrack(path, choices):.

3. Final Answer:

   def backtrack(path, choices): -> Option B

4. Quick Check:

   Python function = def name(params): [OK]

Hint: Python functions start with def and parentheses [OK]

Common Mistakes:

• Using 'function' keyword (not Python)
• Using square brackets instead of parentheses
• Using arrow syntax (not Python)

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

def backtrack(path, choices):
    if not choices:
        print(path)
        return
    for i in range(len(choices)):
        backtrack(path + [choices[i]], choices[:i] + choices[i+1:])

backtrack([], [1, 2])

medium

A. [2, 1]

B. [1, 2]

C. [1, 2]\n[2, 1]

D. []

Solution

1. Step 1: Understand recursion and choices

   The function picks each choice, adds it to path, and recurses with remaining choices.

2. Step 2: Trace calls for [1, 2]

   First call: path=[], choices=[1,2]. Picks 1, calls with path=[1], choices=[2]. Then picks 2, path=[1,2], choices=[]. Prints [1,2]. Backtracks and picks 2 first, then 1, prints [2,1].

3. Final Answer:

   [1, 2] [2, 1] -> Option C

4. Quick Check:

   All permutations of [1,2] printed [OK]

Hint: Backtracking prints all permutations of input list [OK]

Common Mistakes:

• Printing only one permutation
• Not slicing choices correctly
• Confusing path and choices lists

4. Find the error in this backtracking code snippet:

def backtrack(path, choices):
    if len(choices) == 0:
        print(path)
    for i in range(len(choices)):
        backtrack(path + [choices[i]], choices[:i])

medium

A. Incorrect slicing of choices in recursive call

B. Missing return after printing path

C. Using + operator on lists is invalid

D. No base case to stop recursion

Solution

1. Step 1: Analyze recursive call slicing

   The recursive call uses choices[:i], which only takes elements before i, missing elements after i.

2. Step 2: Correct slicing for backtracking

   It should be choices[:i] + choices[i+1:] to exclude the chosen element but keep others.

3. Final Answer:

   Incorrect slicing of choices in recursive call -> Option A

4. Quick Check:

   Choices slicing must exclude chosen element correctly [OK]

Hint: Slice choices before and after index to exclude chosen element [OK]

Common Mistakes:

• Forgetting to exclude chosen element properly
• Not returning after base case
• Thinking list + list is invalid

5. You want to generate all subsets of the list [1, 2, 3] using backtracking. Which approach correctly represents the decision tree visualization for this problem?

hard

A. At each step, decide to include or exclude the current element, then move to next

B. At each step, swap elements to generate permutations

C. At each step, remove one element permanently and recurse

D. At each step, sort the list and pick the smallest element

Solution

1. Step 1: Understand subset generation logic

   Generating subsets means choosing to include or exclude each element in order.

2. Step 2: Match decision tree visualization

   The decision tree branches at each element: include or exclude, then move forward. This matches At each step, decide to include or exclude the current element, then move to next.

3. Final Answer:

   At each step, decide to include or exclude the current element, then move to next -> Option A

4. Quick Check:

   Subset tree = include/exclude choices per element [OK]

Hint: Subsets = choose include or exclude each element [OK]

Common Mistakes:

• Confusing subsets with permutations
• Thinking sorting is needed
• Removing elements permanently instead of choosing